Effective field theories for topological insulators by functional bosonization

NASA Astrophysics Data System (ADS)

Chan, AtMa; Hughes, Taylor L.; Ryu, Shinsei; Fradkin, Eduardo

2013-02-01

Effective field theories that describe the dynamics of a conserved U(1) current in terms of “hydrodynamic” degrees of freedom of topological phases in condensed matter are discussed in general dimension D=d+1 using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the “primary series” of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ (when D is even) terms. For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative “fractional” topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

Bipartite charge fluctuations in one-dimensional Z2 superconductors and insulators

NASA Astrophysics Data System (ADS)

Herviou, Loïc; Mora, Christophe; Le Hur, Karyn

2017-09-01

Bipartite charge fluctuations (BCFs) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems) and can be measured experimentally. We study the BCFs in generic one-dimensional Z2 (topological) models including the Kitaev superconducting wire model, the Ising chain, or various topological insulators such as the Su-Schrieffer-Heeger model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCFs probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a subdominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the X Y Z model.

Plutonium hexaboride is a correlated topological insulator.

PubMed

Deng, Xiaoyu; Haule, Kristjan; Kotliar, Gabriel

2013-10-25

We predict that plutonium hexaboride (PuB(6)) is a strongly correlated topological insulator, with Pu in an intermediate valence state of Pu(2.7+). Within the combination of dynamical mean field theory and density functional theory, we show that PuB(6) is an insulator in the bulk, with nontrivial Z(2) topological invariants. Its metallic surface states have a large Fermi pocket at the X[over ¯] point and the Dirac cones inside the bulk derived electronic states, causing a large surface thermal conductivity. PuB(6) has also a very high melting temperature; therefore, it has ideal solid state properties for a nuclear fuel material.

Electrically controlled band gap and topological phase transition in two-dimensional multilayer germanane

NASA Astrophysics Data System (ADS)

Qi, Jingshan; Li, Xiao; Qian, Xiaofeng

2016-06-01

Electrically controlled band gap and topological electronic states are important for the next-generation topological quantum devices. In this letter, we study the electric field control of band gap and topological phase transitions in multilayer germanane. We find that although the monolayer and multilayer germananes are normal insulators, a vertical electric field can significantly reduce the band gap of multilayer germananes owing to the giant Stark effect. The decrease of band gap eventually leads to band inversion, transforming them into topological insulators with nontrivial Z2 invariant. The electrically controlled topological phase transition in multilayer germananes provides a potential route to manipulate topologically protected edge states and design topological quantum devices. This strategy should be generally applicable to a broad range of materials, including other two-dimensional materials and ultrathin films with controlled growth.

Electrically controlled band gap and topological phase transition in two-dimensional multilayer germanane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qi, Jingshan, E-mail: qijingshan@jsnu.edu.cn, E-mail: feng@tamu.edu; Li, Xiao; Qian, Xiaofeng, E-mail: qijingshan@jsnu.edu.cn, E-mail: feng@tamu.edu

2016-06-20

Electrically controlled band gap and topological electronic states are important for the next-generation topological quantum devices. In this letter, we study the electric field control of band gap and topological phase transitions in multilayer germanane. We find that although the monolayer and multilayer germananes are normal insulators, a vertical electric field can significantly reduce the band gap of multilayer germananes owing to the giant Stark effect. The decrease of band gap eventually leads to band inversion, transforming them into topological insulators with nontrivial Z{sub 2} invariant. The electrically controlled topological phase transition in multilayer germananes provides a potential route tomore » manipulate topologically protected edge states and design topological quantum devices. This strategy should be generally applicable to a broad range of materials, including other two-dimensional materials and ultrathin films with controlled growth.« less

A Novel Quasi-One-Dimensional Topological Insulator in Bismuth Iodide β-Bi4I4: Theoretical Prediction and Experimental Confirmation

NASA Astrophysics Data System (ADS)

Yazyev, Oleg V.; Autès, Gabriel; Isaeva, Anna; Moreschini, Luca; Johannsen, Jens C.; Pisoni, Andrea; Filatova, Taisia G.; Kuznetsov, Alexey N.; Forró, László; van den Broek, Wouter; Kim, Yeongkwan; Denlinger, Jonathan D.; Rotenberg, Eli; Bostwick, Aaron; Grioni, Marco

2015-03-01

A new strong Z2 topological insulator is theoretically predicted and experimentally confirmed in the β-phase of quasi-one-dimensional bismuth iodide Bi4I4. According to our first-principles calculations the material is characterized by Z2 invariants (1;110) making it the first representative of this topological class. Importantly, the electronic structure of β-Bi4I4 is in proximity with both the weak topological insulator phase (0;001) and the trivial phase (0;000), suggesting that a high degree of control over the topological electronic properties of this material can be achieved. Experimentally produced samples of this material appears to be practically defect-free, which results in a low concentration of intrinsic charge carriers. By using angle-resolved photoemission spectroscopy (ARPES) on the (001) surface we confirm the theoretical predictions of a highly anisotropic band structure with a small band gap hosting topological surface states centered at the M point, at the boundary of the surface Brillouin zone. We acknowledge support from Swiss NSF, ERC project ``TopoMat'', NCCR-MARVEL, DFG and US DoE. G.A., A.I., L.M. and J.C.J. contributed equally to this work.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Branch Processes of Vortex Filaments and Hopf Invariant Constraint on Scroll Wave

NASA Astrophysics Data System (ADS)

Zhu, Tao; Ren, Ji-Rong; Mo, Shu-Fan

2009-12-01

In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z(vec x, t). It is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the “exclusion principle" in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the “exclusion principle" is also protected by topology.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

NASA Astrophysics Data System (ADS)

Ahn, Junyeong; Yang, Bohm-Jung

2017-04-01

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

Associating Specific Materials with Topological Insulation Behavior

NASA Astrophysics Data System (ADS)

Zhang, Xiuwen

2014-03-01

The first-principles (a) total-energy/stability calculations combined with (b) electronic structure calculations of band inversion, spin-polarization and topological invariants (Z2) has led to the design and prediction of specific materials that are topological insulators in this study. We classify bulk materials into four types of band-inversion behaviors (TI-1, TI-2, BI-3, BI-4), based on the number of band inversions and their distributions on various time reversal invariant k points. Depending on the inversion type in bulk, the corresponding surface states have different protections e.g., protected by time reversal symmetry (in TI-1 materials), spatial symmetry (in TI-2), or not protected (in BI-3, BI-4). Subject 1 Discovery of new TI by screening materials for a Z2 metric: Such high-throughput search in the framework of Inverse Design methodology predicts a few previously undocumented materials that are TI-1 in their ground state crystal structure. We also predict dozens of materials that are TI-1 however in structures that are not ground states (e.g. perovskite structure of II-Bi-O3). Subject 2 Design Principle to increase the gap of TI-1 materials: In HgTe-like cubic topological materials, the insulating gap is zero since the spin-orbit splitting is positive and so a 4-fold half-filled p-like band is near the Fermi level. By design of hybridization of d-orbitals into the p-like bands, one can create negative spin-orbit splitting and so a finite insulating gap. Subject 3 Unconventional spin textures of TI surface states: Despite the fact that one of our predicted TI-1 KBaBi has inversion symmetry in the bulk-a fact that that would preclude bulk spin polarization-we find a Dresselhaus-like spin texture with non-helical spin texture. This originates from the local spin polarization, anchored on the atomic sites with inversion asymmetric point groups, that is compensated due to global inversion symmetry in bulk. In collaboration with: Jun-Wei Luo, Qihang Liu, Julien Vidal, and Alex Zunger, and supported in part by National Science Foundation DMREF. X.Z. acknowledges the administrative support of REMRSEC at Colorado School of Mines, Golden, Colorado.

Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

NASA Astrophysics Data System (ADS)

Lai, Hsin-Hua; Hung, Hsiang-Hsuan

2015-02-01

Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane-Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry.

PubMed

Miller, Jacob; Miyake, Akimasa

2018-04-27

An emerging insight is that ground states of symmetry-protected topological orders (SPTOs) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the invariance under 3-colorable symmetries of a lattice, we prove that every renormalization fixed-point state of 2D (Z_{2})^{m} SPTO with fractional symmetry can be utilized for universal quantum computation using only Pauli measurements, as long as it belongs to a nontrivial 2D SPTO phase. Our infinite family of fixed-point states may serve as a base model to demonstrate the idea of a "quantum computational phase" of matter, whose states share universal computational complexity ubiquitously.

Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Wang, Chong; Duan, Wenhui; Glazman, Leonid

2018-01-01

The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase (λ ) that is subleading in powers of the field; λ is measurable in the phase offset of the de Haas-van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, λ /π are robustly integer valued, owing to the symmetry of the extremal orbit; i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which λ is a topological invariant, as well as the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalcogenides, 3D Weyl and Dirac metals, and crystalline and Z2 topological insulators. In particular, we point out that a π phase offset in the fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac metal.

Stanene cyanide: a novel candidate of Quantum Spin Hall insulator at high temperature

PubMed Central

Ji, Wei-xiao; Zhang, Chang-wen; Ding, Meng; Li, Ping; Li, Feng; Ren, Miao-juan; Wang, Pei-ji; Hu, Shu-jun; Yan, Shi-shen

2015-01-01

The search for quantum spin Hall (QSH) insulators with high stability, large and tunable gap and topological robustness, is critical for their realistic application at high temperature. Using first-principle calculations, we predict the cyanogen saturated stanene SnCN as novel topological insulators material, with a bulk gap as large as 203 meV, which can be engineered by applying biaxial strain and electric field. The band topology is identified by Z2 topological invariant together with helical edge states, and the mechanism is s-pxy band inversion at G point induced by spin-orbit coupling (SOC). Remarkably, these systems have robust topology against chemical impurities, based on the calculations on halogen and cyano group co-decorated stanene SnXxX′1−x (X,X′  =  F, Cl, Br, I and CN), which makes it an appropriate and flexible candidate material for spintronic devices. PMID:26688269

Manipulating Topological Edge Spins in One-Dimensional Optical Lattice

NASA Astrophysics Data System (ADS)

Liu, Xiong-Jun; Liu, Zheng-Xin; Cheng, Meng

2013-03-01

We propose to observe and manipulate topological edge spins in 1D optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In free-fermion case the SPT phase is classified by a Z invariant which reduces to Z4 with interactions. The zero edge modes of the SPT phase are spin-polarized, with left and right edge spins polarized to opposite directions and forming a topological spin-qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in optical lattice. The manipulation of TSQs has potential applications to quantum computation. We acknowledge the support from JQI-NSF-PFC, Microsoft-Q, and DARPA- QuEST.

Topological phase transitions of (BixSb1-x)2Se3 alloys by density functional theory.

PubMed

Abdalla, L B; Padilha José, E; Schmidt, T M; Miwa, R H; Fazzio, A

2015-07-01

We have performed an ab initio total energy investigation of the topological phase transition, and the electronic properties of topologically protected surface states of (BixSb1-x)2Se3 alloys. In order to provide an accurate alloy concentration for the phase transition, we have considered the special quasirandom structures to describe the alloy system. The trivial → topological transition concentration was obtained by (i) the calculation of the band gap closing as a function of Bi concentration (x), and (ii) the calculation of the Z2 topological invariant number. We show that there is a topological phase transition, for x around 0.4, verified for both procedures (i) and (ii). We also show that in the concentration range 0.4 < x < 0.7, the alloy does not present any other band at the Fermi level besides the Dirac cone, where the Dirac point is far from the bulk states. This indicates that a possible suppression of the scattering process due to bulk states will occur.

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors

NASA Astrophysics Data System (ADS)

Chiu, Ching-Kai; Schnyder, Andreas P.

2014-11-01

While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superconductor), (ii) whether the mirror symmetry commutes or anticommutes with the nonspatial symmetries, and (iii) how the Fermi surfaces (nodal lines or points) transform under the mirror reflection and nonspatial symmetries. The classification is derived by examining all possible symmetry-allowed mass terms that can be added to the Bloch or Bogoliubov-de Gennes Hamiltonian in a given symmetry class and by explicitly deriving topological invariants. We discuss several examples of reflection-symmetry-protected topological semimetals and nodal superconductors, including topological crystalline semimetals with mirror Z2 numbers and topological crystalline nodal superconductors with mirror winding numbers.

Experimental and theoretical study of topology and electronic correlations in PuB4

NASA Astrophysics Data System (ADS)

Choi, Hongchul; Zhu, Wei; Cary, S. K.; Winter, L. E.; Huang, Zhoushen; McDonald, R. D.; Mocko, V.; Scott, B. L.; Tobash, P. H.; Thompson, J. D.; Kozimor, S. A.; Bauer, E. D.; Zhu, Jian-Xin; Ronning, F.

2018-05-01

We synthesize single crystals of PuB4 using an Al-flux technique. Single-crystal diffraction data provide structural parameters for first-principles density functional theory (DFT) calculations. By computing the density of states, the Z2 topological invariant using the Wilson loop method, and the surface electronic structure from slab calculations, we find that PuB4 is a nonmagnetic strong topological insulator with a band gap of 254 meV. Our magnetic susceptibility, heat capacity, and resistivity measurements are consistent with this analysis, albeit with a smaller gap of 35 meV. DFT plus dynamical mean-field theory calculations show that electronic correlations reduce the size of the band gap, and provide better agreement with the value determined by resistivity. These results demonstrate that PuB4 is a promising actinide material to investigate the interplay of electronic correlations and nontrivial topology.

Quark ACM with topologically generated gluon mass

NASA Astrophysics Data System (ADS)

Choudhury, Ishita Dutta; Lahiri, Amitabha

2016-03-01

We investigate the effect of a small, gauge-invariant mass of the gluon on the anomalous chromomagnetic moment (ACM) of quarks by perturbative calculations at one-loop level. The mass of the gluon is taken to have been generated via a topological mass generation mechanism, in which the gluon acquires a mass through its interaction with an antisymmetric tensor field Bμν. For a small gluon mass ( < 10 MeV), we calculate the ACM at momentum transfer q2 = -M Z2. We compare those with the ACM calculated for the gluon mass arising from a Proca mass term. We find that the ACM of up, down, strange and charm quarks vary significantly with the gluon mass, while the ACM of top and bottom quarks show negligible gluon mass dependence. The mechanism of gluon mass generation is most important for the strange quarks ACM, but not so much for the other quarks. We also show the results at q2 = -m t2. We find that the dependence on gluon mass at q2 = -m t2 is much less than at q2 = -M Z2 for all quarks.

Anomalous Z2 antiferromagnetic topological phase in pressurized SmB6

NASA Astrophysics Data System (ADS)

Chang, Kai-Wei; Chen, Peng-Jen

2018-05-01

Antiferromagnetic materials, whose time-reversal symmetry is broken, can be classified into the Z2 topology if they respect some specific symmetry. Since the theoretical proposal, however, no materials have been found to host such Z2 antiferromagnetic topological (Z2-AFT ) phase to date. Here we demonstrate that the topological Kondo insulator SmB6 can be a Z2-AFT system when pressurized to undergo an antiferromagnetic phase transition. In addition to proposing the possible candidate for a Z2-AFT material, in this work we also illustrate the anomalous topological surface states of the Z2-AFT phase which have not been discussed before. Originating from the interplay between the topological properties and the antiferromagnetic surface magnetization, the topological surface states of the Z2-AFT phase behave differently as compared with those of a topological insulator. Besides, the Z2-AFT insulators are also found promising in the generation of tunable spin currents, which is an important application in spintronics.

Classification of topological insulators and superconductors in three spatial dimensions

NASA Astrophysics Data System (ADS)

Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira; Ludwig, Andreas W. W.

2008-11-01

We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced Z2 topological insulator in the symplectic (or spin-orbit) symmetry class. We show that there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in three dimensions, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. Three of the above five topologically nontrivial phases can be realized as time-reversal invariant superconductors. In these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a two-dimensional surface, they support a number (which may be an arbitrary nonvanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin-rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations of the Hamiltonian that preserve the characteristic discrete symmetries, including disorder. In particular, these surface modes completely evade Anderson localization from random impurities. These topological phases can be thought of as three-dimensional analogs of well-known paired topological phases in two spatial dimensions such as the spinless chiral (px±ipy) -wave superconductor (or Moore-Read Pfaffian state). In the corresponding topologically nontrivial (analogous to “weak pairing”) and topologically trivial (analogous to “strong pairing”) 3D phases, the wave functions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the superconducting phases with nonvanishing winding number possess nontrivial topological ground-state degeneracies.

Two-Dimensional Large Gap Topological Insulators with Tunable Rashba Spin-Orbit Coupling in Group-IV films

PubMed Central

Zhang, Shou-juan; Ji, Wei-xiao; Zhang, Chang-wen; Li, Ping; Wang, Pei-ji

2017-01-01

The coexistence of nontrivial topology and giant Rashba splitting, however, has rare been observed in two-dimensional (2D) films, limiting severely its potential applications at room temperature. Here, we through first-principles calculations to propose a series of inversion-asymmetric group-IV films, ABZ2 (A ≠ B = Si, Ge, Sn, Pb; Z = F, Cl, Br), whose stability are confirmed by phonon spectrum calculations. The analyses of electronic structures reveal that they are intrinsic 2D TIs with a bulk gap as large as 0.74 eV, except for GeSiF2, SnSiCl2, GeSiCl2 and GeSiBr2 monolayers which can transform from normal to topological phases under appropriate tensile strain of 4, 4, 5, and 4%, respectively. The nontrivial topology is identified by Z2 topological invariant together with helical edge states, as well as the berry curvature of these systems. Another prominent intriguing feature is the giant Rashba spin splitting with a magnitude reaching 0.15 eV, the largest value reported in 2D films so far. The tunability of Rashba SOC and band topology can be realized through achievable compressive/tensile strains (−4 ~ 6%). Also, the BaTe semiconductor is an ideal substrate for growing ABZ2 films without destroying their nontrivial topology. PMID:28368035

Topological winding properties of spin edge states in the Kane-Mele graphene model

NASA Astrophysics Data System (ADS)

Wang, Zhigang; Hao, Ningning; Zhang, Ping

2009-09-01

We study the spin edge states in the quantum spin-Hall (QSH) effect on a single-atomic layer graphene-ribbon system with both intrinsic and Rashba spin-orbit couplings. The Harper equation for solving the energies of the spin edge states is derived. The results show that in the QSH phase, there are always two pairs of gapless spin-filtered edge states in the bulk energy gap, corresponding to two pairs of zero points of the Bloch function on the complex-energy Riemann surface (RS). The topological aspect of the QSH phase can be distinguished by the difference of the winding numbers of the spin edge states with different polarized directions cross the holes of the RS, which is equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys. Rev. Lett. 95, 146802 (2005)].

Controllable band structure and topological phase transition in two-dimensional hydrogenated arsenene

PubMed Central

Wang, Ya-ping; Ji, Wei-xiao; Zhang, Chang-wen; Li, Ping; Li, Feng; Ren, Miao-juan; Chen, Xin-Lian; Yuan, Min; Wang, Pei-ji

2016-01-01

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature. PMID:26839209

Controllable band structure and topological phase transition in two-dimensional hydrogenated arsenene

NASA Astrophysics Data System (ADS)

Wang, Ya-Ping; Ji, Wei-Xiao; Zhang, Chang-Wen; Li, Ping; Li, Feng; Ren, Miao-Juan; Chen, Xin-Lian; Yuan, Min; Wang, Pei-Ji

2016-02-01

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature.

Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

PubMed Central

Mukherjee, Sebabrata; Spracklen, Alexander; Valiente, Manuel; Andersson, Erika; Öhberg, Patrik; Goldman, Nathan; Thomson, Robert R.

2017-01-01

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime. PMID:28051060

Topological Photonics for Continuous Media

NASA Astrophysics Data System (ADS)

Silveirinha, Mario

Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.

Unexpected Giant-Gap Quantum Spin Hall Insulator in Chemically Decorated Plumbene Monolayer

PubMed Central

Zhao, Hui; Zhang, Chang-wen; Ji, Wei-xiao; Zhang, Run-wu; Li, Sheng-shi; Yan, Shi-shen; Zhang, Bao-min; Li, Ping; Wang, Pei-ji

2016-01-01

Quantum spin Hall (QSH) effect of two-dimensional (2D) materials features edge states that are topologically protected from backscattering by time-reversal symmetry. However, the major obstacles to the application for QSH effect are the lack of suitable QSH insulators with a large bulk gap. Here, we predict a novel class of 2D QSH insulators in X-decorated plumbene monolayers (PbX; X = H, F, Cl, Br, I) with extraordinarily giant bulk gaps from 1.03 eV to a record value of 1.34 eV. The topological characteristic of PbX mainly originates from s-px,y band inversion related to the lattice symmetry, while the effect of spin-orbital coupling (SOC) is only to open up a giant gap. Their QSH states are identified by nontrivial topological invariant Z2 = 1, as well as a single pair of topologically protected helical edge states locating inside the bulk gap. Noticeably, the QSH gaps of PbX are tunable and robust via external strain. We also propose high-dielectric-constant BN as an ideal substrate for the experimental realization of PbX, maintaining its nontrivial topology. These novel QSH insulators with giant gaps are a promising platform to enrich topological phenomena and expand potential applications at high temperature. PMID:26833133

Strain-induced topological quantum phase transition in phosphorene oxide

NASA Astrophysics Data System (ADS)

Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun

Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x < 0.5, and then to decrease with x > 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.

Proton spin: A topological invariant

NASA Astrophysics Data System (ADS)

Tiwari, S. C.

2016-11-01

Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein-Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to ℏ 2, i.e. proton spin decomposition has no meaning in this approach.

GW study of topological insulators Bi2Se3, Bi2Te3, and Sb2Te3: Beyond the perturbative one-shot approach

NASA Astrophysics Data System (ADS)

Aguilera, Irene; Friedrich, Christoph; Bihlmayer, Gustav; Blügel, Stefan

2013-07-01

We present GW calculations of the topological insulators Bi2Se3, Bi2Te3, and Sb2Te3 within the all-electron full-potential linearized augmented-plane-wave formalism. Quasiparticle effects produce significant qualitative changes in the band structures of these materials when compared to density functional theory (DFT), especially at the Γ point, where band inversion takes place. There, the widely used perturbative one-shot GW approach can produce unphysical band dispersions, as the quasiparticle wave functions are forced to be identical to the noninteracting single-particle states. We show that a treatment beyond the perturbative approach, which incorporates the off-diagonal GW matrix elements and thus enables many-body hybridization to be effective in the quasiparticle wave functions, is crucial in these cases to describe the characteristics of the band inversion around the Γ point in an appropriate way. In addition, this beyond one-shot GW approach allows us to calculate the values of the Z2 topological invariants and compare them with those previously obtained within DFT.

Anomalous spin Josephson effect

NASA Astrophysics Data System (ADS)

Wang, Mei-Juan; Wang, Jun; Hao, Lei; Liu, Jun-Feng

2016-10-01

We report a theoretical study on the spin Josephson effect arising from the exchange coupling of the two ferromagnets (Fs), which are deposited on a two-dimensional (2D) time-reversal-invariant topological insulator. An anomalous spin supercurrent Js z˜sin(α +α0) is found to flow in between the two Fs and the ground state of the system is not limited to the magnetically collinear configuration (α =n π ,n is an integer) but determined by a controllable angle α0, where α is the crossed angle between the two F magnetizations. The angle α0 is the dynamic phase of the electrons traveling in between the two Fs and can be controlled electrically by a gate voltage. This anomalous spin Josephson effect, similar to the conventional φ0 superconductor junction, originates from the definite electron chirality of the helical edge states in the 2D topological insulator. These results indicate that the magnetic coupling in a topological system is different from the usual one in conventional materials.

Mixed-pairing superconductivity in 5 d Mott insulators with antisymmetric exchange: Application to Sr2IrO4

NASA Astrophysics Data System (ADS)

Zare, Mohammad-Hossein; Biderang, Mehdi; Akbari, Alireza

2017-11-01

We study the symmetry of the potential superconducting order parameter in 5 d Mott insulators with an eye toward hole-doped Sr2IrO4 . Using a mean-field method, a mixed singlet-triplet superconductivity, d +p , is observed due to the antisymmetric exchange originating from a quasi-spin-orbit coupling. Our calculation on ribbon geometry shows the possible existence of the topologically protected edge states, because of the nodal structure of the superconducting gap. These edge modes are spin polarized and emerge as zero-energy flat bands, supporting a symmetry-protected Majorana state, verified by evaluation of the winding number and Z2 topological invariant. At the end, a possible experimental approach for observation of these edge states and determination of the superconducting gap symmetry is discussed based on the quasiparticle interference technique.

Computer calculation of Witten's 3-manifold invariant

NASA Astrophysics Data System (ADS)

Freed, Daniel S.; Gompf, Robert E.

1991-10-01

Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.

Antimonene Oxides: Emerging Tunable Direct Bandgap Semiconductor and Novel Topological Insulator.

PubMed

Zhang, Shengli; Zhou, Wenhan; Ma, Yandong; Ji, Jianping; Cai, Bo; Yang, Shengyuan A; Zhu, Zhen; Chen, Zhongfang; Zeng, Haibo

2017-06-14

Highly stable antimonene, as the cousin of phosphorene from group-VA, has opened up exciting realms in the two-dimensional (2D) materials family. However, pristine antimonene is an indirect band gap semiconductor, which greatly restricts its applications for optoelectronics devices. Identifying suitable materials, both responsive to incident photons and efficient for carrier transfer, is urgently needed for ultrathin devices. Herein, by means of first-principles computations we found that it is rather feasible to realize a new class of 2D materials with a direct bandgap and high carrier mobility, namely antimonene oxides with different content of oxygen. Moreover, these tunable direct bandgaps cover a wide range from 0 to 2.28 eV, which are crucial for solar cell and photodetector applications. Especially, the antimonene oxide (18Sb-18O) is a 2D topological insulator with a sizable global bandgap of 177 meV, which has a nontrivial Z 2 topological invariant in the bulk and the topological states on the edge. Our findings not only introduce new vitality into 2D group-VA materials family and enrich available candidate materials in this field but also highlight the potential of these 2D semiconductors as appealing ultrathin materials for future flexible electronics and optoelectronics devices.

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

NASA Astrophysics Data System (ADS)

Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten

2018-01-01

We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

(d -2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States

NASA Astrophysics Data System (ADS)

Song, Zhida; Fang, Zhong; Fang, Chen

2017-12-01

We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d =2 , 3). We show that in both cases nontrivial topology is manifested by the presence of the (d -2 )-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through the explicit construction of microscopic models having robust (d -2 )-dimensional edge states.

Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

NASA Astrophysics Data System (ADS)

Wacks, Daniel; Konstantinou, Ilias; Chakraborty, Nilanjan

2018-04-01

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar-turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

PubMed Central

Konstantinou, Ilias; Chakraborty, Nilanjan

2018-01-01

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable. PMID:29740257

Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions

NASA Astrophysics Data System (ADS)

Wen, Xiao-Gang

2017-05-01

We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z2-gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin+ structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of time-reversal symmetry-enriched Z2 topological orders in 2+1 dimensions, and 20 types of simplest time-reversal symmetry-enriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some time-reversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized time-reversal symmetry. We also find that some Z2 SET orders have stringlike excitations that carry anomalous (nononsite) Z2 symmetry, which can be viewed as a fractionalization of Z2 symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory.

How to obtain a cosmological constant from small exotic R4

NASA Astrophysics Data System (ADS)

Asselmeyer-Maluga, Torsten; Król, Jerzy

2018-03-01

In this paper we determine the cosmological constant as a topological invariant by applying certain techniques from low dimensional differential topology. We work with a small exotic R4 which is embedded into the standard R4. Any exotic R4 is a Riemannian smooth manifold with necessary non-vanishing curvature tensor. To determine the invariant part of such curvature we deal with a canonical construction of R4 where it appears as a part of the complex surface K 3 # CP(2) bar. Such R4's admit hyperbolic geometry. This fact simplifies significantly the calculations and enforces the rigidity of the expressions. In particular, we explain the smallness of the cosmological constant with a value consisting of a combination of (natural) topological invariant. Finally, the cosmological constant appears to be a topologically supported quantity.

Search for the lepton flavor violating decay Z → e μ in p p collisions at s = 8 TeV with the ATLAS detector

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aad, G.; Abbott, B.; Abdallah, J.

2014-10-23

We use the ATLAS detector at the Large Hadron Collider to search for the lepton flavor violating process Z→eμ in pp collisions using 20.3 fb -1 of data collected at √s=8 TeV. An enhancement in the eμ invariant mass spectrum is searched for at the Z-boson mass. The number of Z bosons produced in the data sample is estimated using events of similar topology, Z→ee and μμ, significantly reducing the systematic uncertainty in the measurement. In conclusion, there is no evidence of an enhancement at the Z-boson mass, resulting in an upper limit on the branching fraction, B(Z→eμ)<7.5×10 -7 atmore » the 95% confidence level.« less

Room Temperature Quantum Spin Hall Insulator in Ethynyl-Derivative Functionalized Stanene Films

PubMed Central

Zhang, Run-wu; Zhang, Chang-wen; Ji, Wei-xiao; Li, Sheng-shi; Yan, Shi-shen; Hu, Shu-jun; Li, Ping; Wang, Pei-ji; Li, Feng

2016-01-01

Quantum spin Hall (QSH) insulators feature edge states that topologically protected from backscattering. However, the major obstacles to application for QSH effect are the lack of suitable QSH insulators with a large bulk gap. Based on first-principles calculations, we predict a class of large-gap QSH insulators in ethynyl-derivative functionalized stanene (SnC2X; X = H, F, Cl, Br, I), allowing for viable applications at room temperature. Noticeably, the SnC2Cl, SnC2Br, and SnC2I are QSH insulators with a bulk gap of ~0.2 eV, while the SnC2H and SnC2F can be transformed into QSH insulator under the tensile strains. A single pair of topologically protected helical edge states is established for the edge of these systems with the Dirac point locating at the bulk gap, and their QSH states are confirmed with topological invariant Z2 = 1. The films on BN substrate also maintain a nontrivial large-gap QSH effect, which harbors a Dirac cone lying within the band gap. These findings may shed new light in future design and fabrication of large-gap QSH insulators based on two-dimensional honeycomb lattices in spintronics. PMID:26728874

Quantum spin Hall insulator BiXH (XH = OH, SH) monolayers with a large bulk band gap.

PubMed

Hu, Xing-Kai; Lyu, Ji-Kai; Zhang, Chang-Wen; Wang, Pei-Ji; Ji, Wei-Xiao; Li, Ping

2018-05-16

A large bulk band gap is critical for the application of two-dimensional topological insulators (TIs) in spintronic devices operating at room temperature. On the basis of first-principles calculations, we predict BiXH (X = OH, SH) monolayers as TIs with an extraordinarily large bulk gap of 820 meV for BiOH and 850 meV for BiSH, and propose a tight-binding model considering spin-orbit coupling to describe the electronic properties of BiXH. These large gaps are entirely due to the strong spin-orbit interaction related to the pxy orbitals of the Bi atoms of the honeycomb lattice. The orbital filtering mechanism can be used to understand the topological properties of BiXH. The XH groups simply remove one branch of orbitals (pz of Bi) and reduce the trivial 6-band lattice into a 4-band, which is topologically non-trivial. The topological characteristics of BiXH monolayers are confirmed by nonzero topological invariant Z2 and a single pair of gapless helical edge states in the bulk gap. Owing to these features, the BiXH monolayers of the large-gap TIs are an ideal platform to realize many exotic phenomena and fabricate new quantum devices working at room temperature.

Real-space mapping of topological invariants using artificial neural networks

NASA Astrophysics Data System (ADS)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Probing topological protection using a designer surface plasmon structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Fei; Gao, Zhen; Shi, Xihang

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the 'topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can breakmore » the topological protection, but do not exist in electronic topological insulators. Furthermore, this is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.« less

Probing topological protection using a designer surface plasmon structure

DOE PAGES

Gao, Fei; Gao, Zhen; Shi, Xihang; ...

2016-05-20

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the 'topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can breakmore » the topological protection, but do not exist in electronic topological insulators. Furthermore, this is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.« less

Topological phases protected by point group symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Hao; Huang, Sheng -Jie; Fu, Liang

We consider symmetry-protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry and that they can be constructed as stacks and arrays of these lower-dimensional states. This provides the basis for a general framework to classify and characterize bosonic and fermionic pgSPT phases, which can be applied for arbitrary crystalline point group symmetry and in arbitrary spatial dimensions. We develop and illustrate this framework by means of a few examples, focusing on three-dimensional states. We classify bosonic pgSPTmore » phases and fermionic topological crystalline superconductors with Z P 2 (reflection) symmetry, electronic topological crystalline insulators (TCIs) with U(1)×Z P 2 symmetry, and bosonic pgSPT phases with C 2v symmetry, which is generated by two perpendicular mirror reflections. We also study surface properties, with a focus on gapped, topologically ordered surface states. For electronic TCIs, we find a Z 8 × Z 2 classification, where the Z 8 corresponds to known states obtained from noninteracting electrons, and the Z 2 corresponds to a “strongly correlated” TCI that requires strong interactions in the bulk. Lastly, our approach may also point the way toward a general theory of symmetry-enriched topological phases with crystalline point group symmetry.« less

Topology and entanglement in quench dynamics

NASA Astrophysics Data System (ADS)

Chang, Po-Yao

2018-06-01

We classify the topology of the quench dynamics by homotopy groups. A relation between the topological invariant of a postquench order parameter and the topological invariant of a static Hamiltonian is shown in d +1 dimensions (d =1 ,2 ,3 ). The midgap states in the entanglement spectrum of the postquench states reveal their topological nature. When a trivial quantum state is under a sudden quench to a Chern insulator, the midgap states in the entanglement spectrum form rings. These rings are analogous to the boundary Fermi rings in the Hopf insulators. Finally, we show a postquench order parameter in 3+1 dimensions can be characterized by the second Chern number. The number of Dirac cones in the entanglement spectrum is equal to the second Chern number.

Classification and characterization of topological insulators and superconductors

NASA Astrophysics Data System (ADS)

Mong, Roger

Topological insulators (TIs) are a new class of materials which, until recently, have been overlooked despite decades of study in band insulators. Like semiconductors and ordinary insulators, TIs have a bulk gap, but feature robust surfaces excitations which are protected from disorder and interactions which do not close the bulk gap. TIs are distinguished from ordinary insulators not by the symmetries they possess (or break), but by topological invariants characterizing their bulk band structures. These two pictures, the existence of gapless surface modes, and the nontrivial topology of the bulk states, yield two contrasting approaches to the study of TIs. At the heart of the subject, they are connected by the bulk-boundary correspondence, relating bulk and surface degrees of freedom. In this work, we study both aspects of topological insulators, at the same time providing an illumination to their mysterious connection. First, we present a systematic approach to the classification of bulk states of systems with inversion-like symmetries, deriving a complete set of topological invariants for such ensembles. We find that the topological invariants in all dimensions may be computed algebraically via exact sequences. In particular, systems with spatial inversion symmetries in one-, two-, and three-dimensions can be classified by, respectively, 2, 5, and 11 integer invariants. The values of these integers are related to physical observables such as polarization, Hall conductivity, and magnetoelectric coupling. We also find that, for systems with “antiferromagnetic symmetry,” there is a Z2 classification in three-dimensions, and hence a class of “antiferromagnetic topological insulators” (AFTIs) which are distinguished from ordinary antiferromagnets. From the perspective of the bulk, AFTI exhibits the quantized magnetoelectric effect, whereas on the surface, gapless one-dimensional chiral modes emerge at step-defects. Next, we study how the surface spectrum can be computed from bulk quantities. Specifically, we present an analytic prescription for computing the edge dispersion E(k) of a tight-binding Dirac Hamiltonian terminated at an abrupt crystalline edge, based on the bulk Hamiltonian. The result is presented as a geometric formula, relating the existence of surface states as well as their energy dispersion to properties of the bulk Hamiltonian. We further prove the bulk-boundary correspondence for this specific class of systems, connecting the Chern number and the chiral edge modes for quantum Hall systems given in terms of Dirac Hamiltonians. In similar spirit, we examine the existence of Majorana zero modes in superconducting doped-TIs. We find that Majorana zero modes indeed appear but only if the doped Fermi energy is below a critical chemical potential. The critical doping is associated with a topological phase transition of vortex lines, which supports gapless excitations spanning their length. For weak pairing, the critical point is dependent on the non-abelian Berry phase of the bulk Fermi surface. Finally, we investigate the transport properties on the surfaces of TIs. While the surfaces of “strong topological insulators” - TIs with an odd number of Dirac cones in their surface spectrum - have been well studied in literature, studies of their counterpart “weak topological insulators” (WTIs) are meager, with conflicting claims. Because WTIs have an even number of Dirac cones in their surface spectrum, they are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states, rather, presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface. With the inclusion of the mass, the transport properties of the surface of a weak topological insulator follow a two-parameter scaling form, reminiscent of the quantum Hall phase transition.

Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

NASA Astrophysics Data System (ADS)

Qin, Xizhou; Mei, Feng; Ke, Yongguan; Zhang, Li; Lee, Chaohong

2018-01-01

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingale-den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms (Aidelsburger et al 2013 Phys. Rev. Lett. 111, 185301; Miyake et al 2013 Phys. Rev. Lett. 111, 185302). Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

Exact determination of asymptotic CMB temperature-redshift relation

NASA Astrophysics Data System (ADS)

Hahn, Steffen; Hofmann, Ralf

2018-02-01

Based on energy conservation in a Friedmann-Lemaître-Robertson-Walker (FLRW) Universe, on the Legendre transformation between energy density and pressure, and on nonperturbative asymptotic freedom at high temperatures, we derive the coefficient νCMB in the high-temperature (T) — redshift (z) relation, T/T0 = νCMB(z + 1), of the Cosmic Microwave Background (CMB). Theoretically, our calculation relies on a deconfining SU(2) rather than a U(1) photon gas. We prove that νCMB = (1/4)1/3 = 0.629960(5), representing a topological invariant. Interestingly, the relative deviation of νCMB from the critical exponent associated with the correlation length l of the 3D Ising model, νIsing = 0.629971(4), is less than 2 × 10-5. We are not in a position to establish a direct theoretical link between νCMB and νIsing as suggested by the topological nature of νCMB and the fact that both theories are members of the same universality class. We do, however, spell out a somewhat speculative, strictly monotonic map from the physical Ising temperature 𝜃 to a fictitious SU(2) Yang-Mills temperature T, the latter continuing the asymptotic dependence of the scale factor a on T/T0 for T/T0 ≫ 1 down to T = 0, and we identify an exponential map from a to l to reproduce critical Ising behavior.

Cheshire charge in (3+1)-dimensional topological phases

NASA Astrophysics Data System (ADS)

Else, Dominic V.; Nayak, Chetan

2017-07-01

We show that (3 +1 ) -dimensional topological phases of matter generically support loop excitations with topological degeneracy. The loops carry "Cheshire charge": topological charge that is not the integral of a locally defined topological charge density. Cheshire charge has previously been discussed in non-Abelian gauge theories, but we show that it is a generic feature of all (3+1)-D topological phases (even those constructed from an Abelian gauge group). Indeed, Cheshire charge is closely related to nontrivial three-loop braiding. We use a dimensional reduction argument to compute the topological degeneracy of loop excitations in the (3 +1 ) -dimensional topological phases associated with Dijkgraaf-Witten gauge theories. We explicitly construct membrane operators associated with such excitations in soluble microscopic lattice models in Z2×Z2 Dijkgraaf-Witten phases and generalize this construction to arbitrary membrane-net models. We explain why these loop excitations are the objects in the braided fusion 2-category Z (2 VectGω) , thereby supporting the hypothesis that 2-categories are the correct mathematical framework for (3 +1 ) -dimensional topological phases.

Quantum phase transitions and phase diagram for a one-dimensional p-wave superconductor with an incommensurate potential.

PubMed

Cai, X

2014-04-16

The effect of the incommensurate potential is studied for the one-dimensional p-wave superconductor. It is determined by analyzing various properties, such as the superconducting gap, the long-range order of the correlation function, the inverse participation ratio and the Z2 topological invariant, etc. In particular, two important aspects of the effect are investigated: (1) as disorder, the incommensurate potential destroys the superconductivity and drives the system into the Anderson localized phase; (2) as a quasi-periodic potential, the incommensurate potential causes band splitting and turns the system with certain chemical potential into the band insulator phase. A full phase diagram is also presented in the chemical potential-incommensurate potential strength plane.

A New Numerical Method for Z2 Topological Insulators with Strong Disorder

NASA Astrophysics Data System (ADS)

Akagi, Yutaka; Katsura, Hosho; Koma, Tohru

2017-12-01

We propose a new method to numerically compute the Z2 indices for disordered topological insulators in Kitaev's periodic table. All of the Z2 indices are derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties enable highly efficient numerical calculation of the indices of disordered topological insulators. The method, which we propose, is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a Z2 index in two and three dimensions, respectively.

Type-I and type-II topological nodal superconductors with s -wave interaction

NASA Astrophysics Data System (ADS)

Huang, Beibing; Yang, Xiaosen; Xu, Ning; Gong, Ming

2018-01-01

Topological nodal superconductors with protected gapless points in momentum space are generally realized based on unconventional pairings. In this work we propose a minimal model to realize these topological nodal phases with only s -wave interaction. In our model the linear and quadratic spin-orbit couplings along the two orthogonal directions introduce anisotropic effective unconventional pairings in momentum space. This model may support different nodal superconducting phases characterized by either an integer winding number in BDI class or a Z2 index in D class at the particle-hole invariant axes. In the vicinity of the nodal points the effective Hamiltonian can be described by either type-I or type-II Dirac equations, and the Lifshitz transition from type-I nodal phases to type-II nodal phases can be driven by external in-plane magnetic fields. We show that these nodal phases are robust against weak impurities, which only slightly renormalizes the momentum-independent parameters in the impurity-averaged Hamiltonian, thus these phases are possible to be realized in experiments with real semi-Dirac materials. The smoking-gun evidences to verify these phases based on scanning tunneling spectroscopy method are also briefly discussed.

Entropic manifestations of topological order in three dimensions

NASA Astrophysics Data System (ADS)

Bullivant, Alex; Pachos, Jiannis K.

2016-03-01

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by a nonzero vacuum expectation value of contractible loop operators, a topological invariant emerges that increases the entropy if the model consists of nontrivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.

Non-Abelian string and particle braiding in topological order: Modular SL (3 ,Z ) representation and (3 +1 ) -dimensional twisted gauge theory

NASA Astrophysics Data System (ADS)

Wang, Juven C.; Wen, Xiao-Gang

2015-01-01

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.

Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials

NASA Astrophysics Data System (ADS)

Gresch, Dominik; Autès, Gabriel; Yazyev, Oleg V.; Troyer, Matthias; Vanderbilt, David; Bernevig, B. Andrei; Soluyanov, Alexey A.

2017-02-01

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging, problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous k .p models, tight-binding models, and ab initio calculations. We apply the method to compute and identify Chern, Z2, and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with nontrivial topologies. We expect that our work will allow researchers to (a) identify topological materials optimal for experimental probes, (b) classify existing compounds, and (c) reveal materials that host novel, not yet described, topological states.

Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

PubMed

Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang

2015-01-23

The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions

NASA Astrophysics Data System (ADS)

Wang, Juven; Ohmori, Kantaro; Putrov, Pavel; Zheng, Yunqin; Wan, Zheyan; Guo, Meng; Lin, Hai; Gao, Peng; Yau, Shing-Tung

2018-05-01

Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the partition function on various manifolds and ground state degeneracy (GSD), mainly based on continuum/cochain topological quantum field theories (TQFTs), in any dimension. This information can be related to the counting of extended operators of bosonic/fermionic TQFTs. On the lattice scale, anyonic particles/strings live at the ends of line/surface operators. Certain systems in different dimensions are related to each other through dimensional reduction schemes, analogous to (de)categorification. Examples include spin TQFTs derived from gauging the interacting fermionic symmetry-protected topological states (with fermion parity {Z}_2^f) of symmetry groups {Z}_4× {Z}_2 and ({Z}_4)^2 in 3+1D, also {Z}_2 and ({Z}_2)^2 in 2+1D. Gauging the last three cases begets non-Abelian spin TQFTs (fermionic topological order). We consider situations where a TQFT lives on (1) a closed spacetime or (2) a spacetime with a boundary, such that the bulk and boundary are fully gapped and short- or long-range entangled (SRE/LRE). Anyonic excitations can be deconfined on the boundary. We introduce new exotic topological interfaces on which neither particle nor string excitations alone condense, but only fuzzy-composite objects of extended operators can end (e.g., a string-like composite object formed by a set of particles can end on a special 2+1D boundary of 3+1D bulk). We explore the relations between group extension constructions and partially breaking constructions (e.g., 0-form/higher-form/"composite" breaking) of topological boundaries, after gauging. We comment on the implications of entanglement entropy for some such LRE systems.

Simple Z2 lattice gauge theories at finite fermion density

NASA Astrophysics Data System (ADS)

Prosko, Christian; Lee, Shu-Ping; Maciejko, Joseph

2017-11-01

Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-Tc superconductors, and topological phases. However, in many cases gauge fields couple to gapless matter degrees of freedom, and such theories become notoriously difficult to analyze quantitatively. In this paper we study several examples of Z2 lattice gauge theories with gapless fermions at finite density, in one and two spatial dimensions, that are either exactly soluble or whose solution reduces to that of a known problem. We consider complex fermions (spinless and spinful) as well as Majorana fermions and study both theories where Gauss' law is strictly imposed and those where all background charge sectors are kept in the physical Hilbert space. We use a combination of duality mappings and the Z2 slave-spin representation to map our gauge theories to models of gauge-invariant fermions that are either free, or with on-site interactions of the Hubbard or Falicov-Kimball type that are amenable to further analysis. In 1D, the phase diagrams of these theories include free-fermion metals, insulators, and superconductors, Luttinger liquids, and correlated insulators. In 2D, we find a variety of gapped and gapless phases, the latter including uniform and spatially modulated flux phases featuring emergent Dirac fermions, some violating Luttinger's theorem.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsvelik, A. M.; Yevtushenko, O. M.

We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z2 symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axismore » anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localizatioin.« less

Statistical transmutation in doped quantum dimer models.

PubMed

Lamas, C A; Ralko, A; Cabra, D C; Poilblanc, D; Pujol, P

2012-07-06

We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.

The noncommutative index theorem and the periodic table for disordered topological insulators and superconductors

NASA Astrophysics Data System (ADS)

Katsura, Hosho; Koma, Tohru

2018-03-01

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions d ≥ 1. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of the topological invariant, are protected by certain symmetries of the Hamiltonian against disorder. This generic feature is characterized by a generalized index theorem which is a noncommutative analog of the Atiyah-Singer index theorem. The noncommutative index defined in terms of a pair of projections gives a precise formula for the topological invariant in each symmetry class in any dimension (d ≥ 1). Under the assumption on the nonvanishing spectral or mobility gap, we prove that the index formula reproduces Bott periodicity and all of the possible values of topological invariants in the classification table of topological insulators and superconductors. We also prove that the indices are robust against perturbations that do not break the symmetry of the unperturbed Hamiltonian.

Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential: Gauge Invariance and Experimental Detections

PubMed Central

Sun, Fadi; Yu, Xiao-Lu; Ye, Jinwu; Fan, Heng; Liu, Wu-Ming

2013-01-01

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops. PMID:23846153

Tailoring topological states in silicene using different halogen-passivated Si(111) substrates

NASA Astrophysics Data System (ADS)

Derakhshan, Vahid; Moghaddam, Ali G.; Ceresoli, Davide

2018-03-01

We investigate the band structure and topological phases of silicene embedded on halogenated Si(111) surface using density functional theory calculations. Our results show that the Dirac character of low-energy excitations in silicene is almost preserved in the presence of a silicon substrate passivated by various halogens. Nevertheless, the combined effects of symmetry breaking due to both direct and van der Waals interactions between silicene and the substrate, charge transfer from suspended silicene into the substrate, and, finally, the hybridization which leads to the charge redistribution result in a gap in the spectrum of the embedded silicene. We further take the spin-orbit interaction into account and obtain the resulting modification in the gap. The energy gaps with and without spin-orbit coupling vary significantly when different halogen atoms are used for the passivation of the Si surface, and for the case of iodine, they become on the order of 100 meV. To examine the topological properties, we calculate the projected band structure of silicene from which the Berry curvature and Z2 invariant based on the evolution of Wannier charge centers are obtained. As a key finding, it is shown that silicene on halogenated Si substrates has a topological insulating state which can survive even at room temperature for the substrates with iodine and bromine at the surface. Therefore, these results suggest that we can have a reliable, stable, and robust silicene-based two-dimensional topological insulator using the considered substrates.

Exploring 4D quantum Hall physics with a 2D topological charge pump.

PubMed

Lohse, Michael; Schweizer, Christian; Price, Hannah M; Zilberberg, Oded; Bloch, Immanuel

2018-01-03

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant-the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Observation of Topological Links Associated with Hopf Insulators in a Solid-State Quantum Simulator

NASA Astrophysics Data System (ADS)

Yuan, X.-X.; He, L.; Wang, S.-T.; Deng, D.-L.; Wang, F.; Lian, W.-Q.; Wang, X.; Zhang, C.-H.; Zhang, H.-L.; Chang, X.-Y.; Duan, L.-M.

2017-06-01

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including fascinating topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.

Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Xie; Liu Zhengxin; Wen Xiaogang

2011-12-15

Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected topological orders exist. In this paper, we present a model in a two-dimensional (2D) interacting spin system with nontrivial onsite Z{sub 2} symmetry-protected topological order. The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. The construction of this model is related tomore » a nontrivial 3-cocycle of the Z{sub 2} group and can be generalized to any symmetry group. It potentially leads to a complete classification of symmetry-protected topological orders in interacting boson and fermion systems of any dimension. Specifically, this exactly solvable model has a unique gapped ground state on any closed manifold and gapless excitations on the boundary if Z{sub 2} symmetry is not broken. We prove the latter by developing the tool of a matrix product unitary operator to study the nonlocal symmetry transformation on the boundary and reveal the nontrivial 3-cocycle structure of this transformation. Similar ideas are used to construct a 2D fermionic model with onsite Z{sub 2} symmetry-protected topological order.« less

Topological Z2 resonating-valence-bond spin liquid on the square lattice

NASA Astrophysics Data System (ADS)

Chen, Ji-Yao; Poilblanc, Didier

2018-04-01

A one-parameter family of long-range resonating-valence-bond (RVB) state on the square lattice was previously proposed to describe a critical spin liquid (SL) phase of the spin-1/2 frustrated Heisenberg model. We provide evidence that this RVB state in fact also realizes a topological (long-range entangled) Z2 SL, limited by two transitions to critical SL phases. The topological phase is naturally connected to the Z2 gauge symmetry of the local tensor. This Rapid Communication shows that, on one hand, spin-1/2 topological SL with C4 v point-group symmetry and S U (2 ) spin rotation symmetry exists on the square lattice and, on the other hand, criticality and nonbipartiteness are compatible. We also point out that strong similarities between our phase diagram and the ones of classical interacting dimer models suggest both can be described by similar Kosterlitz-Thouless transitions. This scenario is further supported by the analysis of the one-dimensional boundary state. Forms of parent Hamiltonians hosting the Z2 SL are suggested.

Topology versus Anderson localization: Nonperturbative solutions in one dimension

NASA Astrophysics Data System (ADS)

Altland, Alexander; Bagrets, Dmitry; Kamenev, Alex

2015-02-01

We present an analytic theory of quantum criticality in quasi-one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters (g ,χ ) representing localization and topological properties, respectively. Certain critical values of χ (half-integer for Z classes, or zero for Z2 classes) define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two-parameter flow of the integer quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given in terms of the transfer-matrix solution of corresponding supersymmetric nonlinear sigma models. In Z2 classes we uncover a hidden supersymmetry, present at the quantum critical point.

Anomalous electronic structure and magnetoresistance in TaAs 2

DOE PAGES

Luo, Yongkang; McDonald, R. D.; Rosa, P. F. S.; ...

2016-01-01

We report that the change in resistance of a material in a magnetic field reflects its electronic state. In metals with weakly- or non-interacting electrons, the resistance typically increases upon the application of a magnetic field. In contrast, negative magnetoresistance may appear under some circumstances, e.g., in metals with anisotropic Fermi surfaces or with spin-disorder scattering and semimetals with Dirac or Weyl electronic structures. Here we show that the non-magnetic semimetal TaAs 2 possesses a very large negative magnetoresistance, with an unknown scattering mechanism. In conclusion, density functional calculations find that TaAs 2 is a new topological semimetal [Z 2more » invariant (0;111)] without Dirac dispersion, demonstrating that a negative magnetoresistance in non-magnetic semimetals cannot be attributed uniquely to the Adler-Bell-Jackiw chiral anomaly of bulk Dirac/Weyl fermions.« less

Strong gravity and structure of topological solitons

NASA Astrophysics Data System (ADS)

Rybakov, Yu. P.

The unification of Skyrme and Faddeev chiral models describing baryons and leptons respectively as topological solitons is suggested within the framework of 16-spinor field ψ = ψ1 ⊕ ψ2 nonlinear model containing two 8-semispinors ψ1 and ψ2. Using Brioschi identity for 8-spinors and special structure of the Higgs potential V implying the spontaneous symmetry breaking, it is possible to realize topological soliton-like excitations of two kinds due to the choice of S2- or S3- manifolds as phase spaces. The interactions with electromagnetic, Yang--Mills and gravitational fields are exhibited through the extention of derivatives via gauge invariance principle. Specific inclusion in the Higgs potential of the Kretschmann gravitational invariant K = RμνσλRμνσλ/48 permits one to obtain the strong gravity behavior at small distances and guarantee the correspondence with Quantum Mechanics at large distances.

Time, space and equilibrium means of continuous vector functions on the phase space of a dynamical system

NASA Astrophysics Data System (ADS)

Gurevich, Boris M.; Tempel'man, Arcady A.

2010-05-01

For a dynamical system \\tau with 'time' \\mathbb Z^d and compact phase space X, we introduce three subsets of the space \\mathbb R^m related to a continuous function f\\colon X\\to\\mathbb R^m: the set of time means of f and two sets of space means of f, namely those corresponding to all \\tau-invariant probability measures and those corresponding to some equilibrium measures on X. The main results concern topological properties of these sets of means and their mutual position. Bibliography: 18 titles.

Flux-fusion anomaly test and bosonic topological crystalline insulators

DOE PAGES

Hermele, Michael; Chen, Xie

2016-10-13

Here, we introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry-enriched topological (SET) phases. We focus on bosonic systems with Z2 topological order and a symmetry group of the form G=U(1)xG', where G' is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems but can occur at surfaces of d=3 symmetry-protected topological (SPT) phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In somemore » cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by nontrivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry and to show that some fractionalization patterns cannot be extended to a consistent action of G' symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with nontrivial anomalies, including G=U(1)×Z T 2 and G=U(1)×Z P 2, where Z T 2 and Z P 2 are time-reversal and d=2 reflection symmetry, respectively.« less

WKB solutions of difference equations and reconstruction by the topological recursion

NASA Astrophysics Data System (ADS)

Marchal, Olivier

2018-01-01

The purpose of this article is to analyze the connection between Eynard-Orantin topological recursion and formal WKB solutions of a \\hbar -difference equation: \\Psi(x+\\hbar)=≤ft(e\\hbar\\fracd{dx}\\right) \\Psi(x)=L(x;\\hbar)\\Psi(x) with L(x;\\hbar)\\in GL_2( ({C}(x))[\\hbar]) . In particular, we extend the notion of determinantal formulas and topological type property proposed for formal WKB solutions of \\hbar -differential systems to this setting. We apply our results to a specific \\hbar -difference system associated to the quantum curve of the Gromov-Witten invariants of {P}1 for which we are able to prove that the correlation functions are reconstructed from the Eynard-Orantin differentials computed from the topological recursion applied to the spectral curve y=\\cosh-1\\frac{x}{2} . Finally, identifying the large x expansion of the correlation functions, proves a recent conjecture made by Dubrovin and Yang regarding a new generating series for Gromov-Witten invariants of {P}1 .

Kibble-Zurek scaling and string-net coarsening in topologically ordered systems.

PubMed

Chandran, Anushya; Burnell, F J; Khemani, Vedika; Sondhi, S L

2013-10-09

We consider the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now without the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. We illustrate these phenomena in the context of particular phase transitions out of the Abelian Z2 topologically ordered phase of the toric code/Z2 gauge theory, and the non-Abelian SU(2)k ordered phases of the relevant Levin-Wen models.

Topology-Preserving Rigid Transformation of 2D Digital Images.

PubMed

Ngo, Phuc; Passat, Nicolas; Kenmochi, Yukiko; Talbot, Hugues

2014-02-01

We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping.

Index theorem for the flat Andreev bound states at a dirty surface of a nodal superconductor

NASA Astrophysics Data System (ADS)

Ikegaya, Satoshi; Asano, Yasuhiro

2018-03-01

We discuss the stability of at-band Andreev bound states appearing at a surface of a nodal unconventional superconductor. In the clean limit, the existence of the surface bound states is topologically characterized by a momentum-dependent topological invariant: one-dimensional winding number de ned in the restricted Brillouin zone. Thus, such topological invariant is ill-defined in the presence of potential disorder which is inevitable in experiments. By paying attention to chiral symmetry of the Hamiltonian, we provide an alternative topological index N ZES that predicts the number of Andreev bound states at a dirty surface of an unconventional superconductor. Moreover, we demonstrate that the zero-bias differential conductance in a normal metal/unconventional superconductor junction is quantized at (4e 2 /h)|N ZES | in the limit of strong impurity scattering in the normal metal.

Cascade of Quantum Transitions and Magnetocaloric Anomalies in an Open Nanowire

NASA Astrophysics Data System (ADS)

Val'kov, V. V.; Mitskan, V. A.; Shustin, M. S.

2017-12-01

A sequence of magnetocaloric anomalies occurring with the change in a magnetic field H is predicted for an open nanowire with the Rashba spin-orbit coupling and the induced superconducting pairing potential. The nature of such anomalies is due to the cascade of quantum transitions related to the successive changes in the fermion parity of the nanowire ground state with the growth of the magnetic field. It is shown that the critical H c values fall within the parameter range corresponding to the nontrivial values of the Z 2 topological invariant of the corresponding 1D band Hamiltonian characteristic of the D symmetry class. It is demonstrated that such features in the behavior of the open nanowire are retained even in the presence of Coulomb interactions.

Quantum phase transition and protected ideal transport in a Kondo chain

DOE PAGES

Tsvelik, A. M.; Yevtushenko, O. M.

2015-11-30

We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z2 symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axismore » anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localizatioin.« less

Search for high-mass resonant tt¯ production in electron+jets events in 7 TeV pp collisions

NASA Astrophysics Data System (ADS)

Khalatian, Samvel

In this thesis we present a model-independent search for the production of heavy resonances with mass greater than 1 TeV decaying to top quark pairs. Using data samples corresponding to 5.0 fb--1 of integrated luminosity of pp collision data recorded with the Compact Muon Solenoid experiment in 2011 at s = 7 TeV, we select events containing one electron and at least two jets and look for excess above Standard Model background prediction in the top quark pair invariant mass spectrum. The high transverse momenta of the top quarks originating from such decays result in an event topology which requires a dedicated event selection and reconstruction of the invariant top quark pair mass. We use a chi² method in the reconstruction and selection of top quark pairs and apply b-tagging to improve sensitivity. In the absence of evidence for a signal, we evaluate 95% C.L. upper limits on sigma ( pp → Z' → tt¯) · BR as a function of the invariant mass of the resonance.

Momentum space topology of QCD

NASA Astrophysics Data System (ADS)

Zubkov, M. A.

2018-06-01

We discuss the possibility to consider quark matter as the topological material. We consider hadronic phase (HP), the quark-gluon plasma phase (QGP), and the hypothetical color-flavor locking (CFL) phase. In those phases we identify the relevant topological invariants in momentum space. The formalism is developed, which relates those invariants and massless fermions that reside on vortices and at the interphases. This formalism is illustrated by the example of vortices in the CFL phase.

Topological Electride Y2C.

PubMed

Huang, Huaqing; Jin, Kyung-Hwan; Zhang, Shunhong; Liu, Feng

2018-03-14

Two-dimensional (2D) electrides are layered ionic crystals in which anionic electrons are confined in the interlayer space. Here, we report a discovery of nontrivial [Formula: see text] topology in the electronic structures of 2D electride Y 2 C. Based on first-principles calculations, we found a topological [Formula: see text] invariant of (1; 111) for the bulk band and topologically protected surface states in the surfaces of Y 2 C, signifying its nontrivial electronic topology. We suggest a spin-resolved angle-resolved photoemission spectroscopy (ARPES) measurement to detect the unique helical spin texture of the spin-polarized topological surface state, which will provide characteristic evidence for the nontrivial electronic topology of Y 2 C. Furthermore, the coexistence of 2D surface electride states and topological surface state enables us to explain the outstanding discrepancy between the recent ARPES experiments and theoretical calculations. Our findings establish a preliminary link between the electride in chemistry and the band topology in condensed-matter physics, which are expected to inspire further interdisciplinary research between these fields.

Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms

NASA Astrophysics Data System (ADS)

Nobukane, Hiroyoshi; Matsuyama, Toyoki; Tanda, Satoshi

2017-01-01

The quantum anomaly that breaks the symmetry, for example the parity and the chirality, in the quantization leads to a physical quantity with a topological Chern invariant. We report the observation of a Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms by employing electric transport. We observed the superconductor-to-insulator transition by reducing the thickness of Sr2RuO4 single crystals. The appearance of a gap structure in the insulating phase implies local superconductivity. Fractional quantized conductance was observed without an external magnetic field. We found an anomalous induced voltage with temperature and thickness dependence, and the induced voltage exhibited switching behavior when we applied a magnetic field. We suggest that there was fractional magnetic-field-induced electric polarization in the interlayer. These anomalous results are related to topological invariance. The fractional axion angle Θ = π/6 was determined by observing the topological magneto-electric effect in the Bose-insulating phase of Sr2RuO4 nanofilms.

Universal quantum computing using (Zd) 3 symmetry-protected topologically ordered states

NASA Astrophysics Data System (ADS)

Chen, Yanzhu; Prakash, Abhishodh; Wei, Tzu-Chieh

2018-02-01

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically nontrivial, short-ranged entangled states are promising candidates for such a resource. Miller and Miyake [npj Quantum Inf. 2, 16036 (2016), 10.1038/npjqi.2016.36] recently constructed a particular Z2×Z2×Z2 symmetry-protected topological state on the Union Jack lattice and established its quantum-computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting (d -1 ) qudit nontrivial Zd×Zd×Zd symmetry-protected topological states are universal on the triangular lattice, for d being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union Jack lattice.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hermele, Michael; Chen, Xie

Here, we introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry-enriched topological (SET) phases. We focus on bosonic systems with Z2 topological order and a symmetry group of the form G=U(1)xG', where G' is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems but can occur at surfaces of d=3 symmetry-protected topological (SPT) phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In somemore » cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by nontrivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry and to show that some fractionalization patterns cannot be extended to a consistent action of G' symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with nontrivial anomalies, including G=U(1)×Z T 2 and G=U(1)×Z P 2, where Z T 2 and Z P 2 are time-reversal and d=2 reflection symmetry, respectively.« less

Fate of Majorana fermions and Chern numbers after a quantum quench.

PubMed

Sacramento, P D

2014-09-01

In the sequence of quenches to either nontopological phases or other topological phases, we study the stability of Majorana fermions at the edges of a two-dimensional topological superconductor with spin-orbit coupling and in the presence of a Zeeman term. Both instantaneous and slow quenches are considered. In the case of instantaneous quenches, the Majorana modes generally decay, but for a finite system there is a revival time that scales to infinity as the system size grows. Exceptions to this decaying behavior are found in some cases due to the presence of edge states with the same momentum in the final state. Quenches to a topological Z(2) phase reveal some robustness of the Majorana fermions in the sense that even though the survival probability of the Majorana state is small, it does not vanish. If the pairing is not aligned with the spin-orbit Rashba coupling, it is found that the Majorana fermions are fairly robust with a finite survival probability. It is also shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point, beyond which the Chern number fluctuates between increasing values. The effect of varying the rate of change in slow quenches is also analyzed. It is found that the defect production is nonuniversal and does not follow the Kibble-Zurek scaling with the quench rate, as obtained before for other systems with topological edge states.

Gauge invariance of fractionally charged quasiparticles and hidden topological Zn symmetry

NASA Astrophysics Data System (ADS)

Wu, Yong-Shi; Hatsugai, Yasuhiro; Kohmoto, Mahito

1991-02-01

Using the braid-group formalism we study the consequences of gauge invariance for fractionally charged anyonic quasiparticles in a two-dimensional multiply connected system. It is shown that gauge invariance requires multicomponent wave functions, and leads to the emergence of a hidden topological Zn symmetry with associated quantum number and unavoidable occurrence of level crossings for many-body eigenstates. In certain situations, it relates the fractional charge to anyon statistics. The implications for the fractional quantum Hall effect are also discussed.

Disorder-Induced Topological State Transition in Photonic Metamaterials

NASA Astrophysics Data System (ADS)

Liu, Changxu; Gao, Wenlong; Yang, Biao; Zhang, Shuang

2017-11-01

The topological state transition has been widely studied based on the quantized topological band invariant such as the Chern number for the system without intense randomness that may break the band structures. We numerically demonstrate the disorder-induced state transition in the photonic topological systems for the first time. Instead of applying the ill-defined topological band invariant in a disordered system, we utilize an empirical parameter to unambiguously illustrate the state transition of the topological metamaterials. Before the state transition, we observe a robust surface state with well-confined electromagnetic waves propagating unidirectionally, immune to the disorder from permittivity fluctuation up to 60% of the original value. During the transition, a hybrid state composed of a quasiunidirectional surface mode and intensively localized hot spots is established, a result of the competition between the topological protection and Anderson localization.

Z3 topological order in the face-centered-cubic quantum plaquette model

NASA Astrophysics Data System (ADS)

Devakul, Trithep

2018-04-01

We examine the topological order in the resonating singlet valence plaquette (RSVP) phase of the hard-core quantum plaquette model (QPM) on the face centered cubic (FCC) lattice. To do this, we construct a Rohksar-Kivelson type Hamiltonian of local plaquette resonances. This model is shown to exhibit a Z3 topological order, which we show by identifying a Z3 topological constant (which leads to a 33-fold topological ground state degeneracy on the 3-torus) and topological pointlike charge and looplike magnetic excitations which obey Z3 statistics. We also consider an exactly solvable generalization of this model, which makes the geometrical origin of the Z3 order explicitly clear. For other models and lattices, such generalizations produce a wide variety of topological phases, some of which are novel fracton phases.

Effects of topology on the adsorption of singly tethered ring polymers to attractive surfaces.

PubMed

Li, Bing; Sun, Zhao-Yan; An, Li-Jia

2015-07-14

We investigate the effect of topology on the equilibrium behavior of singly tethered ring polymers adsorbed on an attractive surface. We focus on the change of square radius of gyration Rg(2), the perpendicular component Rg⊥(2) and the parallel component Rg‖(2) to the adsorbing surface, the mean contacting number of monomers with the surface , and the monomer distribution along z-direction during transition from desorption to adsorption. We find that both of the critical point of adsorption εc and the crossover exponent ϕ depend on the knot type when the chain length of ring ranges from 48 to 400. The behaviors of Rg(2), Rg⊥(2), and Rg‖(2) are found to be dependent on the topology and the monomer-surface attractive strength. At weak adsorption, the polymer chains with more complex topology are more adsorbable than those with simple topology. However, at strong adsorption, the polymer chains with complex topology are less adsorbable. By analyzing the distribution of monomer along z-direction, we give a possible mechanism for the effect of topology on the adsorption behavior.

Simple anisotropic three-dimensional quantum spin liquid with fractonlike topological order

NASA Astrophysics Data System (ADS)

Petrova, O.; Regnault, N.

2017-12-01

We present a three-dimensional cubic lattice spin model, anisotropic in the z ̂ direction, that exhibits fractonlike order. This order can be thought of as the result of interplay between two-dimensional Z2 topological order and spontaneous symmetry breaking along the z ̂ direction. Fracton order is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground-state degeneracy: On an Lx×Ly×Lz three-torus, it has a 22 Lz topological degeneracy and an additional symmetry-breaking nontopological degeneracy equal to 2LxLy-2. The fractons can be combined into composite excitations that move either in a straight line along the z ̂ direction or freely in the x y plane at a given height z . While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. We find zero energy modes on the surfaces perpendicular to either the x ̂ or y ̂ directions and their absence on the surfaces normal to z ̂. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations.

Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor

PubMed Central

Deng, W. Y.; Geng, H.; Luo, W.; Sheng, L.; Xing, D. Y.

2016-01-01

We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = −2, −1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations. PMID:27148675

Existence and construction of Galilean invariant z ≠2 theories

NASA Astrophysics Data System (ADS)

Grinstein, Benjamín; Pal, Sridip

2018-06-01

We prove a no-go theorem for the construction of a Galilean boost invariant and z ≠2 anisotropic scale invariant field theory with a finite dimensional basis of fields. Two point correlators in such theories, we show, grow unboundedly with spatial separation. Correlators of theories with an infinite dimensional basis of fields, for example, labeled by a continuous parameter, do not necessarily exhibit this bad behavior. Hence, such theories behave effectively as if in one extra dimension. Embedding the symmetry algebra into the conformal algebra of one higher dimension also reveals the existence of an internal continuous parameter. Consideration of isometries shows that the nonrelativistic holographic picture assumes a canonical form, where the bulk gravitational theory lives in a space-time with one extra dimension. This can be contrasted with the original proposal by Balasubramanian and McGreevy, and by Son, where the metric of a (d +2 )-dimensional space-time is proposed to be dual of a d -dimensional field theory. We provide explicit examples of theories living at fixed point with anisotropic scaling exponent z =2/ℓ ℓ+1 , ℓ∈Z .

The topological structure of supergravity: an application to supersymmetric localization

NASA Astrophysics Data System (ADS)

Imbimbo, Camillo; Rosa, Dario

2018-05-01

The BRST algebra of supergravity is characterized by two different bilinears of the commuting supersymmetry ghosts: a vector γ μ and a scalar ϕ, the latter valued in the Yang-Mills Lie algebra. We observe that under BRST transformations γ and ϕ transform as the superghosts of, respectively, topological gravity and topological Yang-Mills coupled to topological gravity. This topological structure sitting inside any supergravity leads to universal equivariant cohomological equations for the curvatures 2-forms which hold on supersymmetric bosonic backgrounds. Additional equivariant cohomological equations can be derived for supersymmetric backgrounds of supergravities for which certain gauge invariant scalar bilinears of the commuting ghosts exist. Among those, N = (2 , 2) in d = 2, which we discuss in detail in this paper, and N = 2 in d = 4.

dRGT theory of massive gravity from spontaneous symmetry breaking

NASA Astrophysics Data System (ADS)

Torabian, Mahdi

2018-05-01

In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory. We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the Einstein-Hilbert action plus the dRGT potential terms. In this vacuum, there are five (three from Goldstone modes) propagating degrees of freedom which form polarizations of a massive spin 2 particle, an extra healthy heavy scalar (Higgs) mode and no Boulware-Deser ghost mode. We further show that the action can be derived in a limit from a topological de Sitter invariant gauge theory in 4 dimensions.

Experimental demonstration of anomalous Floquet topological insulator for sound

NASA Astrophysics Data System (ADS)

Peng, Yu-Gui; Qin, Cheng-Zhi; Zhao, De-Gang; Shen, Ya-Xi; Xu, Xiang-Yuan; Bao, Ming; Jia, Han; Zhu, Xue-Feng

2016-11-01

Time-reversal invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin-based topological protection, the absence of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics to photonics, phononics and mechanics as well, bringing about not only involved new physics but also potential applications in robust wave transport. Despite the growing interests in topologically protected acoustic wave transport, T-invariant acoustic topological insulator has not yet been achieved. Here we report experimental demonstration of anomalous Floquet topological insulator for sound: a strongly coupled metamaterial ring lattice that supports one-way propagation of pseudo-spin-dependent edge states under T-symmetry. We also demonstrate the formation of pseudo-spin-dependent interface states due to lattice dislocations and investigate the properties of pass band and band gap states.

Experimental demonstration of anomalous Floquet topological insulator for sound

PubMed Central

Peng, Yu-Gui; Qin, Cheng-Zhi; Zhao, De-Gang; Shen, Ya-Xi; Xu, Xiang-Yuan; Bao, Ming; Jia, Han; Zhu, Xue-Feng

2016-01-01

Time-reversal invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin-based topological protection, the absence of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics to photonics, phononics and mechanics as well, bringing about not only involved new physics but also potential applications in robust wave transport. Despite the growing interests in topologically protected acoustic wave transport, T-invariant acoustic topological insulator has not yet been achieved. Here we report experimental demonstration of anomalous Floquet topological insulator for sound: a strongly coupled metamaterial ring lattice that supports one-way propagation of pseudo-spin-dependent edge states under T-symmetry. We also demonstrate the formation of pseudo-spin-dependent interface states due to lattice dislocations and investigate the properties of pass band and band gap states. PMID:27834375

The Role Of Painleve II In Predicting New Liquid Crystal Self-Assembly Mechanisms

NASA Astrophysics Data System (ADS)

Troy, William C.

2018-01-01

We prove the existence of a new class of solutions, called shadow kinks, of the Painleve II equation {d2 w}/{dz2}=2w3 +zw+α,} where {α < 0} is a constant. Shadow kinks are sign changing solutions which satisfy { w(z) ˜ -{√ {-z/2}} as z \\to - ∞} and w(z) ˜ -{α}/{z} as z \\to ∞. These solutions play a critical role in the prediction of a new class of topological defects, one dimensional shadow kinks and two dimensional shadow vortices, in light-matter interaction experiments on nematic liquid crystals. These new defects are physically important since it has recently been shown ( Wang et al. in Nat Mater 15:106-112, 2016) that topological defects are a "template for molecular self-assembly" in liquid crystals. Connections with the modified KdV equation are also discussed.

Interfacial Dirac cones from alternating topological invariant superlattice structures of Bi2Se3.

PubMed

Song, Jung-Hwan; Jin, Hosub; Freeman, Arthur J

2010-08-27

When the three-dimensional topological insulators Bi2Se3 and Bi2Te3 have an interface with vacuum, i.e., a surface, they show remarkable features such as topologically protected and spin-momentum locked surface states. However, for practical applications, one often requires multiple interfaces or channels rather than a single surface. Here, for the first time, we show that an interfacial and ideal Dirac cone is realized by alternating band and topological insulators. The multichannel Dirac fermions from the superlattice structures open a new way for applications such as thermoelectric and spintronics devices. Indeed, utilizing the interfacial Dirac fermions, we also demonstrate the possible power factor improvement for thermoelectric applications.

Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms

PubMed Central

Nobukane, Hiroyoshi; Matsuyama, Toyoki; Tanda, Satoshi

2017-01-01

The quantum anomaly that breaks the symmetry, for example the parity and the chirality, in the quantization leads to a physical quantity with a topological Chern invariant. We report the observation of a Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms by employing electric transport. We observed the superconductor-to-insulator transition by reducing the thickness of Sr2RuO4 single crystals. The appearance of a gap structure in the insulating phase implies local superconductivity. Fractional quantized conductance was observed without an external magnetic field. We found an anomalous induced voltage with temperature and thickness dependence, and the induced voltage exhibited switching behavior when we applied a magnetic field. We suggest that there was fractional magnetic-field-induced electric polarization in the interlayer. These anomalous results are related to topological invariance. The fractional axion angle Θ = π/6 was determined by observing the topological magneto-electric effect in the Bose-insulating phase of Sr2RuO4 nanofilms. PMID:28112269

Photonic topological boundary pumping as a probe of 4D quantum Hall physics

NASA Astrophysics Data System (ADS)

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P.; Kraus, Yaacov E.; Rechtsman, Mikael C.

2018-01-01

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Photonic topological boundary pumping as a probe of 4D quantum Hall physics.

PubMed

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P; Kraus, Yaacov E; Rechtsman, Mikael C

2018-01-03

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Boundary states in the chiral symmetric systems with a spatial symmetry

NASA Astrophysics Data System (ADS)

Xiao, Jinpeng; An, Jin

2018-02-01

We study topological systems with both a chiral and a spatial symmetry which result in an additional spatial chiral symmetry. We distinguish the topologically nontrivial states according to the chiral symmetries protecting them and study several models in 1D and 3D systems. The perturbations breaking the spatial symmetry can break only one of the two chiral symmetries while the perturbations preserving the spatial symmetry always break or preserve both of them. In 3D systems, besides the 3D symmetries, the topologically nontrivial boundary modes may also be protected by the hidden lower dimensional symmetries. We then figure out the corresponding topological invariants and connect them with the 3D invariants.

Anisotropic Weyl symmetry and cosmology

NASA Astrophysics Data System (ADS)

Moon, Taeyoon; Oh, Phillial; Sohn, Jongsu

2010-11-01

We construct an anisotropic Weyl invariant theory in the ADM formalism and discuss its cosmological consequences. It extends the original anisotropic Weyl invariance of Hořava-Lifshitz gravity using an extra scalar field. The action is invariant under the anisotropic transformations of the space and time metric components with an arbitrary value of the critical exponent z. One of the interesting features is that the cosmological constant term maintains the anisotropic symmetry for z = -3. We also include the cosmological fluid and show that it can preserve the anisotropic Weyl invariance if the equation of state satisfies P = zρ/3. Then, we study cosmology of the Einstein-Hilbert-anisotropic Weyl (EHaW) action including the cosmological fluid, both with or without anisotropic Weyl invariance. The correlation of the critical exponent z and the equation of state parameter bar omega provides a new perspective of the cosmology. It is also shown that the EHaW action admits a late time accelerating universe for an arbitrary value of z when the anisotropic conformal invariance is broken, and the anisotropic conformal scalar field is interpreted as a possible source of dark energy.

An accuracy improvement method for the topology measurement of an atomic force microscope using a 2D wavelet transform.

PubMed

Yoon, Yeomin; Noh, Suwoo; Jeong, Jiseong; Park, Kyihwan

2018-05-01

The topology image is constructed from the 2D matrix (XY directions) of heights Z captured from the force-feedback loop controller. For small height variations, nonlinear effects such as hysteresis or creep of the PZT-driven Z nano scanner can be neglected and its calibration is quite straightforward. For large height variations, the linear approximation of the PZT-driven Z nano scanner fail and nonlinear behaviors must be considered because this would cause inaccuracies in the measurement image. In order to avoid such inaccuracies, an additional strain gauge sensor is used to directly measure displacement of the PZT-driven Z nano scanner. However, this approach also has a disadvantage in its relatively low precision. In order to obtain high precision data with good linearity, we propose a method of overcoming the low precision problem of the strain gauge while its feature of good linearity is maintained. We expect that the topology image obtained from the strain gauge sensor showing significant noise at high frequencies. On the other hand, the topology image obtained from the controller output showing low noise at high frequencies. If the low and high frequency signals are separable from both topology images, the image can be constructed so that it is represented with high accuracy and low noise. In order to separate the low frequencies from high frequencies, a 2D Haar wavelet transform is used. Our proposed method use the 2D wavelet transform for obtaining good linearity from strain gauge sensor and good precision from controller output. The advantages of the proposed method are experimentally validated by using topology images. Copyright © 2018 Elsevier B.V. All rights reserved.

Disorder effects in topological states: Brief review of the recent developments

NASA Astrophysics Data System (ADS)

Wu, Binglan; Song, Juntao; Zhou, Jiaojiao; Jiang, Hua

2016-11-01

Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review the work completed over the last few years, including our own, regarding recent developments in several topics about disorder effects in topological states. For weak disorder, the robustness of topological states is demonstrated, especially for both quantum spin Hall states with Z 2 = 1 and size induced nontrivial topological insulators with Z 2 = 0. For moderate disorder, by increasing the randomness of both the impurity distribution and the impurity induced potential, the topological insulator states can be created from normal metallic or insulating states. These phenomena and their mechanisms are summarized. For strong disorder, the disorder causes a metal-insulator transition. Due to their topological nature, the phase diagrams are much richer in topological state systems. Finally, the trends in these areas of disorder research are discussed. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374219, 11474085, and 11534001) and the Natural Science Foundation of Jiangsu Province, China (Grant No BK20160007).

Entanglement entropy and entanglement spectrum of the Kitaev model.

PubMed

Yao, Hong; Qi, Xiao-Liang

2010-08-20

In this letter, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S = SG+SF, with SF the entanglement entropy of a free Majorana fermion system and SG that of a Z2 gauge field. The Z2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the nonlocal entanglement carried by the Z2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the st ates with and without topologically protected gapless entanglement spectrum.

Inconsistency of topologically massive hypergravity

NASA Technical Reports Server (NTRS)

Aragone, C.; Deser, S.

1985-01-01

The coupled topologically massive spin-5/2 gravity system in D = 3 dimensions whose kinematics represents dynamical propagating gauge invariant massive spin-5/2 and spin-2 excitations, is shown to be inconsistent, or equivalently, not locally hypersymmetric. In contrast to D = 4, the local constraints on the system arising from failure of the fermionic Bianchi identities do not involve the 'highest spin' components of the field, but rather the auxiliary spinor required to construct a consistent massive model.

Massless spectra and gauge couplings at one-loop on non-factorisable toroidal orientifolds

NASA Astrophysics Data System (ADS)

Berasaluce-González, Mikel; Honecker, Gabriele; Seifert, Alexander

2018-01-01

So-called 'non-factorisable' toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al. [1] provides a new avenue to Conformal Field Theory methods, by which the vector-like massless matter spectrum - and thereby the type of gauge group enhancement on orientifold invariant fractional D6-branes - and the one-loop corrections to the gauge couplings in Type IIA orientifold theories can be computed in addition to the well-established chiral matter spectrum derived from topological intersection numbers among three-cycles. We demonstrate this framework for the Z4 × ΩR orientifolds on the A3 ×A1 ×B2-type torus. As observed before for factorisable backgrounds, also here the one-loop correction can drive the gauge groups to stronger coupling as demonstrated by means of a four-generation Pati-Salam example.

Multiflavor string-net models

NASA Astrophysics Data System (ADS)

Lin, Chien-Hung

2017-05-01

We generalize the string-net construction to multiple flavors of strings, each of which is labeled by the elements of an Abelian group Gi. The same flavor of strings can branch, while different flavors of strings can cross one another and thus they form intersecting string nets. We systematically construct the exactly soluble lattice Hamiltonians and the ground-state wave functions for the intersecting string-net condensed phases. We analyze the braiding statistics of the low-energy quasiparticle excitations and find that our model can realize all the topological phases as the string-net model with group G =∏iGi . In this respect, our construction provides various ways of building lattice models which realize topological order G , corresponding to different partitions of G and thus different flavors of string nets. In fact, our construction concretely demonstrates the Künneth formula by constructing various lattice models with the same topological order. As an example, we construct the G =Z2×Z2×Z2 string-net model which realizes a non-Abelian topological phase by properly intersecting three copies of toric codes.

Recoverable information and emergent conservation laws in fracton stabilizer codes

NASA Astrophysics Data System (ADS)

Schmitz, A. T.; Ma, Han; Nandkishore, Rahul M.; Parameswaran, S. A.

2018-04-01

We introduce a new quantity that we term recoverable information, defined for stabilizer Hamiltonians. For such models, the recoverable information provides a measure of the topological information as well as a physical interpretation, which is complementary to topological entanglement entropy. We discuss three different ways to calculate the recoverable information and prove their equivalence. To demonstrate its utility, we compute recoverable information for fracton models using all three methods where appropriate. From the recoverable information, we deduce the existence of emergent Z2 Gauss-law-type constraints, which in turn imply emergent Z2 conservation laws for pointlike quasiparticle excitations of an underlying topologically ordered phase.

Adventures in Topological Field Theory

NASA Astrophysics Data System (ADS)

Horne, James H.

1990-01-01

This thesis consists of 5 parts. In part I, the topological Yang-Mills theory and the topological sigma model are presented in a superspace formulation. This greatly simplifies the field content of the theories, and makes the Q-invariance more obvious. The Feynman rules for the topological Yang -Mills theory are derived. We calculate the one-loop beta-functions of the topological sigma model in superspace. The lattice version of these theories is presented. The self-duality constraints of both models lead to spectrum doubling. In part II, we show that conformally invariant gravity in three dimensions is equivalent to the Yang-Mills gauge theory of the conformal group in three dimensions, with a Chern-Simons action. This means that conformal gravity is finite and exactly soluble. In part III, we derive the skein relations for the fundamental representations of SO(N), Sp(2n), Su(m| n), and OSp(m| 2n). These relations can be used recursively to calculate the expectation values of Wilson lines in three-dimensional Chern-Simons gauge theory with these gauge groups. A combination of braiding and tying of Wilson lines completely describes the skein relations. In part IV, we show that the k = 1 two dimensional gravity amplitudes at genus 3 agree precisely with the results from intersection theory on moduli space. Predictions for the genus 4 intersection numbers follow from the two dimensional gravity theory. In part V, we discuss the partition function in two dimensional gravity. For the one matrix model at genus 2, we use the partition function to derive a recursion relation. We show that the k = 1 amplitudes completely determine the partition function at arbitrary genus. We present a conjecture for the partition function for the arbitrary topological field theory coupled to topological gravity.

Topological nodal-line fermions in spin-orbit metal PbTaSe2

PubMed Central

Bian, Guang; Chang, Tay-Rong; Sankar, Raman; Xu, Su-Yang; Zheng, Hao; Neupert, Titus; Chiu, Ching-Kai; Huang, Shin-Ming; Chang, Guoqing; Belopolski, Ilya; Sanchez, Daniel S.; Neupane, Madhab; Alidoust, Nasser; Liu, Chang; Wang, BaoKai; Lee, Chi-Cheng; Jeng, Horng-Tay; Zhang, Chenglong; Yuan, Zhujun; Jia, Shuang; Bansil, Arun; Chou, Fangcheng; Lin, Hsin; Hasan, M. Zahid

2016-01-01

Topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe2 with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe2 are not only protected by the reflection symmetry but also characterized by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems. PMID:26829889

Bulk and interface quantum states of electrons in multi-layer heterostructures with topological materials

NASA Astrophysics Data System (ADS)

Nikolic, Aleksandar; Zhang, Kexin; Barnes, C. H. W.

2018-06-01

In this article we describe the bulk and interface quantum states of electrons in multi-layer heterostructures in one dimension, consisting of topological insulators (TIs) and topologically trivial materials. We use and extend an effective four-band continuum Hamiltonian by introducing position dependence to the eight material parameters of the Hamiltonian. We are able to demonstrate complete conduction-valence band mixing in the interface states. We find evidence for topological features of bulk states of multi-layer TI heterostructures, as well as demonstrating both complete and incomplete conduction-valence band inversion at different bulk state energies. We show that the linear k z terms in the low-energy Hamiltonian, arising from overlap of p z orbitals between different atomic layers in the case of chalcogenides, control the amount of tunneling from TIs to trivial insulators. Finally, we show that the same linear k z terms in the low-energy Hamiltonian affect the material’s ability to form the localised interface state, and we demonstrate that due to this effect the spin and probability density localisation in a thin film of Sb2Te3 is incomplete. We show that changing the parameter that controls the magnitude of the overlap of p z orbitals affects the transport characteristics of the topologically conducting states, with incomplete topological state localisation resulting in increased backscattering.

Bulk and interface quantum states of electrons in multi-layer heterostructures with topological materials.

PubMed

Nikolic, Aleksandar; Zhang, Kexin; Barnes, C H W

2018-06-13

In this article we describe the bulk and interface quantum states of electrons in multi-layer heterostructures in one dimension, consisting of topological insulators (TIs) and topologically trivial materials. We use and extend an effective four-band continuum Hamiltonian by introducing position dependence to the eight material parameters of the Hamiltonian. We are able to demonstrate complete conduction-valence band mixing in the interface states. We find evidence for topological features of bulk states of multi-layer TI heterostructures, as well as demonstrating both complete and incomplete conduction-valence band inversion at different bulk state energies. We show that the linear k z terms in the low-energy Hamiltonian, arising from overlap of p z orbitals between different atomic layers in the case of chalcogenides, control the amount of tunneling from TIs to trivial insulators. Finally, we show that the same linear k z terms in the low-energy Hamiltonian affect the material's ability to form the localised interface state, and we demonstrate that due to this effect the spin and probability density localisation in a thin film of Sb 2 Te 3 is incomplete. We show that changing the parameter that controls the magnitude of the overlap of p z orbitals affects the transport characteristics of the topologically conducting states, with incomplete topological state localisation resulting in increased backscattering.

Topological triplon modes and bound states in a Shastry-Sutherland magnet

NASA Astrophysics Data System (ADS)

McClarty, P. A.; Krüger, F.; Guidi, T.; Parker, S. F.; Refson, K.; Parker, A. W.; Prabhakaran, D.; Coldea, R.

2017-08-01

The twin discoveries of the quantum Hall effect, in the 1980s, and of topological band insulators, in the 2000s, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have taught us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side effects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has initiated a hunt for topological insulators in bosonic systems: in photonic crystals, in the vibrational modes of crystals, and in the excitations of ordered magnets. Using inelastic neutron scattering along with theoretical calculations, we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu2(BO3)2 is a bosonic topological insulator with topologically protected chiral edge modes of triplon excitations.

Exactly solved models on planar graphs with vertices in {Z}^3

NASA Astrophysics Data System (ADS)

Kels, Andrew P.

2017-12-01

It is shown how exactly solved edge interaction models on the square lattice, may be extended onto more general planar graphs, with edges connecting a subset of next nearest neighbour vertices of {Z}3 . This is done by using local deformations of the square lattice, that arise through the use of the star-triangle relation. Similar to Baxter’s Z-invariance property, these local deformations leave the partition function invariant up to some simple factors coming from the star-triangle relation. The deformations used here extend the usual formulation of Z-invariance, by requiring the introduction of oriented rapidity lines which form directed closed paths in the rapidity graph of the model. The quasi-classical limit is also considered, in which case the deformations imply a classical Z-invariance property, as well as a related local closure relation, for the action functional of a system of classical discrete Laplace equations.

Scaling theory of topological phase transitions

NASA Astrophysics Data System (ADS)

Chen, Wei

2016-02-01

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.

The phase transitions between Z n × Z n bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

DOE PAGES

Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen; ...

2017-03-27

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here in this paper we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n × Z n. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transitionmore » and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.« less

The phase transitions between Z n × Z n bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here in this paper we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n × Z n. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transitionmore » and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.« less

Topological T-duality, automorphisms and classifying spaces

NASA Astrophysics Data System (ADS)

Pande, Ashwin S.

2014-08-01

We extend the formalism of Topological T-duality to spaces which are the total space of a principal S1-bundle p:E→W with an H-flux in H3(E,Z) together with an automorphism of the continuous-trace algebra on E determined by H. The automorphism is a ‘topological approximation’ to a gerby gauge transformation of spacetime. We motivate this physically from Buscher’s Rules for T-duality. Using the Equivariant Brauer Group, we connect this problem to the C∗-algebraic formalism of Topological T-duality of Mathai and Rosenberg (2005). We show that the study of this problem leads to the study of a purely topological problem, namely, Topological T-duality of triples (p,b,H) consisting of isomorphism classes of a principal circle bundle p:X→B and classes b∈H2(X,Z) and H∈H3(X,Z). We construct a classifying space R for triples in a manner similar to the work of Bunke and Schick (2005). We characterize R up to homotopy and study some of its properties. We show that it possesses a natural self-map which induces T-duality for triples. We study some properties of this map.

Observation of Z decays to four leptons with the CMS detector at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatrchyan, S.; Khachatryan, V.; Sirunyan, A. M.

The first observation of the Z boson decaying to four leptons in proton-proton collisions is presented. The analyzed data set corresponds to an integrated luminosity of 5.02 inverse femtobarns at sqrt(s) = 7 TeV collected by the CMS detector at the Large Hadron Collider. A pronounced resonance peak, with a statistical significance of 9.7 sigma, is observed in the distribution of the invariant mass of four leptons (electrons and/or muons) with mass and width consistent with expectations for Z boson decays. The branching fraction and cross section reported here are defined by phase space restrictions on the leptons, namely, 80more » < m[4l] < 100 GeV, where m[4l] is the invariant mass of the four leptons, and m[ll] > 4 GeV for all pairs of leptons, where m[ll] is the two-lepton invariant mass. The measured branching fraction is B(Z to 4l) = (4.2 /+0.9/-0.8 (stat.) +/- 0.2 (syst.)) 10E-6 and agrees with the standard model prediction of 4.45 10E-6. The measured cross section times branching fraction is sigma(pp to Z) B(Z to 4 l) = 112 +23/-20 (stat.) +7/-5 (syst.) +3/-2 (lumi.) fb, also consistent with the standard model prediction of 120 fb. The four-lepton mass peak arising from Z to 4 l decays provides a calibration channel for the Higgs boson search in the H to ZZ to 4 l decay mode.« less

Higher-order topological insulators and superconductors protected by inversion symmetry

NASA Astrophysics Data System (ADS)

Khalaf, Eslam

2018-05-01

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that propagate along one-dimensional curves (hinges) or are localized at some points (corners) on the surface. We provide a complete classification of inversion-protected higher-order topological insulators and superconductors in any spatial dimension for the 10 symmetry classes by means of a layer construction. We discuss possible physical realizations of such states starting with a time-reversal-invariant topological insulator (class AII) in three dimensions or a time-reversal-invariant topological superconductor (class DIII) in two or three dimensions. The former exhibits one-dimensional chiral or helical modes propagating along opposite edges, whereas the latter hosts Majorana zero modes localized to two opposite corners. Being protected by inversion, such states are not pinned to a specific pair of edges or corners, thus offering the possibility of controlling their location by applying inversion-symmetric perturbations such as magnetic field.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flammia, Steven T.; Hamma, Alioscia; Hughes, Taylor L.

We generalize the topological entanglement entropy to a family of topological Renyi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Renyi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.

Cognitive Invariants of Geographic Event Conceptualization: What Matters and What Refines?

NASA Astrophysics Data System (ADS)

Klippel, Alexander; Li, Rui; Hardisty, Frank; Weaver, Chris

Behavioral experiments addressing the conceptualization of geographic events are few and far between. Our research seeks to address this deficiency by developing an experimental framework on the conceptualization of movement patterns. In this paper, we report on a critical experiment that is designed to shed light on the question of cognitively salient invariants in such conceptualization. Invariants have been identified as being critical to human information processing, particularly for the processing of dynamic information. In our experiment, we systematically address cognitive invariants of one class of geographic events: single entity movement patterns. To this end, we designed 72 animated icons that depict the movement patterns of hurricanes around two invariants: size difference and topological equivalence class movement patterns endpoints. While the endpoint hypothesis, put forth by Regier (2007), claims a particular focus of human cognition to ending relations of events, other research suggests that simplicity principles guide categorization and, additionally, that static information is easier to process than dynamic information. Our experiments show a clear picture: Size matters. Nonetheless, we also find categorization behaviors consistent with experiments in both the spatial and temporal domain, namely that topology refines these behaviors and that topological equivalence classes are categorized consistently. These results are critical steppingstones in validating spatial formalism from a cognitive perspective and cognitively grounding work on ontologies.

Symmetry-protected gapless Z2 spin liquids

NASA Astrophysics Data System (ADS)

Lu, Yuan-Ming

2018-03-01

Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work, we discuss a large class of robust gapless quantum spin liquids in frustrated magnets made of half-integer spins, which are described by gapless fermionic spinons coupled to dynamical Z2 gauge fields. Requiring U(1 ) spin conservation, time-reversal, and certain space-group symmetries, we show that certain spinon symmetry fractionalization class necessarily leads to a gapless spectrum. These gapless excitations are stable against any perturbations, as long as the required symmetries are preserved. Applying these gapless criteria to spin-1/2 systems on square, triangular, and kagome lattices, we show that all gapped symmetric Z2 spin liquids in Abrikosov-fermion representation can also be realized in Schwinger-boson representation. This leads to 64 gapped Z2 spin liquids on square lattice, and 8 gapped states on both kagome and triangular lattices.

Topological order, entanglement, and quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Mazáč, Dalimil; Hamma, Alioscia

2012-09-01

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z2 gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed.

Topological entanglement Rényi entropy and reduced density matrix structure.

PubMed

Flammia, Steven T; Hamma, Alioscia; Hughes, Taylor L; Wen, Xiao-Gang

2009-12-31

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.

Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure

NASA Astrophysics Data System (ADS)

Flammia, Steven T.; Hamma, Alioscia; Hughes, Taylor L.; Wen, Xiao-Gang

2009-12-01

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter α, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of α for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.

Machine learning Z2 quantum spin liquids with quasiparticle statistics

NASA Astrophysics Data System (ADS)

Zhang, Yi; Melko, Roger G.; Kim, Eun-Ah

2017-12-01

After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a Z2 quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

Enriched classification of parafermionic gapped phases with time-reversal symmetry

NASA Astrophysics Data System (ADS)

Xu, Wen-Tao; Zhang, Guang-Ming

2018-03-01

Based on the recently established parafermionic matrix product states, we study the classification of one-dimensional gapped phases of parafermions with time-reversal (TR) symmetry satisfying T2=1 . Without extra symmetry, it has been found that Zp parafermionic gapped phases can be classified as topological phases, spontaneous symmetry breaking (SSB) phases, and a trivial phase, which are uniquely labeled by the divisors n of p . In the presence of TR symmetry, however, the enriched classification is characterized by three indices n , κ , and μ , where κ ∈Z2 denotes the linear or projective TR actions on the edges, and μ ∈Z2 indicates the commutation relations between the TR and (fractionalized) charge operator. For the Zr-symmetric parafermionic ground states, where r =p for trivial or topological phases, and r =p /n for SSB phases, each original gapped phase with odd r is divided into two phases, while each phase with even r is further separated into four phases. The gapped parafermionic phases with the TR symmetry include the symmetry protected topological phases, symmetry enriched topological phases, and the SSB coexisting symmetry protected topological phases. From analyzing the structures and symmetries of their reduced density matrices of these resulting topological phases, we can obtain the topologically protected degeneracies of their entanglement spectra.

Chern-Simons theory and Wilson loops in the Brillouin zone

NASA Astrophysics Data System (ADS)

Lian, Biao; Vafa, Cumrun; Vafa, Farzan; Zhang, Shou-Cheng

2017-03-01

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3D) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the six-dimensional phase space, where the physical space defects play the role of topological D-branes.

Dynamical Chern-Simons Theory in the Brillouin Zone

NASA Astrophysics Data System (ADS)

Lian, Biao; Vafa, Cumrun; Vafa, Farzan; Zhang, Shou-Cheng

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a dynamical fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the 6 dimensional phase space, where the physical space defects play the role of topological D-branes.

Accessing the topological susceptibility via the Gribov horizon

NASA Astrophysics Data System (ADS)

Dudal, D.; Felix, C. P.; Guimaraes, M. S.; Sorella, S. P.

2017-10-01

The topological susceptibility, χ4 , following the work of Witten and Veneziano, plays a key role in identifying the relative magnitude of the η' mass, the so-called U (1 )A problem. A nonzero χ4 is caused by the Veneziano ghost, the occurrence of an unphysical massless pole in the correlation function of the topological current Kμ. In this paper, we investigate the topological susceptibility, χ4, in S U (3 ) and S U (2 ) Euclidean Yang-Mills theory using an appropriate Padé approximation tool and a nonperturbative gluon propagator, within a Becchi-Rouet-Stora-Tyutin invariant framework and by taking into account Gribov copies in a general linear covariant gauge.

Topological nodal-line fermions in spin-orbit metal PbTaSe2

DOE PAGES

Bian, Guang; Chang, Tay-Rong; Sankar, Raman; ...

2016-02-02

Here we discuss how topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe 2 with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe 2 are not only protected by the reflection symmetry butmore » also characterized by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems.« less

Effect of strong disorder on three-dimensional chiral topological insulators: Phase diagrams, maps of the bulk invariant, and existence of topological extended bulk states

NASA Astrophysics Data System (ADS)

Song, Juntao; Fine, Carolyn; Prodan, Emil

2014-11-01

The effect of strong disorder on chiral-symmetric three-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the noncommutative winding number, as functions of disorder strength and model's parameters. The localized/delocalized characteristic of the quantum states is probed with level statistics analysis. Our study reconfirms the accurate quantization of the noncommutative winding number in the presence of strong disorder, and its effectiveness as a numerical tool. Extended bulk states are detected above and below the Fermi level, which are observed to undergo the so-called "levitation and pair annihilation" process when the system is driven through a topological transition. This suggests that the bulk invariant is carried by these extended states, in stark contrast with the one-dimensional case where the extended states are completely absent and the bulk invariant is carried by the localized states.

The Critical Z-Invariant Ising Model via Dimers: Locality Property

NASA Astrophysics Data System (ADS)

Boutillier, Cédric; de Tilière, Béatrice

2011-01-01

We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher (J Math Phys 7:1776-1781, 1966) introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model, consisting of explicit expressions which only depend on the local geometry of the underlying isoradial graph. Our main result is an explicit local formula for the inverse Kasteleyn matrix, in the spirit of Kenyon (Invent Math 150(2):409-439, 2002), as a contour integral of the discrete exponential function of Mercat (Discrete period matrices and related topics, 2002) and Kenyon (Invent Math 150(2):409-439, 2002) multiplied by a local function. Using results of Boutillier and de Tilière (Prob Theor Rel Fields 147(3-4):379-413, 2010) and techniques of de Tilière (Prob Th Rel Fields 137(3-4):487-518, 2007) and Kenyon (Invent Math 150(2):409-439, 2002), this yields an explicit local formula for a natural Gibbs measure, and a local formula for the free energy. As a corollary, we recover Baxter's formula for the free energy of the critical Z-invariant Ising model (Baxter, in Exactly solved models in statistical mechanics, Academic Press, London, 1982), and thus a new proof of it. The latter is equal, up to a constant, to the logarithm of the normalized determinant of the Laplacian obtained in Kenyon (Invent Math 150(2):409-439, 2002).

Exotic Lifshitz transitions in topological materials

NASA Astrophysics Data System (ADS)

Volovik, G. E.

2018-01-01

Topological Lifshitz transitions involve many types of topological structures in momentum and frequency-momentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl points, etc., each of which has its own stability-supporting topological invariant ( N_1, N_2, N_3, {\\tilde N}_3, etc.). The topology of the shape of Fermi surfaces and Dirac lines and the interconnection of objects of different dimensionalities produce a variety of Lifshitz transition classes. Lifshitz transitions have important implications for many areas of physics. To give examples, transition-related singularities can increase the superconducting transition temperature; Lifshitz transitions are the possible origin of the small masses of elementary particles in our Universe, and a black hole horizon serves as the surface of the Lifshitz transition between vacua with type-I and type-II Weyl points.

Topological Qubits from Valence Bond Solids

NASA Astrophysics Data System (ADS)

Wang, Dong-Sheng; Affleck, Ian; Raussendorf, Robert

2018-05-01

Topological qubits based on S U (N )-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with twofold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical Z rotation by an angle 2 π /N , for any integer N >2 , is provided by a global twist operation, which is of a topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.

Flavor and topological current correlators in parity-invariant three-dimensional QED

NASA Astrophysics Data System (ADS)

Karthik, Nikhil; Narayanan, Rajamani

2017-09-01

We use lattice regularization to study the flow of the flavor-triplet fermion current central charge CJf from its free field value in the ultraviolet limit to its conformal value in the infrared limit of the parity-invariant three-dimensional QED with two flavors of two-component fermions. The dependence of CJf on the scale is weak with a tendency to be below the free field value at intermediate distances. Our numerical data suggest that the flavor-triplet fermion current and the topological current correlators become degenerate within numerical errors in the infrared limit, thereby supporting an enhanced O(4) symmetry predicted by strong self-duality. Further, we demonstrate that fermion dynamics is necessary for the scale-invariant behavior of parity-invariant three-dimensional QED by showing that the pure gauge theory with noncompact gauge action has a nonzero bilinear condensate.

Strain-induced topological magnon phase transitions: applications to kagome-lattice ferromagnets

NASA Astrophysics Data System (ADS)

Owerre, S. A.

2018-06-01

A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the index. This quantity distinguishes a nontrivial topological system from a trivial one. A topological phase transition may occur when there are two topologically distinct phases, and it is usually defined by a gap closing point where the topologically invariant quantity is ill-defined. In this paper, we show that the magnon bands in the strained (distorted) kagome-lattice ferromagnets realize an example of a topological magnon phase transition in the realistic parameter regime of the system. When spin–orbit coupling (SOC) is neglected (i.e. no Dzyaloshinskii–Moriya interaction), we show that all three magnon branches are dispersive with no flat band, and there exists a critical point where tilted Dirac and semi-Dirac point coexist in the magnon spectra. The critical point separates two gapless magnon phases as opposed to the usual phase transition. Upon the inclusion of SOC, we realize a topological magnon phase transition point at the critical strain , where D and J denote the perturbative SOC and the Heisenberg spin exchange interaction respectively. It separates two distinct topological magnon phases with different Chern numbers for and for . The associated anomalous thermal Hall conductivity develops an abrupt change at , due to the divergence of the Berry curvature in momentum space. The proposed topological magnon phase transition is experimentally feasible by applying external perturbations such as uniaxial strain or pressure.

Quantum phase transitions between a class of symmetry protected topological states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Jiang, Hong -Chen; Lu, Yuan -Ming

2015-04-30

The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, H d+1(G,U(1)), contains at least one Z 2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z 2n or Z groups can be induced on the boundary of a (d+1)-dimensional G x Z T 2-symmetric SPT by a Z T 2 symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realizedmore » in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less

Topological Triplon Modes and Bound States in a Shastry-Sutherland Magnet

NASA Astrophysics Data System (ADS)

McClarty, Paul; Kruger, Frank; Guidi, Tatiana; Parker, Stewart; Refson, Keith; Parker, Tony; Prabhakaran, Dharmalingam; Coldea, Radu

The twin discoveries of the quantum Hall effect, in the 1980's, and of topoogical band insulators, in the 2000's, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have taught us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side effects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has led to proposals of topological insulators in bosonic systems: in photonic crystals, in the vibrational modes of crystals, and in the excitations of ordered magnets. Using inelastic neutron scattering along with theoretical calculations we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu2(BO3)2 is a bosonic topological insulator with nonzero Chern number in the triplon bands and topologically protected chiral edge excitations.

Recent Progress in the Study of Topological Semimetals

NASA Astrophysics Data System (ADS)

Bernevig, Andrei; Weng, Hongming; Fang, Zhong; Dai, Xi

2018-04-01

The topological semimetal is a new, theoretically predicted and experimentally discovered, topological state of matter. In one of its several realizations, the topological semimetal hosts Weyl fermions, elusive particles predicted more than 85 years ago, sought after in high-energy experiments, but only recently found in a condensed-matter setting. In the present review, we catalogue the most recent progress in this fast-developing research field. We give special attention to topological invariants and the material realization of three different types of topological semimetal. We also discuss various photo emission, transport and optical experimental observables that characterize the appearance of topological semimetal phases.

Scalar neutrinos at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demir, Durmus A.; Frank, Mariana; Selbuz, Levent

2011-05-01

We study a softly broken supersymmetric model whose gauge symmetry is that of the standard model gauge group times an extra Abelian symmetry U(1){sup '}. We call this gauge-extended model the U(1){sup '} model, and we study a U(1){sup '} model with a secluded sector such that neutrinos acquire Dirac masses via higher-dimensional terms allowed by the U(1){sup '} invariance. In this model the {mu} term of the minimal supersymmetric model (MSSM) is dynamically induced by the vacuum expectation value of a singlet scalar. In addition, the model contains exotic particles necessary for anomaly cancellation, and extra singlet bosons formore » achieving correct Z{sup '}/Z mass hierarchy. The neutrinos are charged under U(1){sup '}, and thus, their production and decay channels differ from those in the MSSM in strength and topology. We implement the model into standard packages and perform a detailed analysis of sneutrino production and decay at the Large Hadron Collider, for various mass scenarios, concentrating on three types of signals: (1) 0l+MET, (2) 2l+MET, and (3) 4l+MET. We compare the results with those of the MSSM whenever possible, and analyze the standard model background for each signal. The sneutrino production and decays provide clear signatures enabling distinction of the U(1){sup '} model from the MSSM at the LHC.« less

The singularity structure of scale-invariant rank-2 Coulomb branches

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Long, Cody; Martone, Mario

2018-05-01

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 N=2 superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. A set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

Evolution of heliospheric magnetized configurations via topological invariants

NASA Astrophysics Data System (ADS)

Roth, Ilan

2013-07-01

The analogy between magnetohydrodynamics (MHD) and knot theory is utilized in presenting a new method for an analysis of stability and evolution of complex magnetic heliospheric flux tubes. Planar projection of a three-dimensional magnetic configuration depicts the structure as a two-dimensional diagram with crossings, to which one may assign mathematical operations leading to robust topological invariants. These invariants enrich the topological information of magnetic configurations beyond helicity. It is conjectured that the field which emerges from the solar photosphere is structured as one of the simplest knots-unknot or prime knot-and these flux ropes are then stretched while carried by the solar wind into the interplanetary medium. Preservation of invariants for small diffusivity and large cross section of the emerging magnetic flux makes them impervious to large scale reconnection, allowing us to predict the observed structures at 1 AU as elongated prime knots. Similar structures may be observed in magnetic clouds which got disconnected from their footpoints and in ion drop-out configurations from a compact flare source in solar impulsive solar events. Observation of small scale magnetic features consistent with prime knots may indicate spatial intermittency and non-Gaussian statistics in the turbulent cascade process. For flux tubes with higher resistivity, magnetic energy decay rate should decrease with increased knot complexity as the invariants are then harder to be violated. These observations could be confirmed if adjacent satellites happen to measure distinctly oriented magnetic fields with directionally varying suprathermal particle fluxes.

Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective

NASA Astrophysics Data System (ADS)

Xiong, Charles Zhaoxi; Alexandradinata, A.

2018-03-01

It is demonstrated that fermionic/bosonic symmetry-protected topological (SPT) phases across different dimensions and symmetry classes can be organized using geometric constructions that increase dimensions and symmetry-reduction maps that change symmetry groups. Specifically, it is shown that the interacting classifications of SPT phases with and without glide symmetry fit into a short exact sequence, so that the classification with glide is constrained to be a direct sum of cyclic groups of order 2 or 4. Applied to fermionic SPT phases in the Wigner-Dyson class AII, this implies that the complete interacting classification in the presence of glide is Z4⊕Z2⊕Z2 in three dimensions. In particular, the hourglass-fermion phase recently realized in the band insulator KHgSb must be robust to interactions. Generalizations to spatiotemporal glide symmetries are discussed.

Observation of dynamical vortices after quenches in a system with topology

NASA Astrophysics Data System (ADS)

Fläschner, N.; Vogel, D.; Tarnowski, M.; Rem, B. S.; Lühmann, D.-S.; Heyl, M.; Budich, J. C.; Mathey, L.; Sengstock, K.; Weitenberg, C.

2018-03-01

Topological phases constitute an exotic form of matter characterized by non-local properties rather than local order parameters1. The paradigmatic Haldane model on a hexagonal lattice features such topological phases distinguished by an integer topological invariant known as the first Chern number2. Recently, the identification of non-equilibrium signatures of topology in the dynamics of such systems has attracted particular attention3-6. Here, we experimentally study the dynamical evolution of the wavefunction using time- and momentum-resolved full state tomography for spin-polarized fermionic atoms in driven optical lattices7. We observe the appearance, movement and annihilation of dynamical vortices in momentum space after sudden quenches close to the topological phase transition. These dynamical vortices can be interpreted as dynamical Fisher zeros of the Loschmidt amplitude8, which signal a so-called dynamical phase transition9,10. Our results pave the way to a deeper understanding of the connection between topological phases and non-equilibrium dynamics.

Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains

NASA Astrophysics Data System (ADS)

Cao, Ting; Zhao, Fangzhou; Louie, Steven G.

2017-08-01

We show that semiconducting graphene nanoribbons (GNRs) of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for their topological invariants and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisting of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1 /2 chain with tunable exchange interaction. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.

Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains.

PubMed

Cao, Ting; Zhao, Fangzhou; Louie, Steven G

2017-08-18

We show that semiconducting graphene nanoribbons (GNRs) of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for their topological invariants and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisting of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1/2 chain with tunable exchange interaction. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.

Functionalized Thallium Antimony Films as Excellent Candidates for Large-Gap Quantum Spin Hall Insulator

PubMed Central

Zhang, Run-wu; Zhang, Chang-wen; Ji, Wei-xiao; Li, Sheng-shi; Yan, Shi-shen; Li, Ping; Wang, Pei-ji

2016-01-01

Group III-V films are of great importance for their potential application in spintronics and quantum computing. Search for two-dimensional III-V films with a nontrivial large-gap are quite crucial for the realization of dissipationless transport edge channels using quantum spin Hall (QSH) effects. Here we use first-principles calculations to predict a class of large-gap QSH insulators in functionalized TlSb monolayers (TlSbX2; (X = H, F, Cl, Br, I)), with sizable bulk gaps as large as 0.22 ~ 0.40 eV. The QSH state is identified by Z2 topological invariant together with helical edge states induced by spin-orbit coupling (SOC). Noticeably, the inverted band gap in the nontrivial states can be effectively tuned by the electric field and strain. Additionally, these films on BN substrate also maintain a nontrivial QSH state, which harbors a Dirac cone lying within the band gap. These findings may shed new light in future design and fabrication of QSH insulators based on two-dimensional honeycomb lattices in spintronics. PMID:26882865

Functionalized Thallium Antimony Films as Excellent Candidates for Large-Gap Quantum Spin Hall Insulator.

PubMed

Zhang, Run-wu; Zhang, Chang-wen; Ji, Wei-xiao; Li, Sheng-shi; Yan, Shi-shen; Li, Ping; Wang, Pei-ji

2016-02-17

Group III-V films are of great importance for their potential application in spintronics and quantum computing. Search for two-dimensional III-V films with a nontrivial large-gap are quite crucial for the realization of dissipationless transport edge channels using quantum spin Hall (QSH) effects. Here we use first-principles calculations to predict a class of large-gap QSH insulators in functionalized TlSb monolayers (TlSbX2; (X = H, F, Cl, Br, I)), with sizable bulk gaps as large as 0.22~0.40 eV. The QSH state is identified by Z2 topological invariant together with helical edge states induced by spin-orbit coupling (SOC). Noticeably, the inverted band gap in the nontrivial states can be effectively tuned by the electric field and strain. Additionally, these films on BN substrate also maintain a nontrivial QSH state, which harbors a Dirac cone lying within the band gap. These findings may shed new light in future design and fabrication of QSH insulators based on two-dimensional honeycomb lattices in spintronics.

Majorana fermion surface code for universal quantum computation

DOE PAGES

Vijay, Sagar; Hsieh, Timothy H.; Fu, Liang

2015-12-10

In this study, we introduce an exactly solvable model of interacting Majorana fermions realizing Z 2 topological order with a Z 2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physicalmore » ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.« less

Experimental evidence for s-wave pairing symmetry in superconducting Cu(x)Bi2Se3 single crystals using a scanning tunneling microscope.

PubMed

Levy, Niv; Zhang, Tong; Ha, Jeonghoon; Sharifi, Fred; Talin, A Alec; Kuk, Young; Stroscio, Joseph A

2013-03-15

Topological superconductors represent a newly predicted phase of matter that is topologically distinct from conventional superconducting condensates of Cooper pairs. As a manifestation of their topological character, topological superconductors support solid-state realizations of Majorana fermions at their boundaries. The recently discovered superconductor Cu(x)Bi(2)Se(3) has been theoretically proposed as an odd-parity superconductor in the time-reversal-invariant topological superconductor class, and point-contact spectroscopy measurements have reported the observation of zero-bias conductance peaks corresponding to Majorana states in this material. Here we report scanning tunneling microscopy measurements of the superconducting energy gap in Cu(x)Bi(2)Se(3) as a function of spatial position and applied magnetic field. The tunneling spectrum shows that the density of states at the Fermi level is fully gapped without any in-gap states. The spectrum is well described by the Bardeen-Cooper-Schrieffer theory with a momentum independent order parameter, which suggests that Cu(x)Bi(2)Se(3) is a classical s-wave superconductor contrary to previous expectations and measurements.

Study of anyon condensation and topological phase transitions from a Z4 topological phase using the projected entangled pair states approach

NASA Astrophysics Data System (ADS)

Iqbal, Mohsin; Duivenvoorden, Kasper; Schuch, Norbert

2018-05-01

We use projected entangled pair states (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement of anyons and serve as substitutes for conventional order parameters. We apply these order parameters, together with anyon-anyon correlation functions and some further probes, to characterize topological phases and phase transitions within a family of models based on a Z4 symmetry, which contains Z4 quantum double, toric code, double semion, and trivial phases. We find a diverse phase diagram which exhibits a variety of different phase transitions of both first and second order which we comprehensively characterize, including direct transitions between the toric code and the double semion phase.

Radical chiral Floquet phases in a periodically driven Kitaev model and beyond

NASA Astrophysics Data System (ADS)

Po, Hoi Chun; Fidkowski, Lukasz; Vishwanath, Ashvin; Potter, Andrew C.

2017-12-01

We theoretically discover a family of nonequilibrium fractional topological phases in which time-periodic driving of a 2D system produces excitations with fractional statistics, and produces chiral quantum channels that propagate a quantized fractional number of qubits along the sample edge during each driving period. These phases share some common features with fractional quantum Hall states, but are sharply distinct dynamical phenomena. Unlike the integer-valued invariant characterizing the equilibrium quantum Hall conductance, these phases are characterized by a dynamical topological invariant that is a square root of a rational number, inspiring the label: radical chiral Floquet phases. We construct solvable models of driven and interacting spin systems with these properties, and identify an unusual bulk-boundary correspondence between the chiral edge dynamics and bulk "anyon time-crystal" order characterized by dynamical transmutation of electric-charge into magnetic-flux excitations in the bulk.

Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo; Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso

2009-06-15

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter gravity action in four dimensions recovers the standard regularization given by the holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows one to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as T{sub j}{sup i}={+-}(l{sup 2}/8{pi}G)C{sub j}{sup i}, which has been observed in recent literature in solitonicmore » solutions and hydrodynamic models. A general procedure to generate the counterterm series for anti-de Sitter gravity in any even dimension from the corresponding Euler term is also briefly discussed.« less

Nobel Lecture: Topological quantum matter*

NASA Astrophysics Data System (ADS)

Haldane, F. Duncan M.

2017-10-01

Nobel Lecture, presented December 8, 2016, Aula Magna, Stockholm University. I will describe the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator or quantum anomalous Hall effect, and its role in the later discovery of time-reversal-invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. I will summarize how these early beginnings have led to the exciting, and currently extremely active, field of "topological matter."

Topological quantization in units of the fine structure constant.

PubMed

Maciejko, Joseph; Qi, Xiao-Liang; Drew, H Dennis; Zhang, Shou-Cheng

2010-10-15

Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant α=e²/ℏc. In this Letter, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other.

Strain-induced topological magnon phase transitions: applications to kagome-lattice ferromagnets.

PubMed

Owerre, S A

2018-06-20

A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the [Formula: see text] index. This quantity distinguishes a nontrivial topological system from a trivial one. A topological phase transition may occur when there are two topologically distinct phases, and it is usually defined by a gap closing point where the topologically invariant quantity is ill-defined. In this paper, we show that the magnon bands in the strained (distorted) kagome-lattice ferromagnets realize an example of a topological magnon phase transition in the realistic parameter regime of the system. When spin-orbit coupling (SOC) is neglected (i.e. no Dzyaloshinskii-Moriya interaction), we show that all three magnon branches are dispersive with no flat band, and there exists a critical point where tilted Dirac and semi-Dirac point coexist in the magnon spectra. The critical point separates two gapless magnon phases as opposed to the usual phase transition. Upon the inclusion of SOC, we realize a topological magnon phase transition point at the critical strain [Formula: see text], where D and J denote the perturbative SOC and the Heisenberg spin exchange interaction respectively. It separates two distinct topological magnon phases with different Chern numbers for [Formula: see text] and for [Formula: see text]. The associated anomalous thermal Hall conductivity develops an abrupt change at [Formula: see text], due to the divergence of the Berry curvature in momentum space. The proposed topological magnon phase transition is experimentally feasible by applying external perturbations such as uniaxial strain or pressure.

Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields

NASA Astrophysics Data System (ADS)

Zhu, Xiaoyu

2018-05-01

A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We investigate a time-reversal-invariant topological superconductor in two dimensions and demonstrate that an in-plane magnetic field could transform it into a second-order topological superconductor. A detailed analysis reveals that the magnetic field gives rise to mass terms which take distinct values among the edges, and Majorana corner states naturally emerge at the intersection of two adjacent edges with opposite masses. With the rotation of the magnetic field, Majorana corner states localized around the boundary may hop from one corner to a neighboring one and eventually make a full circle around the system when the field rotates by 2 π . In the end, we briefly discuss physical realizations of this system.

Scale invariance in natural and artificial collective systems: a review

PubMed Central

Huepe, Cristián

2017-01-01

Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynamics. We then provide examples of scale invariance from different domains in science, describe their origins and main features and discuss potential challenges and approaches for designing and engineering artificial systems with scale-invariant properties. PMID:29093130

Phase transition studies of Na3Bi system under uniaxial strain

NASA Astrophysics Data System (ADS)

Nie, Tiaoping; Meng, Lijun; Li, Yanru; Luan, Yanhua; Yu, Jun

2018-03-01

We investigated the electronic properties and phase transitions of Na3Bi in four structural phases (space groups P63/mmc, P \\overline{3} c1, Fm \\overline{3} m and Cmcm) under constant-volume uniaxial strain using the first-principles method. For P63/mmc and P \\overline{3} c1-Na3Bi, an important phase transition from a topological Dirac semimetal (TDS) to a topological insulator appears under compression strain around 4.5%. The insulating gap increases with the increasing compressive strain and up to around 0.1 eV at a strain of 10%. However, both P63/mmc and P \\overline{3} c1-Na3Bi still keep the properties of a TDS within a tensile strain of 0-10%, although the Dirac points move away from the Γ point along Γ-A in reciprocal space as the tensile strain increases. The Na3Bi with space group Fm \\overline{3} m is identified as a topological semimetal with the inverted bands between Na-3s and Bi-6p and a parabolic dispersion in the vicinity of Γ point. Interestingly, for Fm \\overline{3} m-Na3Bi, both compression and tensile strain lead to a TDS which is identified by calculating surface Fermi arcs and topological invariants at time-reversal planes (k z   =  0 and k z   =  π/c) in reciprocal space. Additionally, we confirmed the high pressure phase Cmcm-Na3Bi is an ordinary insulator with a gap of about 0.62 eV. It is noteworthy that its gap almost keeps constant around 0.60 eV within a compression strain of 0-10%. In contrast, a remarkable phase transition from an insulator to a metal phase appears under tensile strain. Moreover, this phase transition is highly sensitive to tensile strain and takes place only at a strain 1.0%. These strain-induced electronic structures and phase transitions of the Na3Bi system in various phases are important due to their possible applications under high pressure in future electronic devices.

Probing topological order with Rényi entropy

NASA Astrophysics Data System (ADS)

Halász, Gábor B.; Hamma, Alioscia

2012-12-01

We present an analytical study of the quantum phase transition between the topologically ordered toric-code-model ground state and the disordered spin-polarized state. The phase transition is induced by applying an external magnetic field, and the variation in topological order is detected via two nonlocal quantities: the Wilson loop and the topological Rényi entropy of order 2. By exploiting an equivalence with the transverse-field Ising model and considering two different variants of the problem, we investigate the field dependence of these quantities by means of an exact treatment in the exactly solvable variant and complementary perturbation theories around the limits of zero and infinite fields in both variants. We find strong evidence that the phase transition point between topological order and disorder is marked by a discontinuity in the topological Rényi entropy and that the two phases around the phase transition point are characterized by its different constant values. Our results therefore indicate that the topological Rényi entropy is a proper topological invariant: its allowed values are discrete and can be used to distinguish between different phases of matter.

Protected Pseudohelical Edge States in Z2-Trivial Proximitized Graphene

NASA Astrophysics Data System (ADS)

Frank, Tobias; Högl, Petra; Gmitra, Martin; Kochan, Denis; Fabian, Jaroslav

2018-04-01

We investigate topological properties of models that describe graphene on realistic substrates which induce proximity spin-orbit coupling in graphene. A Z2 phase diagram is calculated for the parameter space of (generally different) intrinsic spin-orbit coupling on the two graphene sublattices, in the presence of Rashba coupling. The most fascinating case is that of staggered intrinsic spin-orbit coupling which, despite being topologically trivial, Z2=0 , does exhibit edge states protected by time-reversal symmetry for zigzag ribbons as wide as micrometers. We call these states pseudohelical as their helicity is locked to the sublattice. The spin character and robustness of the pseudohelical modes is best exhibited on a finite flake, which shows that the edge states have zero g factor, carry a pure spin current in the cross section of the flake, and exhibit spin-flip reflectionless tunneling at the armchair edges.

Floquet topological phases in a spin-1 /2 double kicked rotor

NASA Astrophysics Data System (ADS)

Zhou, Longwen; Gong, Jiangbin

2018-06-01

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008), 10.1103/PhysRevA.77.031405] already suggested the importance of periodic driving to the generation of Floquet topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1 /2 degree of freedom. The latter has been experimentally engineered in a quantum kicked rotor recently by loading 87Rb condensates into a periodically pulsed optical lattice. Theoretically, we found that under the on-resonance condition, the spin-1 /2 double kicked rotor admits rich topological phases due to the interplay between its external and internal degrees of freedom. Each of these topological phases is characterized by a pair of winding numbers, whose combination predicts the number of topologically protected zero and π -quasienergy edge states in the system. Topological phases with arbitrarily large winding numbers can be easily found by tuning the kicking strength. We discuss an experimental proposal to realize this model in kicked 87Rb condensates, and suggest detecting its topological invariants by measuring the mean chiral displacement in momentum space.

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

Topological vortices in gauge models of graphene

NASA Astrophysics Data System (ADS)

Zhang, Xin-Hui; Li, Xueqin; Hao, Jin-Bo

2018-06-01

Graphene-like structure possessing the topological vortices and knots, and the magnetic flux of the vortices configuration quantized, are proposed in this paper. The topological charges of the vortices are characterized by Hopf indices and Brower degrees. The Abelian background field action (BF action) is a topological invariant for the knot family, which is just the total sum of all the self-linking numbers and all the linking numbers. Flux quantization opens the possibility of having Aharonov-Bohm-type effects in graphene without external electromagnetic field.

Quantum entanglement properties of geometrical and topological quantum gates

NASA Astrophysics Data System (ADS)

Sezer, Hasan Cavit; Duy, Hoang Ngoc; Heydari, Hoshang

2011-03-01

In this paper we will investigate the action of holonomic and topological quantum gates on different classes of four qubit states. In particular, we review the construction of holonomic quantum gate based on geometric phase and topological quantum gate based on braid group. Then, we investigate the entanglement properties of three different classes of four-qubit states based on geometric invariants. The result shows that entanglement properties of the two most generic classes of four-qubit states can be controlled by holonomic and topological quantum gate..

Hodge numbers for CICYs with symmetries of order divisible by 4

NASA Astrophysics Data System (ADS)

Candelas, Philip; Constantin, Andrei; Mishra, Challenger

2016-06-01

We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant K\\"ahler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, $G$, that arise in the classification are either $Z_2$ or contain $Z_4$, $Z_2 \\times Z_2$, $Z_3$ or $Z_5$ as a subgroup. The Hodge numbers for the quotients for which the group $G$ contains $Z_3$ or $Z_5$ have been computed previously. This paper deals with the remaining cases, for which $G \\supseteq Z_4$ or $G\\supseteq Z_2 \\times Z_2$. We also compute the Hodge numbers for 99 of the 166 CICY's which have $Z_2$ quotients.

Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2

NASA Astrophysics Data System (ADS)

Deng, Ke; Wan, Guoliang; Deng, Peng; Zhang, Kenan; Ding, Shijie; Wang, Eryin; Yan, Mingzhe; Huang, Huaqing; Zhang, Hongyun; Xu, Zhilin; Denlinger, Jonathan; Fedorov, Alexei; Yang, Haitao; Duan, Wenhui; Yao, Hong; Wu, Yang; Fan, Shoushan; Zhang, Haijun; Chen, Xi; Zhou, Shuyun

2016-12-01

Weyl semimetal is a new quantum state of matter hosting the condensed matter physics counterpart of the relativistic Weyl fermions originally introduced in high-energy physics. The Weyl semimetal phase realized in the TaAs class of materials features multiple Fermi arcs arising from topological surface states and exhibits novel quantum phenomena, such as a chiral anomaly-induced negative magnetoresistance and possibly emergent supersymmetry. Recently it was proposed theoretically that a new type (type-II) of Weyl fermion that arises due to the breaking of Lorentz invariance, which does not have a counterpart in high-energy physics, can emerge as topologically protected touching between electron and hole pockets. Here, we report direct experimental evidence of topological Fermi arcs in the predicted type-II Weyl semimetal MoTe2 (refs ,,). The topological surface states are confirmed by directly observing the surface states using bulk- and surface-sensitive angle-resolved photoemission spectroscopy, and the quasi-particle interference pattern between the putative topological Fermi arcs in scanning tunnelling microscopy. By establishing MoTe2 as an experimental realization of a type-II Weyl semimetal, our work opens up opportunities for probing the physical properties of this exciting new state.

Topological BF Theories

NASA Astrophysics Data System (ADS)

Sǎraru, Silviu-Constantin

Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.

Switching chiral solitons for algebraic operation of topological quaternary digits

NASA Astrophysics Data System (ADS)

Kim, Tae-Hwan; Cheon, Sangmo; Yeom, Han Woong

2017-02-01

Chiral objects can be found throughout nature; in condensed matter chiral objects are often excited states protected by a system's topology. The use of chiral topological excitations to carry information has been demonstrated, where the information is robust against external perturbations. For instance, reading, writing, and transfer of binary information have been demonstrated with chiral topological excitations in magnetic systems, skyrmions, for spintronic devices. The next step is logic or algebraic operations of such topological bits. Here, we show experimentally the switching between chiral topological excitations or chiral solitons of different chirality in a one-dimensional electronic system with Z4 topological symmetry. We found that a fast-moving achiral soliton merges with chiral solitons to switch their handedness. This can lead to the realization of algebraic operation of Z4 topological charges. Chiral solitons could be a platform for storage and operation of robust topological multi-digit information.

Relativized problems with abelian phase group in topological dynamics.

PubMed

McMahon, D

1976-04-01

Let (X, T) be the equicontinuous minimal transformation group with X = pi(infinity)Z(2), the Cantor group, and S = [unk](infinity)Z(2) endowed with the discrete topology acting on X by right multiplication. For any countable group T we construct a function F:X x S --> T such that if (Y, T) is a minimal transformation group, then (X x Y, S) is a minimal transformation group with the action defined by (x, y)s = [xs, yF(x, s)]. If (W, T) is a minimal transformation group and varphi:(Y, T) --> (W, T) is a homomorphism, then identity x varphi:(X x Y, S) --> (X x W, S) is a homomorphism and has many of the same properties that varphi has. For this reason, one may assume that the phase group is abelian (or S) without loss of generality for many relativized problems in topological dynamics.

Left-invariant Einstein metrics on S3 ×S3

NASA Astrophysics Data System (ADS)

Belgun, Florin; Cortés, Vicente; Haupt, Alexander S.; Lindemann, David

2018-06-01

The classification of homogeneous compact Einstein manifolds in dimension six is an open problem. We consider the remaining open case, namely left-invariant Einstein metrics g on G = SU(2) × SU(2) =S3 ×S3. Einstein metrics are critical points of the total scalar curvature functional for fixed volume. The scalar curvature S of a left-invariant metric g is constant and can be expressed as a rational function in the parameters determining the metric. The critical points of S, subject to the volume constraint, are given by the zero locus of a system of polynomials in the parameters. In general, however, the determination of the zero locus is apparently out of reach. Instead, we consider the case where the isotropy group K of g in the group of motions is non-trivial. When K ≇Z2 we prove that the Einstein metrics on G are given by (up to homothety) either the standard metric or the nearly Kähler metric, based on representation-theoretic arguments and computer algebra. For the remaining case K ≅Z2 we present partial results.

Theoretical crystal chemistry of M{sub x}(TO{sub 4}){sub y} sulfates and selenates: Topological analysis and classification of suprapolyhedral invariants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ilyushin, G. D.; Blatov, V. A.

2006-05-15

A geometric topological analysis of orthotetrahedral phases M{sub x}(TO{sub 4}){sub y} (T = S or Se) is performed for 46 sulfates and 17 selenates with the TOPOS 3.2 software package. The values of coordination sequences {l_brace}N{sub k}{r_brace} of T atoms are used as classification parameters of topologically different MTO nets. The crystal structures are analyzed within 12 coordination spheres of T sites and assigned to 26 topological types. It is established that only 7 types are common for the structures of sulfates and selenates, 16 types include only sulfates, and 3 types include only selenates. The average values of themore » bond lengths are determined: = 1.48(2) A and = 1.63(2) A. The hierarchical ordering of the crystal structure is performed using the concept of a polyhedral microensemble of the structure.« less

Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators.

PubMed

Mross, David F; Essin, Andrew; Alicea, Jason; Stern, Ady

2016-01-22

We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of weak topological insulator surfaces manifests itself in a nontrivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap Z_{4} parafermion zero modes.

Topological nanophononic states by band inversion

NASA Astrophysics Data System (ADS)

Esmann, Martin; Lamberti, Fabrice Roland; Senellart, Pascale; Favero, Ivan; Krebs, Olivier; Lanco, Loïc; Gomez Carbonell, Carmen; Lemaître, Aristide; Lanzillotti-Kimura, Norberto Daniel

2018-04-01

Nanophononics is essential for the engineering of thermal transport in nanostructured electronic devices, it greatly facilitates the manipulation of mechanical resonators in the quantum regime, and it could unveil a new route in quantum communications using phonons as carriers of information. Acoustic phonons also constitute a versatile platform for the study of fundamental wave dynamics, including Bloch oscillations, Wannier-Stark ladders, and other localization phenomena. Many of the phenomena studied in nanophononics were inspired by their counterparts in optics and electronics. In these fields, the consideration of topological invariants to control wave dynamics has already had a great impact for the generation of robust confined states. Interestingly, the use of topological phases to engineer nanophononic devices remains an unexplored and promising field. Conversely, the use of acoustic phonons could constitute a rich platform to study topological states. Here, we introduce the concept of topological invariants to nanophononics and experimentally implement a nanophononic system supporting a robust topological interface state at 350 GHz. The state is constructed through band inversion, i.e., by concatenating two semiconductor superlattices with inverted spatial mode symmetries. The existence of this state is purely determined by the Zak phases of the constituent superlattices, i.e., the one-dimensional Berry phase. We experimentally evidenced the mode through Raman spectroscopy. The reported robust topological interface states could become part of nanophononic devices requiring resonant structures such as sensors or phonon lasers.

A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grines, V Z; Pochinka, O V; Kapkaeva, S Kh

In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces. Bibliography: 25 titles.

A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases

DOE PAGES

Belopolski, Ilya; Xu, Su -Yang; Koirala, Nikesh; ...

2017-03-24

Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfacesmore » act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial phase in our superlattice band structure. We argue that the superlattice may be characterized in a significant way by a one-dimensional topological invariant, closely related to the invariant of the Su-Schrieffer-Heeger model. Our topological insulator heterostructure demonstrates a novel experimental platform where we can engineer band structures by directly controlling how electrons hop between lattice sites.« less

A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belopolski, Ilya; Xu, Su -Yang; Koirala, Nikesh

Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfacesmore » act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial phase in our superlattice band structure. We argue that the superlattice may be characterized in a significant way by a one-dimensional topological invariant, closely related to the invariant of the Su-Schrieffer-Heeger model. Our topological insulator heterostructure demonstrates a novel experimental platform where we can engineer band structures by directly controlling how electrons hop between lattice sites.« less

Robust Controller Design: A Bounded-Input-Bounded-Output Worst-Case Approach

DTIC Science & Technology

1992-03-01

show that 2 implies 1, suppose 1 does not hold, i.e., that p(M) > 1. The Perron - Frobenius theory for nonnegative matrices states that p(M) is itself an...Pz denote the positive cones inside X, Z consisting of elements with nonnegative pointwise components. Define the operator .4 : X -* Z, decomposed...topology.) The dual cone P! again consists of the nonnegative elements in Z*. The Lagrangian can be defined as L(x,z ’) {< x,c" > + < Ax - b,z

Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator

NASA Astrophysics Data System (ADS)

Wu, Liang; Salehi, M.; Koirala, N.; Moon, J.; Oh, S.; Armitage, N. P.

2016-12-01

Topological insulators have been proposed to be best characterized as bulk magnetoelectric materials that show response functions quantized in terms of fundamental physical constants. Here, we lower the chemical potential of three-dimensional (3D) Bi2Se3 films to ~30 meV above the Dirac point and probe their low-energy electrodynamic response in the presence of magnetic fields with high-precision time-domain terahertz polarimetry. For fields higher than 5 tesla, we observed quantized Faraday and Kerr rotations, whereas the dc transport is still semiclassical. A nontrivial Berry’s phase offset to these values gives evidence for axion electrodynamics and the topological magnetoelectric effect. The time structure used in these measurements allows a direct measure of the fine-structure constant based on a topological invariant of a solid-state system.

Fracton topological order from nearest-neighbor two-spin interactions and dualities

NASA Astrophysics Data System (ADS)

Slagle, Kevin; Kim, Yong Baek

2017-10-01

Fracton topological order describes a remarkable phase of matter, which can be characterized by fracton excitations with constrained dynamics and a ground-state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions, which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order [Vijay, Haah, and Fu, Phys. Rev. B 94, 235157 (2016), 10.1103/PhysRevB.94.235157] but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of six sites. The model is constructed from two orthogonal stacks of Z2 topologically ordered Kitaev honeycomb layers [Kitaev, Ann. Phys. 321, 2 (2006), 10.1016/j.aop.2005.10.005], which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D Z2 topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first-order transitions.

Visualizing the Topologically Induced States of Strongly Correlated Electrons in SmB6

NASA Astrophysics Data System (ADS)

Pirie, Harris; Hoffman, Jennifer E.; He, Yang; Yee, Michael M.; Soumyanarayanan, Anjan; Kim, Dae-Jeong; Fisk, Zachary; Morr, Dirk; Hamidian, Mohammad

The synergy between strong correlations and a topological invariant is predicted to generate exotic topological order, fractional quasiparticles and new platforms for quantum computation. SmB6 is a promising candidate in which interactions generate an insulating state whose gap arises from heavy fermion hybridization of low lying f-states with a Fermi sea. We used spectroscopic imaging scanning tunneling microscopy to visualize the hybridization of distinct crystal-field-split f-levels and the temperature-dependent evolution of an insulating gap spanning the chemical potential. Here, armed with a clear description of the bulk bands, we look within the insulating gap and directly image two dispersing surface states converging to a Dirac point close to the chemical potential. We show that these measurements are consistent with Dirac cones centered at the X and Γ points in the surface Brillouin zone corresponding to a strong topological invariant. The observation of topological states induced from strong correlations establishes SmB6 as an exciting playground for exotic physics. This work was supported by the Moore foundation, Canada Excellence Research Chair Program and the US National Science Foundation under the Grant DMR-1401480.

Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in R+4

NASA Astrophysics Data System (ADS)

Llibre, Jaume; Xiao, Dongmei

2017-02-01

In this paper we first give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in R+4 are Hamiltonian systems. Then we study the integrability of these Hamiltonian systems in the Liouville sense. Finally, we investigate the global dynamics of the completely integrable Lotka-Volterra Hamiltonian systems in R+4. As an application of the invariant subsets of these systems, we obtain topological classifications of the 3-submanifolds in R+4 defined by the hypersurfaces axy + bzw + cx2 y + dxy2 + ez2 w + fzw2 = h, where a , b , c , d , e , f , w and h are real constants.

Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

Exploring 4D quantum Hall physics with a 2D topological charge pump

NASA Astrophysics Data System (ADS)

Lohse, Michael; Schweizer, Christian; Price, Hannah M.; Zilberberg, Oded; Bloch, Immanuel

2018-01-01

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Gravity Duals of Lifshitz-Like Fixed Points

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC; Liu, Xiao

2008-11-05

We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t {yields} {lambda}{sup z}t, x {yields} {lambda}x; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arisemore » at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.« less

Topology mapping to characterize cyanobacterial bicarbonate transporters: BicA (SulP/SLC26 family) and SbtA.

PubMed

Price, G Dean; Howitt, Susan M

2014-09-01

This mini-review addresses advances in understanding the transmembrane topologies of two unrelated, single-subunit bicarbonate transporters from cyanobacteria, namely BicA and SbtA. BicA is a Na(+)-dependent bicarbonate transporter that belongs to the SulP/SLC26 family that is widespread in both eukaryotes and prokaryotes. Topology mapping of BicA via the phoA/lacZ fusion reporter method identified 12 transmembrane helices with an unresolved hydrophobic region just beyond helix 8. Re-interpreting this data in the light of a recent topology study on rat prestin leads to a consensus topology of 14 transmembrane domains with a 7+7 inverted repeat structure. SbtA is also a Na(+)-dependent bicarbonate transporter, but of considerably higher affinity (Km 2-5 μM versus >100 μM for BicA). Whilst SbtA is widespread in cyanobacteria and a few bacteria, it appears to be absent from eukaryotes. Topology mapping of SbtA via the phoA/lacZ fusion reporter method identified 10 transmembrane helices. The topology consists of a 5+5 inverted repeat, with the two repeats separated by a large intracellular loop. The unusual location of the N and C-termini outside the cell raises the possibility that SbtA forms a novel fold, not so far identified by structural and topological studies on transport proteins.

Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids

NASA Astrophysics Data System (ADS)

Sonnenschein, Jonas; Reuther, Johannes

2017-12-01

Spin liquids are exotic quantum states characterized by the existence of fractional and deconfined quasiparticle excitations, referred to as spinons and visons. Their fractional nature establishes topological properties such as a protected ground-state degeneracy. This work investigates spin-orbit coupled spin liquids where, additionally, topology enters via nontrivial band structures of the spinons. We revisit the Z2 spin-liquid phases that have recently been identified in a projective symmetry-group analysis on the square lattice when spin-rotation symmetry is maximally lifted [J. Reuther et al., Phys. Rev. B 90, 174417 (2014), 10.1103/PhysRevB.90.174417]. We find that in the case of nearest-neighbor couplings only, Z2 spin liquids on the square lattice always exhibit trivial spinon bands. Adding second-neighbor terms, the simplest projective symmetry-group solution closely resembles the Bernevig-Hughes-Zhang model for topological insulators. Assuming that the emergent gauge fields are static, we investigate vison excitations, which we confirm to be deconfined in all investigated spin phases. Particularly, if the spinon bands are topological, the spinons and visons form bound states consisting of several spinon-Majorana zero modes coupling to one vison. The existence of such zero modes follows from an exact mapping between these spin phases and topological p +i p superconductors with vortices. We propose experimental probes to detect such states in real materials.

How the axial anomaly controls flavor mixing among mesons

NASA Astrophysics Data System (ADS)

Giacosa, Francesco; Koenigstein, Adrian; Pisarski, Robert D.

2018-05-01

It is well known that, because of the axial anomaly in QCD, mesons with JP=0- are close to S U (3 )V eigenstates; the η'(958 ) meson is largely a singlet, and the η meson an octet. In contrast, states with JP=1- are flavor diagonal; e.g., the ϕ (1020 ) is almost pure s ¯s . Using effective Lagrangians, we show how this generalizes to states with higher spin, assuming that they can be classified according to the unbroken chiral symmetry of Gfl=S U (3 )L×S U (3 )R. We construct effective Lagrangians from terms invariant under Gfl and introduce the concept of hetero- and homochiral multiplets. Because of the axial anomaly, only terms invariant under the Z (3 )A subgroup of the axial U (1 )A enter. For heterochiral multiplets, which begin with that including the η and η'(958 ), there are Z (3 )A invariant terms with low mass dimension which cause states to mix according to S U (3 )V flavor. For homochiral multiplets, which begin with that including the ϕ (1020 ), there are no Z (3 )A invariant terms with low mass dimension, and so states are diagonal in flavor. In this way, we predict the flavor mixing for the heterochiral multiplet with spin 1 as well as for hetero- and homochiral multiplets with spin 2 and spin 3.

(3+1)-Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

NASA Astrophysics Data System (ADS)

Kumar, R.; Mukhopadhyay, Debmalya

2018-06-01

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations corresponding to the combined "scalar" and "vector" gauge symmetry transformations for the (3+1)-dimensional (4D) topologically massive non-Abelian (B \\wedge F) theory with the help of geometrical superfield formalism. For this purpose, we use three horizontality conditions (HCs). The first HC produces the (anti-)BRST transformations for the 1-form gauge field and corresponding (anti-)ghost fields whereas the second HC yields the (anti-)BRST transformations for 2-form field and associated (anti-)ghost fields. The integrability of second HC produces third HC. The latter HC produces the (anti-)BRST symmetry transformations for the compensating auxiliary vector field and corresponding ghosts. We obtain five (anti-)BRST invariant Curci-Ferrari (CF)-type conditions which emerge very naturally as the off-shoots of superfield formalism. Out of five CF-type conditions, two are fermionic in nature. These CF-type conditions play a decisive role in providing the absolute anticommutativity of the (anti-)BRST transformations and also responsible for the derivation of coupled but equivalent (anti-)BRST invariant Lagrangian densities. Furthermore, we capture the (anti-)BRST invariance of the coupled Lagrangian densities in terms of the superfields and translation generators along the Grassmannian directions θ and \\bar{θ }.

Engineering one-dimensional topological phases on p -wave superconductors

NASA Astrophysics Data System (ADS)

Sahlberg, Isac; Westström, Alex; Pöyhönen, Kim; Ojanen, Teemu

2017-05-01

In this paper, we study how, with the aid of impurity engineering, two-dimensional p -wave superconductors can be employed as a platform for one-dimensional topological phases. We discover that, while chiral and helical parent states themselves are topologically nontrivial, a chain of scalar impurities on both systems supports multiple topological phases and Majorana end states. We develop an approach which allows us to extract the topological invariants and subgap spectrum, even away from the center of the gap, for the representative cases of spinless, chiral, and helical superconductors. We find that the magnitude of the topological gaps protecting the nontrivial phases may be a significant fraction of the gap of the underlying superconductor.

Disorder-induced topological phase transitions in two-dimensional spin-orbit coupled superconductors

PubMed Central

Qin, Wei; Xiao, Di; Chang, Kai; Shen, Shun-Qing; Zhang, Zhenyu

2016-01-01

Normal superconductors with Rashba spin-orbit coupling have been explored as candidate systems of topological superconductors. Here we present a comparative theoretical study of the effects of different types of disorder on the topological phases of two-dimensional Rashba spin-orbit coupled superconductors. First, we show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorder, which close and reopen the quasiparticle gap of the paired electrons in a nontrivial manner. Secondly, the superconducting nature of a topological superconductor is found to be robust against Anderson disorder, but the topological nature is not, converting the system into a topologically trivial state even in the weak scattering limit. These topological phase transitions are distinctly characterized by variations in the topological invariant. We discuss the central findings in connection with existing experiments, and provide new schemes towards eventual realization of topological superconductors. PMID:27991541

Disorder-induced topological phase transitions in two-dimensional spin-orbit coupled superconductors

NASA Astrophysics Data System (ADS)

Qin, Wei; Xiao, Di; Chang, Kai; Shen, Shun-Qing; Zhang, Zhenyu

2016-12-01

Normal superconductors with Rashba spin-orbit coupling have been explored as candidate systems of topological superconductors. Here we present a comparative theoretical study of the effects of different types of disorder on the topological phases of two-dimensional Rashba spin-orbit coupled superconductors. First, we show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorder, which close and reopen the quasiparticle gap of the paired electrons in a nontrivial manner. Secondly, the superconducting nature of a topological superconductor is found to be robust against Anderson disorder, but the topological nature is not, converting the system into a topologically trivial state even in the weak scattering limit. These topological phase transitions are distinctly characterized by variations in the topological invariant. We discuss the central findings in connection with existing experiments, and provide new schemes towards eventual realization of topological superconductors.

Non-renormalization for non-supersymmetric black holes

DOE PAGES

Charles, Anthony M.; Larsen, Finn; Mayerson, Daniel R.

2017-08-11

We analyze large logarithmic corrections to 4D black hole entropy and relate them to the Weyl anomaly. We use duality to show that counter-terms in EinsteinMaxwell theory can be expressed in terms of geometry alone, with no dependence on matter terms. We analyze the two known N = 2 supersymmetric invariants for various non-supersymmetric black holes and find that both reduce to the Euler invariant. The c-anomaly therefore vanishes in these theories and the coefficient of the large logarithms becomes topological. It is therefore independent of continuous black hole parameters, such as the mass, even far from extremality.

Non-renormalization for non-supersymmetric black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Charles, Anthony M.; Larsen, Finn; Mayerson, Daniel R.

We analyze large logarithmic corrections to 4D black hole entropy and relate them to the Weyl anomaly. We use duality to show that counter-terms in EinsteinMaxwell theory can be expressed in terms of geometry alone, with no dependence on matter terms. We analyze the two known N = 2 supersymmetric invariants for various non-supersymmetric black holes and find that both reduce to the Euler invariant. The c-anomaly therefore vanishes in these theories and the coefficient of the large logarithms becomes topological. It is therefore independent of continuous black hole parameters, such as the mass, even far from extremality.

Nonlinear Dirac cones

NASA Astrophysics Data System (ADS)

Bomantara, Raditya Weda; Zhao, Wenlei; Zhou, Longwen; Gong, Jiangbin

2017-09-01

Physics arising from two-dimensional (2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such 2D Dirac cones are often characterized by a π Berry phase and are destroyed by a perturbative mass term. By considering mean-field nonlinearity in a minimal two-band Chern insulator model, we obtain a different type of Dirac cone that is robust to local perturbations without symmetry restrictions. Due to a different pseudospin texture, the Berry phase of the Dirac cone is no longer quantized in π , and can be continuously tuned as an order parameter. Furthermore, in an Aharonov-Bohm (AB) interference setup to detect such Dirac cones, the adiabatic AB phase is found to be π both theoretically and computationally, offering an observable topological invariant and a fascinating example where the Berry phase and AB phase are fundamentally different. We hence discover a nonlinearity-induced quantum phase transition from a known topological insulating phase to an unusual gapless topological phase.

Observation of scale invariance and conformal symmetry breaking in expanding Fermi gases

NASA Astrophysics Data System (ADS)

Elliott, Ethan; Joseph, James; Thomas, John

2014-05-01

We precisely test scale invariance and examine local thermal equilibrium in the hydrodynamic expansion of a Fermi gas of atoms as a function of interaction strength. After release from an anisotropic optical trap, we observe that a resonantly interacting gas obeys scale-invariant hydrodynamics, where the mean square cloud size = expands ballistically (like a noninteracting gas) and the energy-averaged bulk viscosity is consistent with zero, 0 . 00 (0 . 04) ℏ n , with n the density. In contrast, the aspect ratios of the cloud exhibit anisotropic ``elliptic'' flow with an energy-dependent shear viscosity. Tuning away from resonance, we observe conformal symmetry breaking, where deviates from ballistic flow. NSF, DOE, ARO, AFO.

Non-Abelian S =1 chiral spin liquid on the kagome lattice

NASA Astrophysics Data System (ADS)

Liu, Zheng-Xin; Tu, Hong-Hao; Wu, Ying-Hai; He, Rong-Qiang; Liu, Xiong-Jun; Zhou, Yi; Ng, Tai-Kai

2018-05-01

We study S =1 spin liquid states on the kagome lattice constructed by Gutzwiller-projected px+i py superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices S and T , we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the S O (3) 1 (or, equivalently, S U (2) 2 ) field-theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study, we observe a topological phase transition from the NACSL to the Z2 Abelian spin liquid.

The mass-metallicity and fundamental metallicity relations at z > 2 using very large telescope and Subaru near-infrared spectroscopy of zCOSMOS galaxies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maier, C.; Ziegler, B. L.; Lilly, S. J.

2014-09-01

In the local universe, there is good evidence that, at a given stellar mass M, the gas-phase metallicity Z is anti-correlated with the star formation rate (SFR) of the galaxies. It has also been claimed that the resulting Z(M, SFR) relation is invariant with redshift—the so-called 'fundamental metallicity relation' (FMR). Given a number of difficulties in determining metallicities, especially at higher redshifts, the form of the Z(M, SFR) relation and whether it is really independent of redshift is still very controversial. To explore this issue at z > 2, we used VLT-SINFONI and Subaru-MOIRCS near-infrared spectroscopy of 20 zCOSMOS-deep galaxiesmore » at 2.1 < z < 2.5 to measure the strengths of up to five emission lines: [O II] λ3727, Hβ, [O III] λ5007, Hα, and [N II] λ6584. This near-infrared spectroscopy enables us to derive O/H metallicities, and also SFRs from extinction corrected Hα measurements. We find that the mass-metallicity relation (MZR) of these star-forming galaxies at z ≈ 2.3 is lower than the local Sloan Digital Sky Survey (SDSS) MZR by a factor of three to five, a larger change than found by Erb et al. using [N II]/Hα-based metallicities from stacked spectra. We discuss how the different selections of the samples and metallicity calibrations used may be responsible for this discrepancy. The galaxies show direct evidence that the SFR is still a second parameter in the MZR at these redshifts. However, determining whether the Z(M, SFR) relation is invariant with epoch depends on the choice of extrapolation used from local samples, because z > 2 galaxies of a given mass have much higher SFRs than the local SDSS galaxies. We find that the zCOSMOS galaxies are consistent with a non-evolving FMR if we use the physically motivated formulation of the Z(M, SFR) relation from Lilly et al., but not if we use the empirical formulation of Mannucci et al.« less

Nonreciprocal lasing in topological cavities of arbitrary geometries

NASA Astrophysics Data System (ADS)

Bahari, Babak; Ndao, Abdoulaye; Vallini, Felipe; El Amili, Abdelkrim; Fainman, Yeshaiahu; Kanté, Boubacar

2017-11-01

Resonant cavities are essential building blocks governing many wave-based phenomena, but their geometry and reciprocity fundamentally limit the integration of optical devices. We report, at telecommunication wavelengths, geometry-independent and integrated nonreciprocal topological cavities that couple stimulated emission from one-way photonic edge states to a selected waveguide output with an isolation ratio in excess of 10 decibels. Nonreciprocity originates from unidirectional edge states at the boundary between photonic structures with distinct topological invariants. Our experimental demonstration of lasing from topological cavities provides the opportunity to develop complex topological circuitry of arbitrary geometries for the integrated and robust generation and transport of photons in classical and quantum regimes.

Coherent Structure Detection using Persistent Homology and other Topological Tools

NASA Astrophysics Data System (ADS)

Smith, Spencer; Roberts, Eric; Sindi, Suzanne; Mitchell, Kevin

2017-11-01

For non-autonomous, aperiodic fluid flows, coherent structures help organize the dynamics, much as invariant manifolds and periodic orbits do for autonomous or periodic systems. The prevalence of such flows in nature and industry has motivated many successful techniques for defining and detecting coherent structures. However, often these approaches require very fine trajectory data to reconstruct velocity fields and compute Cauchy-Green-tensor-related quantities. We use topological techniques to help detect coherent trajectory sets in relatively sparse 2D advection problems. More specifically, we have developed a homotopy-based algorithm, the ensemble-based topological entropy calculation (E-tec), which assigns to each edge in an initial triangulation of advected points a topologically forced lower bound on its future stretching rate. The triangulation and its weighted edges allow us to analyze flows using persistent homology. This topological data analysis tool detects clusters and loops in the triangulation that are robust in the presence of noise and in this case correspond to coherent trajectory sets.

Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides

NASA Astrophysics Data System (ADS)

Liu, Ting-Wei; Semperlotti, Fabio

2018-01-01

We investigate the occurrence of acoustic topological edge states in a 2D phononic elastic waveguide due to a phenomenon that is the acoustic analog of the quantum valley Hall effect. We show that a topological transition takes place between two lattices having broken space-inversion symmetry due to the application of a tunable strain field. This condition leads to the formation of gapless edge states at the domain walls, as further illustrated by the analysis of the bulk-edge correspondence and of the associated topological invariants. Interestingly, topological edge states can also be triggered at the boundary of a single domain, when boundary conditions are properly selected. We also show that the static modulation of the strain field allows us to tune the response of the material between the different supported edge states. Although time-reversal symmetry is still intact in this material system, the edge states are topologically protected when intervalley mixing is either weak or negligible. This characteristic enables selective valley injection, which is achieved via synchronized source strategy.

Quasi-topological Ricci polynomial gravities

NASA Astrophysics Data System (ADS)

Li, Yue-Zhou; Liu, Hai-Shan; Lü, H.

2018-02-01

Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasitopological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.

Topological transport in Dirac nodal-line semimetals

NASA Astrophysics Data System (ADS)

Rui, W. B.; Zhao, Y. X.; Schnyder, Andreas P.

2018-04-01

Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion P and time-reversal T . The stability of these Dirac rings is guaranteed by a quantized ±π Berry phase and their low-energy physics is described by a one-parameter family of (2+1)-dimensional quantum field theories exhibiting the parity anomaly. Here we study the Berry-phase supported topological transport of P T -invariant nodal-line semimetals. We find that small inversion breaking allows for an electric-field-induced anomalous transverse current, whose universal component originates from the parity anomaly. Due to this Hall-like current, carriers at opposite sides of the Dirac nodal ring flow to opposite surfaces when an electric field is applied. To detect the topological currents, we propose a dumbbell device, which uses surface states to filter charges based on their momenta. Suggestions for experiments and device applications are discussed.

Localization Protection and Symmetry Breaking in One-dimensional Potts Chains

NASA Astrophysics Data System (ADS)

Friedman, Aaron; Vasseur, Romain; Potter, Andrew; Parameswaran, Siddharth

Recent work on the 3-state Potts and Z3 clock models has demonstrated that their ordered phases are connected by duality to a phase that hosts topologically protected parafermionic zero modes at the system's boundary. The analogy with Kitaev's example of the one-dimensional Majorana chain (similarly related by duality to the Ising model) suggests that such zero modes may also be stabilized in highly excited states by many-body localization (MBL). However, the Potts model has a non-Abelian S3 symmetry believed to be incompatible with MBL; hence any MBL state must spontaneously break this symmetry, either completely or into one of its abelian subgroups (Z2 or Z3), with the topological phase corresponding to broken Z3 symmetry. We therefore study the excited state phase structure of random three-state Potts and clock models in one dimension using exact diagonalization and real-space renormalization group techniques. We also investigate the interesting possibility of a direct excited-state transition between MBL phases that break either Z3 or Z2 symmetry, forbidden within Landau theory. NSF DGE-1321846 (AJF), NSF DMR-1455366 and President's Research Catalyst Award No. CA-15-327861 from the University of California Office of the President (SAP), LDRD Program of LBNL (RV), NSF PHY11-25915 at the KITP (AJF, RV, SAP).

Noether symmetries in Gauss-Bonnet-teleparallel cosmology.

PubMed

Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F

2016-01-01

A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.

Variational Method in the Statistical Theory of Turbulence

DTIC Science & Technology

1991-01-01

3.1.4) where 6 and c are the Kronecker and Levi - Civita tensors, respectively. Th u AB AB functions Z1, Z 2 and Z3 are invariant under rotations around...flow profide and certain two point correlation functions of a cylindrically syrametric free jet were carried out using the Rayleigh-Ritz method. A...reasonable agreement with experimental data. 14. SUBJECT TERMS 15. NUMBER OF PAGES 33 Two Phase Flow, Turbulence, Statistical Turbulence 16. PRICE CODE 17

Mathematics of Periodic Tables for Benzenoid Hydrocarbons.

PubMed

Dias, Jerry Ray

2007-01-01

The upper and lower bounds for invariants of polyhex systems based on the Harary and Harborth inequalities are studied. It is shown that these invariants are uniquely correlated by the Periodic Table for Benzenoid Hydrocarbons. A modified periodic table for total resonant sextet (TRS) benzenoids based on the invariants of Ds and r(empty) is presented; Ds is the number of disconnections among the empty rings for fused TRS benzenoid hydrocarbons. This work represents a contribution toward deciphering the topological information content of benzenoid formulas.

Domain topology and domain switching kinetics in a hybrid improper ferroelectric

PubMed Central

Huang, F. -T.; Xue, F.; Gao, B.; Wang, L. H.; Luo, X.; Cai, W.; Lu, X. -Z.; Rondinelli, J. M.; Chen, L. Q.; Cheong, S. -W.

2016-01-01

Charged polar interfaces such as charged ferroelectric walls or heterostructured interfaces of ZnO/(Zn,Mg)O and LaAlO3/SrTiO3, across which the normal component of electric polarization changes suddenly, can host large two-dimensional conduction. Charged ferroelectric walls, which are energetically unfavourable in general, were found to be mysteriously abundant in hybrid improper ferroelectric (Ca,Sr)3Ti2O7 crystals. From the exploration of antiphase boundaries in bilayer-perovskites, here we discover that each of four polarization-direction states is degenerate with two antiphase domains, and these eight structural variants form a Z4 × Z2 domain structure with Z3 vortices and five distinct types of domain walls, whose topology is directly relevant to the presence of abundant charged walls. We also discover a zipper-like nature of antiphase boundaries, which are the reversible creation/annihilation centres of pairs of two types of ferroelectric walls (and also Z3-vortex pairs) in 90° and 180° polarization switching. Our results demonstrate the unexpectedly rich nature of hybrid improper ferroelectricity. PMID:27215944

Elliptic CY3folds and non-perturbative modular transformation

NASA Astrophysics Data System (ADS)

Iqbal, Amer; Shabbir, Khurram

2016-03-01

We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections.

Accuracy of topological entanglement entropy on finite cylinders.

PubMed

Jiang, Hong-Chen; Singh, Rajiv R P; Balents, Leon

2013-09-06

Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.

The species-area relationship, self-similarity, and the true meaning of the z-value.

PubMed

Tjørve, Even; Tjørve, Kathleen M Calf

2008-12-01

The power model, S= cA(z) (where S is number of species, A is area, and c and z are fitted constants), is the model most commonly fitted to species-area data assessing species diversity. We use the self-similarity properties of this model to reveal patterns implicated by the z parameter. We present the basic arithmetic leading both to the fraction of new species added when two areas are combined and to species overlap between two areas of the same size, given a continuous sampling scheme. The fraction of new species resulting from expansion of an area can be expressed as alpha(z)-1, where alpha is the expansion factor. Consequently, z-values can be converted to a scale-invariant species overlap between two equally sized areas, since the proportion of species in common between the two areas is 2-2(z). Calculating overlap when adding areas of the same size reveals the intrinsic effect of distance assumed by the bisectional scheme. We use overlap area relationships from empirical data sets to illustrate how answers to the single large or several small reserves (SLOSS) question vary between data sets and with scale. We conclude that species overlap and the effect of distance between sample areas or isolates should be addressed when discussing species area relationships, and lack of fit to the power model can be caused by its assumption of a scale-invariant overlap relationship.

Heat kernel and Weyl anomaly of Schrödinger invariant theory

NASA Astrophysics Data System (ADS)

Pal, Sridip; Grinstein, Benjamín

2017-12-01

We propose a method inspired by discrete light cone quantization to determine the heat kernel for a Schrödinger field theory (Galilean boost invariant with z =2 anisotropic scaling symmetry) living in d +1 dimensions, coupled to a curved Newton-Cartan background, starting from a heat kernel of a relativistic conformal field theory (z =1 ) living in d +2 dimensions. We use this method to show that the Schrödinger field theory of a complex scalar field cannot have any Weyl anomalies. To be precise, we show that the Weyl anomaly Ad+1 G for Schrödinger theory is related to the Weyl anomaly of a free relativistic scalar CFT Ad+2 R via Ad+1 G=2 π δ (m )Ad+2 R , where m is the charge of the scalar field under particle number symmetry. We provide further evidence of the vanishing anomaly by evaluating Feynman diagrams in all orders of perturbation theory. We present an explicit calculation of the anomaly using a regulated Schrödinger operator, without using the null cone reduction technique. We generalize our method to show that a similar result holds for theories with a single time-derivative and with even z >2 .

Lattice-matched heterojunctions between topological and normal insulators: A first-principles study

NASA Astrophysics Data System (ADS)

Lee, Hyungjun; Yazyev, Oleg V.

2017-02-01

Gapless boundary modes at the interface between topologically distinct regions are one of the most salient manifestations of topology in physics. Metallic boundary states of time-reversal-invariant topological insulators (TIs), a realization of topological order in condensed matter, have been of much interest not only due to such a fundamental nature, but also due to their practical significance. These boundary states are immune to backscattering and localization owing to their topological origin, thereby opening up the possibility to tailor them for potential uses in spintronics and quantum computing. The heterojunction between a TI and a normal insulator (NI) is a representative playground for exploring such a topologically protected metallic boundary state and expected to constitute a building block for future electronic and spintronic solid-state devices based on TIs. Here, we report a first-principles study of two experimentally realized lattice-matched heterojunctions between TIs and NIs, Bi2Se3 (0001)/InP(111) and Bi2Te3 (0001)/BaF2(111). We evaluate the band offsets at these interfaces from many-body perturbation theory within the G W approximation as well as density-functional theory. Furthermore, we investigate the topological interface states, demonstrating that at these lattice-matched heterointerfaces, they are strictly localized and their helical spin textures are as well preserved as those at the vacuum-facing surfaces. These results taken together may help in designing devices relying on spin-helical metallic boundary states of TIs.

NOTE: Circular symmetry in topologically massive gravity

NASA Astrophysics Data System (ADS)

Deser, S.; Franklin, J.

2010-05-01

We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.

Robustness and percolation of holes in complex networks

NASA Astrophysics Data System (ADS)

Zhou, Andu; Maletić, Slobodan; Zhao, Yi

2018-07-01

Efficient robustness and fault tolerance of complex network is significantly influenced by its connectivity, commonly modeled by the structure of pairwise relations between network elements, i.e., nodes. Nevertheless, aggregations of nodes build higher-order structures embedded in complex network, which may be more vulnerable when the fraction of nodes is removed. The structure of higher-order aggregations of nodes can be naturally modeled by simplicial complexes, whereas the removal of nodes affects the values of topological invariants, like the number of higher-dimensional holes quantified with Betti numbers. Following the methodology of percolation theory, as the fraction of nodes is removed, new holes appear, which have the role of merger between already present holes. In the present article, relationship between the robustness and homological properties of complex network is studied, through relating the graph-theoretical signatures of robustness and the quantities derived from topological invariants. The simulation results of random failures and intentional attacks on networks suggest that the changes of graph-theoretical signatures of robustness are followed by differences in the distribution of number of holes per cluster under different attack strategies. In the broader sense, the results indicate the importance of topological invariants research for obtaining further insights in understanding dynamics taking place over complex networks.

Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group

NASA Astrophysics Data System (ADS)

Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.

2016-11-01

We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.

Duality and topology

NASA Astrophysics Data System (ADS)

Sacramento, P. D.; Vieira, V. R.

2018-04-01

Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.

Wideband FM Demodulation and Multirate Frequency Transformations

DTIC Science & Technology

2016-12-15

FM signals. 2.2.1 Adaptive Linear Predictive IF Tracking For a pure FM signal, the IF demodulation approach employing adaptive filters was proposed...desired signal. As summarized in [5], the prediction error filter is given by: E (z) = 1− L∑ l=1 goptl z −l, (8) 2 Approved for public release...assumption and the further assumption that the message signal remains es- sentially invariant over the sampling range of the linear prediction filter , we end

Chiral topological insulator of magnons

NASA Astrophysics Data System (ADS)

Li, Bo; Kovalev, Alexey A.

2018-05-01

We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to opening of the gap. Finally, we show that by changing certain parameters, the system can be tuned between the chiral topological insulator, three-dimensional magnon anomalous Hall, and Weyl magnon phases.

Mass-deformed ABJM and black holes in AdS4

NASA Astrophysics Data System (ADS)

Bobev, Nikolay; Min, Vincent S.; Pilch, Krzysztof

2018-03-01

We find a class of new supersymmetric dyonic black holes in four-dimensional maximal gauged supergravity which are asymptotic to the SU(3) × U(1) invariant AdS4 Warner vacuum. These black holes can be embedded in eleven-dimensional supergravity where they describe the backreaction of M2-branes wrapped on a Riemann surface. The holographic dual description of these supergravity backgrounds is given by a partial topological twist on a Riemann surface of a three-dimensional N=2 SCFT that is obtained by a mass-deformation of the ABJM theory. We compute explicitly the topologically twisted index of this SCFT and show that it accounts for the entropy of the black holes.

Topological Floquet-Thouless Energy Pump

NASA Astrophysics Data System (ADS)

Kolodrubetz, Michael H.; Nathan, Frederik; Gazit, Snir; Morimoto, Takahiro; Moore, Joel E.

2018-04-01

We explore adiabatic pumping in the presence of a periodic drive, finding a new phase in which the topologically quantized pumped quantity is energy rather than charge. The topological invariant is given by the winding number of the micromotion with respect to time within each cycle, momentum, and adiabatic tuning parameter. We show numerically that this pump is highly robust against both disorder and interactions, breaking down at large values of either in a manner identical to the Thouless charge pump. Finally, we suggest experimental protocols for measuring this phenomenon.

Two-leg SU ( 2 n ) spin ladder: A low-energy effective field theory approach

DOE PAGES

Lecheminant, P.; Tsvelik, A. M.

2015-05-07

We present a field-theory analysis of a model of two SU( 2n)-invariant magnetic chains coupled by a generic interaction preserving time reversal and inversion symmetry. Contrary to the SU(2)-invariant case the zero-temperature phase diagram of such two-leg spin ladder does not contain topological phases. Thus, only generalized Valence Bond Solid phases are stabilized when n > 1 with different wave vectors and ground-state degeneracies. In particular, we find a phase which is made of a cluster of 2n spins put in an SU( 2n) singlet state. For n = 3, this cluster phase is relevant to ¹⁷³Yb ultracold atoms, withmore » an emergent SU(6) symmetry, loaded in a double-well optical lattice.« less

Dark matter from a classically scale-invariant S U (3 )X

NASA Astrophysics Data System (ADS)

Karam, Alexandros; Tamvakis, Kyriakos

2016-09-01

In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra S U (3 )X gauge factor gets completely broken by the vacuum expectation values of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic Z2×Z2' discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability of the predicted multi-Higgs sector imposing theoretical and experimental constraints. We perform a comprehensive analysis of the dark matter predictions of the model solving numerically the set of coupled Boltzmann equations involving all relevant dark matter processes and explore the direct detection prospects of the dark matter candidates.

Numerosity as a topological invariant.

PubMed

Kluth, Tobias; Zetzsche, Christoph

2016-01-01

The ability to quickly recognize the number of objects in our environment is a fundamental cognitive function. However, it is far from clear which computations and which actual neural processing mechanisms are used to provide us with such a skill. Here we try to provide a detailed and comprehensive analysis of this issue, which comprises both the basic mathematical foundations and the peculiarities imposed by the structure of the visual system and by the neural computations provided by the visual cortex. We suggest that numerosity should be considered as a mathematical invariant. Making use of concepts from mathematical topology--like connectedness, Betti numbers, and the Gauss-Bonnet theorem--we derive the basic computations suited for the computation of this invariant. We show that the computation of numerosity is possible in a neurophysiologically plausible fashion using only computational elements which are known to exist in the visual cortex. We further show that a fundamental feature of numerosity perception, its Weber property, arises naturally, assuming noise in the basic neural operations. The model is tested on an extended data set (made publicly available). It is hoped that our results can provide a general framework for future research on the invariance properties of the numerosity system.

The chaotic set and the cross section for chaotic scattering in three degrees of freedom

NASA Astrophysics Data System (ADS)

Jung, C.; Merlo, O.; Seligman, T. H.; Zapfe, W. P. K.

2010-10-01

This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.

Effective Hamiltonian for protected edge states in graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winkler, R.; Deshpande, H.

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.« less

Effective Hamiltonian for protected edge states in graphene

DOE PAGES

Winkler, R.; Deshpande, H.

2017-06-15

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.« less

Instantons, quivers and noncommutative Donaldson-Thomas theory

NASA Astrophysics Data System (ADS)

Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

2011-12-01

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

Filtration of the classical knot concordance group and Casson-Gordon invariants

NASA Astrophysics Data System (ADS)

Kim, Taehee

2004-09-01

It is known that if every prime power branched cyclic cover of a knot in S(3) is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in S(3) whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of scrf_{(1.0)}/scrf_{(1.5)} for which Casson-Gordon invariants vanish in Cochran-Orr-Teichner's filtration of the classical knot concordance group. As a corollary, it follows that Casson-Gordon invariants are not a complete set of obstructions to a second layer of Whitney disks.

On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems

NASA Astrophysics Data System (ADS)

Junge, Oliver; Kevrekidis, Ioannis G.

2017-06-01

We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments.

On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems.

PubMed

Junge, Oliver; Kevrekidis, Ioannis G

2017-06-01

We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments.

High-order computer-assisted estimates of topological entropy

NASA Astrophysics Data System (ADS)

Grote, Johannes

The concept of Taylor Models is introduced, which offers highly accurate C0-estimates for the enclosures of functional dependencies, combining high-order Taylor polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified interval arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly nonlinear dynamical systems. A method to obtain sharp rigorous enclosures of Poincare maps for certain types of flows and surfaces is developed and numerical examples are presented. Differential algebraic techniques allow the efficient and accurate computation of polynomial approximations for invariant curves of certain planar maps around hyperbolic fixed points. Subsequently we introduce a procedure to extend these polynomial curves to verified Taylor Model enclosures of local invariant manifolds with C0-errors of size 10-10--10 -14, and proceed to generate the global invariant manifold tangle up to comparable accuracy through iteration in Taylor Model arithmetic. Knowledge of the global manifold structure up to finite iterations of the local manifold pieces enables us to find all homoclinic and heteroclinic intersections in the generated manifold tangle. Combined with the mapping properties of the homoclinic points and their ordering we are able to construct a subshift of finite type as a topological factor of the original planar system to obtain rigorous lower bounds for its topological entropy. This construction is fully automatic and yields homoclinic tangles with several hundred homoclinic points. As an example rigorous lower bounds for the topological entropy of the Henon map are computed, which to the best knowledge of the authors yield the largest such estimates published so far.

The impact of inversion and mirror reflection symmetry on Raman scattering of T'transition metal dichalcogenides

NASA Astrophysics Data System (ADS)

Yan, Jun; Chen, Shao-Yu; Naylor, Carl; Goldstein, Thomas; Johnson, Charlie; Venkataraman, Dhandapani; Ramasubramaniam, Ashwin

Distorted octahedral (T') transition metal dichalcogenides (TMDCs) are topologically interesting material systems. Inversion-symmetry-broken bulk T'-TMDCs are predicted to be type II Weyl semimetals and inversion-symmetric monolayer (1L) T'-TMDCs are shown to be 2D topological insulators. In this talk, I will show that both the inversion symmetry and the mirror symmetry are important for understanding the lattice dynamics and Raman scattering of T'-TMDCs. The mirror plane that is perpendicular to the zigzag transition metal atomic chain classifies lattice vibrations into z-modes and m-modes where ` z' stands for zigzag and ` m' stands for mirror. Raman active z- and m- modes can be experimentally determined with light-polarization and crystal angle-resolved Raman tensor analysis. We report observation of all 9 even-parity zone-center phonons in 1L-T'-MoTe2. In bulk T'-MoTe2, we monitor inversion symmetry breaking with the shear lattice vibrations, which is important for supporting Weyl fermions. This work is supported by the Armstrong Fund for Science and NSF EFRI 2DARE EFMA-1542879.

Bandwidth and Electron Correlation-Tuned Superconductivity in Rb 0.8 Fe 2 ( Se 1 - z S z ) 2

DOE PAGES

Yi, M.; Wang, Meng; Kemper, A. F.; ...

2015-12-15

Here, we present a systematic angle-resolved photoemission spectroscopy study of the substitution dependence of the electronic structure of Rb 0.8Fe 2(Se 1-zS z) 2 (z = 0, 0.5, 1), where superconductivity is continuously suppressed into a metallic phase. Going from the nonsuperconducting Rb 0.8Fe 2S 2 to superconducting Rb 0.8Fe 2Se 2, we observe little change of the Fermi surface topology, but a reduction of the overall bandwidth by a factor of 2. Hence, for these heavily electron-doped iron chalcogenides, we have identified electron correlation as explicitly manifested in the quasiparticle bandwidth to be the important tuning parameter for superconductivity,more » and that moderate correlation is essential to achieving high T C.« less

On universal knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Mkrtchyan, R.; Morozov, A.

2016-02-01

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds

NASA Astrophysics Data System (ADS)

Gray, James; Haupt, Alexander S.; Lukas, Andre

2014-09-01

We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in ref. [1]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded from http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html.

Translation Invariant Extensions of Finite Volume Measures

NASA Astrophysics Data System (ADS)

Goldstein, S.; Kuna, T.; Lebowitz, J. L.; Speer, E. R.

2017-02-01

We investigate the following questions: Given a measure μ _Λ on configurations on a subset Λ of a lattice L, where a configuration is an element of Ω ^Λ for some fixed set Ω , does there exist a measure μ on configurations on all of L, invariant under some specified symmetry group of L, such that μ _Λ is its marginal on configurations on Λ ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L=Z^d and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance ( LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ subset Z is not an interval, or when Λ subset Z^d with d>1, the LTI condition is necessary but not sufficient for extendibility. For Z^d with d>1, extendibility is in some sense undecidable.

Topological geons with self-gravitating phantom scalar field

NASA Astrophysics Data System (ADS)

Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.

2017-12-01

A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.

A study of the topology of dissipating motions in direct numerical simulations of time-developing compressible and incompressible mixing layers

NASA Technical Reports Server (NTRS)

Chen, J. H.; Chong, M. S.; Soria, J.; Sondergaard, R.; Perry, A. E.; Rogers, M.; Moser, R.; Cantwell, B. J.

1990-01-01

A preliminary investigation of the geometry of flow patterns in numerically simulated compressible and incompressible mixing layers was carried out using 3-D critical point methodology. Motions characterized by high rates of kinetic energy dissipation and/or high enstrophy were of particular interest. In the approach the partial derivatives of the velocity field are determined at every point in the flow. These are used to construct the invariants of the velocity gradient tensor and the rate-of-strain tensor (P, Q, R, and P(sub s), Q(sub s), R(sub s) respectively). For incompressible flow the first invariant is zero. For the conditions of the compressible simulation, the first invariant is found to be everywhere small, relative to the second and third invariants, and so in both cases the local topology at a point is mainly determined by the second and third invariants. The data at every grid point is used to construct scatter plots of Q versus R and Q(sub s) versus R(sub s). Most points map to a cluster near the origin in Q-R space. However, fine scale motions, that is motions which are characterized by velocity derivatives which scale with the square root of R(sub delta), tend to map to regions which lie far from the origin. Definite trends are observed for motions characterized by high enstrophy and/or high dissipation. The observed trends suggest that, for these motions, the second and third invariants of the velocity gradient and rate-of-strain tensors are strongly correlated. The second and third invariants of the rate-of-strain tensor are related by K(-Q(sub s))(exp 3/2), which is consistent with the above scaling of velocity derivatives. The quantity K appears to depend on Reynolds number with an upper limit K = 2(the square root of 3)/9 corresponding to locally axisymmetric flow. For both the compressible and incompressible mixing layer, regions corresponding to high rates of dissipation are found to be characterized by comparable magnitudes of R(sub ij)R(sub ij) and S(sub ij)S(sub ij). For the incompressible mixing layer, regions characterized by the highest values of enstrophy are found to have relatively low strain rates.

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Topological String Theory and Enumerative Geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Y. S

In this thesis we investigate several problems which have their roots in both topological string theory and enumerative geometry. In the former case, underlying theories are topological field theories, whereas the latter case is concerned with intersection theories on moduli spaces. A permeating theme in this thesis is to examine the close interplay between these two complementary fields of study. The main problems addressed are as follows: In considering the Hurwitz enumeration problem of branched covers of compact connected Riemann surfaces, we completely solve the problem in the case of simple Hurwitz numbers. In addition, utilizing the connection between Hurwitzmore » numbers and Hodge integrals, we derive a generating function for the latter on the moduli space {bar M}{sub g,2} of 2-pointed, genus-g Deligne-Mumford stable curves. We also investigate Givental's recent conjecture regarding semisimple Frobenius structures and Gromov-Witten invariants, both of which are closely related to topological field theories; we consider the case of a complex projective line P{sup 1} as a specific example and verify his conjecture at low genera. In the last chapter, we demonstrate that certain topological open string amplitudes can be computed via relative stable morphisms in the algebraic category.« less

Topological nonsymmorphic metals from band inversion

DOE PAGES

Muechler, Lukas; Alexandradinata, A.; Neupert, Titus; ...

2016-12-29

Here, we expand the phase diagram of two-dimensional, nonsymmorphic crystals at integer fillings that do not guarantee gaplessness. In addition to the trivial, gapped phase that is expected, we find that band inversion leads to a class of topological, gapless phases. These topological phases are exemplified by the monolayers of MTe 2 (M ¼ W; Mo) if spin-orbit coupling is neglected. We characterize the Dirac band touching of these topological metals by theWilson loop of the non-Abelian Berry gauge field. Furthermore, we develop a criterion for the proximity of these topological metals to 2D and 3D Z 2 topological insulatorsmore » when spinorbit coupling is included; our criterion is based on nonsymmorphic symmetry eigenvalues, and may be used to identify topological materials without inversion symmetry. An additional feature of the Dirac cone in monolayer MTe 2 is that it tilts over in a Lifshitz transition to produce electron and hole pockets—a type-II Dirac cone. These pockets, together with the pseudospin structure of the Dirac electrons, suggest a unified, topological explanation for the recently reported, nonsaturating magnetoresistance in WTe 2, as well as its circular dichroism in photoemission. We complement our analysis and first-principles band structure calculations with an ab-initio-derived tight-binding model for the WTe 2 monolayer.« less

Magnetic second-order topological insulators and semimetals

NASA Astrophysics Data System (ADS)

Ezawa, Motohiko

2018-04-01

We propose magnetic second-order topological insulators (SOTIs). First, we study a three-dimensional model. It is pointed out that the previously proposed topological hinge insulator has actually surface states along the [001] direction in addition to hinge states. We gap out these surface states by introducing magnetization, obtaining a SOTI only with hinge states. The bulk topological number is the Z2 index protected by the combined symmetry of the fourfold rotation and the inversion symmetry. We next study two-dimensional magnetic SOTIs, where the corner states are robust also in the presence of the magnetization. Finally, we construct a magnetic second-order topological semimetal by layering the two-dimensional magnetic SOTIs, where hinge-arc states are robust also in the presence of the magnetization.

On the Prognostic Efficiency of Topological Descriptors for Magnetograms of Active Regions

NASA Astrophysics Data System (ADS)

Knyazeva, I. S.; Urtiev, F. A.; Makarenko, N. G.

2017-12-01

Solar flare prediction remains an important practical task of space weather. An increase in the amount and quality of observational data and the development of machine-learning methods has led to an improvement in prediction techniques. Additional information has been retrieved from the vector magnetograms; these have been recently supplemented by traditional line-of-sight (LOS) magnetograms. In this work, the problem of the comparative prognostic efficiency of features obtained on the basis of vector data and LOS magnetograms is discussed. Invariants obtained from a topological analysis of LOS magnetograms are used as complexity characteristics of magnetic patterns. Alternatively, the so-called SHARP parameters were used; they were calculated by the data analysis group of the Stanford University Laboratory on the basis of HMI/SDO vector magnetograms and are available online at the website (http://jsoc.stanford.edu/) with the solar dynamics observatory (SDO) database for the entire history of SDO observations. It has been found that the efficiency of large-flare prediction based on topological descriptors of LOS magnetograms in epignosis mode is at least s no worse than the results of prognostic schemes based on vector features. The advantages of the use of topological invariants based on LOS data are discussed.

A topological approach unveils system invariances and broken symmetries in the brain.

PubMed

Tozzi, Arturo; Peters, James F

2016-05-01

Symmetries are widespread invariances underscoring countless systems, including the brain. A symmetry break occurs when the symmetry is present at one level of observation but is hidden at another level. In such a general framework, a concept from algebraic topology, namely, the Borsuk-Ulam theorem (BUT), comes into play and sheds new light on the general mechanisms of nervous symmetries. The BUT tells us that we can find, on an n-dimensional sphere, a pair of opposite points that have the same encoding on an n - 1 sphere. This mapping makes it possible to describe both antipodal points with a single real-valued vector on a lower dimensional sphere. Here we argue that this topological approach is useful for the evaluation of hidden nervous symmetries. This means that symmetries can be found when evaluating the brain in a proper dimension, although they disappear (are hidden or broken) when we evaluate the same brain only one dimension lower. In conclusion, we provide a topological methodology for the evaluation of the most general features of brain activity, i.e., the symmetries, cast in a physical/biological fashion that has the potential to be operationalized. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Fivebranes and 3-manifold homology

NASA Astrophysics Data System (ADS)

Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun

2017-07-01

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[ M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.

Evaluation of the topological characteristics of the turbulent flow in a `box of turbulence' through 2D time-resolved particle image velocimetry

NASA Astrophysics Data System (ADS)

Lian, Huan; Soulopoulos, Nikolaos; Hardalupas, Yannis

2017-09-01

The experimental evaluation of the topological characteristics of the turbulent flow in a `box' of homogeneous and isotropic turbulence (HIT) with zero mean velocity is presented. This requires an initial evaluation of the effect of signal noise on measurement of velocity invariants. The joint probability distribution functions (pdfs) of experimentally evaluated, noise contaminated, velocity invariants have a different shape than the corresponding noise-free joint pdfs obtained from the DNS data of the Johns Hopkins University (JHU) open resource HIT database. A noise model, based on Gaussian and impulsive Salt and Pepper noise, is established and added artificially to the DNS velocity vector field of the JHU database. Digital filtering methods, based on Median and Wiener Filters, are chosen to eliminate the modeled noise source and their capacity to restore the joint pdfs of velocity invariants to that of the noise-free DNS data is examined. The remaining errors after filtering are quantified by evaluating the global mean velocity, turbulent kinetic energy and global turbulent homogeneity, assessed through the behavior of the ratio of the standard deviation of the velocity fluctuations in two directions, the energy spectrum of the velocity fluctuations and the eigenvalues of the rate-of-strain tensor. A method of data filtering, based on median filtered velocity using different median filter window size, is used to quantify the clustering of zero velocity points of the turbulent field using the radial distribution function (RDF) and Voronoï analysis to analyze the 2D time-resolved particle image velocimetry (TR-PIV) velocity measurements. It was found that a median filter with window size 3 × 3 vector spacing is the effective and efficient approach to eliminate the experimental noise from PIV measured velocity images to a satisfactory level and extract the statistical two-dimensional topological turbulent flow patterns.

Squeezed Dirac and topological magnons in a bosonic honeycomb optical lattice

NASA Astrophysics Data System (ADS)

Owerre, S. A.; Nsofini, J.

2017-11-01

Quantum information storage using charge-neutral quasiparticles is expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-1/2 XYZ Heisenberg model on the honeycomb lattice with discrete Z2 symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z2 anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.

Squeezed Dirac and Topological Magnons in a Bosonic Honeycomb Optical Lattice.

PubMed

Owerre, Solomon; Nsofini, Joachim

2017-09-20

Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z$_2$ anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators. . © 2017 IOP Publishing Ltd.

Knotty structures of the evolving heliospheric magnetic fields.

NASA Astrophysics Data System (ADS)

Roth, Ilan

2013-04-01

The analogy between MHD and knot theory is utilized in an analysis of structure, stability and evolution of complex magnetic heliospheric flux tubes. Planar projection of a three-dimensional magnetic configuration depicts the structure as a two-dimensional diagram with crossings, to which one may assign mathematical operations leading to robust topological invariants. These invariants enrich the topological information of magnetic configurations beyond helicity. It is conjectured that the field which emerges from the solar photosphere is structured as one of simplest knot invariants - unknot or prime knot, and these flux ropes are then stretched while carried by the solar wind into the interplanetary medium. Preservation of invariants for small diffusivity and large cross section of the emerging magnetic flux makes them impervious to large scale reconnection, allowing us to predict the observed structures at 1AU as elongated prime knots. Similar structures may be observed in magnetic clouds which got disconnected from their foot-points and in ion drop-out configurations from a compact flare source in solar impulsive solar events. Observation of small scale magnetic features consistent with prime knot may indicate spatial intermittency and non-Gaussian statistics in the turbulent cascade process. For flux tubes with higher resistivity, magnetic energy decay rate should decrease with increased knot complexity as the invariants are then harder to be violated. Future measurements are suggested for distinctly oriented magnetic fields with directionally varying suprathermal particle fluxes.

Classification of symmetry-protected phases for interacting fermions in two dimensions

NASA Astrophysics Data System (ADS)

Cheng, Meng; Bi, Zhen; You, Yi-Zhuang; Gu, Zheng-Cheng

2018-05-01

Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H3( G ,U (1 ) ) . Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional H1(G ,Z2) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G ×Z2f is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.

Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes

NASA Astrophysics Data System (ADS)

Escalante, Alberto; Medel-Portugal, C.

2018-04-01

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev-Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.

Gauged BPS baby Skyrmions with quantized magnetic flux

NASA Astrophysics Data System (ADS)

Adam, C.; Wereszczynski, A.

2017-06-01

A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of 2 π , which allows, in principle, to define this theory on a compact manifold without boundary, unlike all gauged baby Skyrme models considered so far.

Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.

PubMed

Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond

2017-02-24

Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

The ATLAS Level-1 Topological Trigger performance in Run 2

NASA Astrophysics Data System (ADS)

Riu, Imma; ATLAS Collaboration

2017-10-01

The Level-1 trigger is the first event rate reducing step in the ATLAS detector trigger system, with an output rate of up to 100 kHz and decision latency smaller than 2.5 μs. During the LHC shutdown after Run 1, the Level-1 trigger system was upgraded at hardware, firmware and software levels. In particular, a new electronics sub-system was introduced in the real-time data processing path: the Level-1 Topological trigger system. It consists of a single electronics shelf equipped with two Level-1 Topological processor blades. They receive real-time information from the Level-1 calorimeter and muon triggers, which is processed to measure angles between trigger objects, invariant masses or other kinematic variables. Complementary to other requirements, these measurements are taken into account in the final Level-1 trigger decision. The system was installed and commissioning started in 2015 and continued during 2016. As part of the commissioning, the decisions from individual algorithms were simulated and compared with the hardware response. An overview of the Level-1 Topological trigger system design, commissioning process and impact on several event selections are illustrated.

Gapless edges of 2d topological orders and enriched monoidal categories

NASA Astrophysics Data System (ADS)

Kong, Liang; Zheng, Hao

2018-02-01

In this work, we give a mathematical description of a chiral gapless edge of a 2d topological order (without symmetry). We show that the observables on the 1+1D world sheet of such an edge consist of a family of topological edge excitations, boundary CFT's and walls between boundary CFT's. These observables can be described by a chiral algebra and an enriched monoidal category. This mathematical description automatically includes that of gapped edges as special cases. Therefore, it gives a unified framework to study both gapped and gapless edges. Moreover, the boundary-bulk duality also holds for gapless edges. More precisely, the unitary modular tensor category that describes the 2d bulk phase is exactly the Drinfeld center of the enriched monoidal category that describes the gapless/gapped edge. We propose a classification of all gapped and chiral gapless edges of a given bulk phase. In the end, we explain how modular-invariant bulk rational conformal field theories naturally emerge on certain gapless walls between two trivial phases.

Immirzi parameter and Noether charges in first order gravity

NASA Astrophysics Data System (ADS)

Durka, Remigiusz

2012-02-01

The framework of SO(3,2) constrained BF theory applied to gravity makes it possible to generalize formulas for gravitational diffeomorphic Noether charges (mass, angular momentum, and entropy). It extends Wald's approach to the case of first order gravity with a negative cosmological constant, the Holst modification and the topological terms (Nieh-Yan, Euler, and Pontryagin). Topological invariants play essential role contributing to the boundary terms in the regularization scheme for the asymptotically AdS spacetimes, so that the differentiability of the action is automatically secured. Intriguingly, it turns out that the black hole thermodynamics does not depend on the Immirzi parameter for the AdS-Schwarzschild, AdS-Kerr, and topological black holes, whereas a nontrivial modification appears for the AdS-Taub-NUT spacetime, where it impacts not only the entropy, but also the total mass.

Quantum phase transitions between a class of symmetry protected topological states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Jiang, Hong-Chen; Lu, Yuan-Ming

2015-07-01

The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional View the MathML source-symmetric SPT by a View the MathML source symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice modelsmore » as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less

Topological Band Theory for Non-Hermitian Hamiltonians

NASA Astrophysics Data System (ADS)

Shen, Huitao; Zhen, Bo; Fu, Liang

2018-04-01

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.

Majorana Kramers pair in a nematic vortex

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Fengcheng; Martin, Ivar

A time-reversal (TR) invariant topological superconductor is characterized by a Kramers pair of Majorana zero-energy modes on boundaries and in a core of a TR invariant vortex. A vortex defect that preserves TR symmetry has remained primarily of theoretical interest, since typically a magnetic field, which explicitly breaks TR, needs to be applied to create vortices in superconductors. In this paper, we show that an odd-parity topological superconductor with a nematic pairing order parameter can host a nematic vortex that preserves TR symmetry and binds a Majorana Kramers pair. Such a nematic superconductor could be realized in metal-doped Bi 2Semore » 3, as suggested by recent experiments. We provide an analytic solution for the zero modes in a continuous nematic vortex. In lattice, crystalline anisotropy can pin the two-component order parameter along high-symmetry directions. We show that a discrete nematic vortex, which forms when three nematic domains meet, also supports a TR pair of Majorana modes. Lastly, we discuss possible experiments to probe the zero modes.« less

Majorana Kramers pair in a nematic vortex

DOE PAGES

Wu, Fengcheng; Martin, Ivar

2017-06-05

A time-reversal (TR) invariant topological superconductor is characterized by a Kramers pair of Majorana zero-energy modes on boundaries and in a core of a TR invariant vortex. A vortex defect that preserves TR symmetry has remained primarily of theoretical interest, since typically a magnetic field, which explicitly breaks TR, needs to be applied to create vortices in superconductors. In this paper, we show that an odd-parity topological superconductor with a nematic pairing order parameter can host a nematic vortex that preserves TR symmetry and binds a Majorana Kramers pair. Such a nematic superconductor could be realized in metal-doped Bi 2Semore » 3, as suggested by recent experiments. We provide an analytic solution for the zero modes in a continuous nematic vortex. In lattice, crystalline anisotropy can pin the two-component order parameter along high-symmetry directions. We show that a discrete nematic vortex, which forms when three nematic domains meet, also supports a TR pair of Majorana modes. Lastly, we discuss possible experiments to probe the zero modes.« less

Topological solitons in 8-spinor mie electrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rybakov, Yu. P., E-mail: soliton4@mail.ru

2013-10-15

We investigate the effective 8-spinor field model suggested earlier as the generalization of nonlinear Mie electrodynamics. We first study in pure spinorial model the existence of topological solitons endowed with the nontrivial Hopf invariant Q{sub H}, which can be interpreted as the lepton number. Electromagnetic field being included as the perturbation, we estimate the energy and the spin of the localized charged configuration.

Topological BF field theory description of topological insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cho, Gil Young; Moore, Joel E., E-mail: jemoore@berkeley.edu; Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

2011-06-15

Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version ofmore » abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.« less

Laser angle-resolved photoemission as a probe of initial state k z dispersion, final-state band gaps, and spin texture of Dirac states in the Bi 2Te 3 topological insulator

DOE PAGES

Ärrälä, Minna; Hafiz, Hasnain; Mou, Daixiang; ...

2016-10-27

Here, we have obtained angle-resolved photoemission (ARPES) spectra from single crystals of the topological insulator material Bi 2Te 3 using tunable laser spectrometer. The spectra were collected for eleven different photon energies ranging from 5.57 to 6.70 eV for incident light polarized linearly along two different in-plane directions. Parallel first-principles, fully relativistic computations of photo-intensities were carried out using the experimental geometry within the framework of the one-step model of photoemission. Good overall accord between theory and experiment is used to gain insight into how properties of the initial and final state band structures as well as those of themore » topological surface states and their spin-textures are reflected in the laser-ARPES spectra. In conclusion, our analysis reveals that laser-ARPES is sensitive to both the initial state k z dispersion and the presence of delicate gaps in the final state electronic spectrum.« less

Topological defects in the Georgi-Machacek model

NASA Astrophysics Data System (ADS)

Chatterjee, Chandrasekar; Kurachi, Masafumi; Nitta, Muneto

2018-06-01

We study topological defects in the Georgi-Machacek model in a hierarchical symmetry breaking in which extra triplets acquire vacuum expectation values before the doublet. We find a possibility of topologically stable non-Abelian domain walls and non-Abelian flux tubes (vortices or cosmic strings) in this model. In the limit of the vanishing U (1 )Y gauge coupling in which the custodial symmetry becomes exact, the presence of a vortex spontaneously breaks the custodial symmetry, giving rise to S2 Nambu-Goldstone (NG) modes localized around the vortex corresponding to non-Abelian fluxes. Vortices are continuously degenerated by these degrees of freedom, thereby called non-Abelian. By taking into account the U (1 )Y gauge coupling, the custodial symmetry is explicitly broken, the NG modes are lifted to become pseudo-NG modes, and all non-Abelian vortices fall into a topologically stable Z string. This is in contrast to the standard model in which Z strings are nontopological and are unstable in the realistic parameter region. Non-Abelian domain walls also break the custodial symmetry and are accompanied by localized S2 NG modes. Finally, we discuss the existence of domain wall solutions bounded by flux tubes, where their S2 NG modes match. The domain walls may quantum mechanically decay by creating a hole bounded by a flux tube loop, and would be cosmologically safe. Gravitational waves produced from unstable domain walls could be detected by future experiments.

Topological semimetals with Riemann surface states

NASA Astrophysics Data System (ADS)

Fang, Chen; Lu, Ling; Liu, Junwei; Fu, Liang

Topological semimetals have robust bulk band crossings between the conduction and the valence bands. Among them, Weyl semimetals are so far the only class having topologically protected signatures on the surface known as the ``Fermi arcs''. Here we theoretically find new classes of topological semimetals protected by nonsymmorphic glide reflection symmetries. On a symmetric surface, there are multiple Fermi arcs protected by nontrivial Z2 spectral flows between two high-symmetry lines (or two segments of one line) in the surface Brillouin zone. We observe that so far topological semimetals with protected Fermi arcs have surface dispersions that can be mapped to noncompact Riemann surfaces representing simple holomorphic functions. We propose perovskite superlattice [(SrIrO3)2m, (CaIrO3)2n] as a nonsymmorphic Dirac semimetal. C.F. and L.F. were supported by the S3TEC Solid State Solar Thermal Energy Conversion Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0001299/DE.

Structure-based analysis of CysZ-mediated cellular uptake of sulfate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Assur Sanghai, Zahra; Liu, Qun; Clarke, Oliver B.

Sulfur, most abundantly found in the environment as sulfate (SO 4 2-), is an essential element in metabolites required by all living cells, including amino acids, co-factors and vitamins. However, current understanding of the cellular delivery of SO 4 2- at the molecular level is limited. CysZ has been described as a SO 4 2- permease, but its sequence family is without known structural precedent. Based on crystallographic structure information, SO 4 2- binding and flux experiments, we provide insight into the molecular mechanism of CysZ-mediated translocation of SO 4 2- across membranes. CysZ structures from three different bacterial speciesmore » display a hitherto unknown fold and have subunits organized with inverted transmembrane topology. CysZ from Pseudomonas denitrificans assembles as a trimer of antiparallel dimers and the CysZ structures from two other species recapitulate dimers from this assembly. In conclusion, mutational studies highlight the functional relevance of conserved CysZ residues.« less

Structure-based analysis of CysZ-mediated cellular uptake of sulfate

DOE PAGES

Assur Sanghai, Zahra; Liu, Qun; Clarke, Oliver B.; ...

2018-05-24

Sulfur, most abundantly found in the environment as sulfate (SO 4 2-), is an essential element in metabolites required by all living cells, including amino acids, co-factors and vitamins. However, current understanding of the cellular delivery of SO 4 2- at the molecular level is limited. CysZ has been described as a SO 4 2- permease, but its sequence family is without known structural precedent. Based on crystallographic structure information, SO 4 2- binding and flux experiments, we provide insight into the molecular mechanism of CysZ-mediated translocation of SO 4 2- across membranes. CysZ structures from three different bacterial speciesmore » display a hitherto unknown fold and have subunits organized with inverted transmembrane topology. CysZ from Pseudomonas denitrificans assembles as a trimer of antiparallel dimers and the CysZ structures from two other species recapitulate dimers from this assembly. In conclusion, mutational studies highlight the functional relevance of conserved CysZ residues.« less

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Zhou, Qi

2018-06-01

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

Fivebranes and 3-manifold homology

DOE PAGES

Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun

2017-07-14

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that vebrane compacti cations provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N = 2 theory T[M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categori cation of Chern-Simons partition function.more » Finally, some of the new key elements include the explicit form of the S-transform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in Chern-Simons theory.« less

Squeezed Dirac and topological magnons in a bosonic honeycomb optical lattice.

PubMed

Owerre, S A; Nsofini, J

2017-10-19

Quantum information storage using charge-neutral quasiparticles is expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-[Formula: see text] XYZ Heisenberg model on the honeycomb lattice with discrete Z 2 symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z 2 anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.

The Green-Schwarz mechanism and geometric anomaly relations in 2d (0,2) F-theory vacua

NASA Astrophysics Data System (ADS)

Weigand, Timo; Xu, Fengjun

2018-04-01

We study the structure of gauge and gravitational anomalies in 2d N = (0 , 2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory. We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms. These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon. Cancellation of anomalies in the effective theory predicts intricate topological identities which must hold on every elliptically fibered Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but their proof from a purely mathematical perspective remains as an interesting open problem. Some of the identities we find on elliptic 5-folds are related in an intriguing way to previously studied topological identities governing the structure of anomalies in 6d N = (1 , 0) and 4d N = 1 theories obtained from F-theory.

Relativistic Fermions Generated by Square Lattices in Layered Compounds

NASA Astrophysics Data System (ADS)

Mao, Zhiqiang

Recent discoveries of topological semimetals have generated immense interests since they represent new topological states of quantum matters. In this talk, I will present our recent studies on topological semimetals, which are focused on Dirac/Weyl fermions generated by square lattices in layered compounds. I will first report on our discoveries of two new Dirac materials Sr1-yMn1-zSb2 and BaMnSb2 in which nearly massless Dirac fermions are generated by 2D Sb layers. In Sr1-yMn1-zSb2, Dirac fermions are found to coexist with ferromagnetism, offering a rare opportunity to investigate the interplay between relativistic fermions and spontaneous time reversal symmetry breaking and explore a possible magnetic Weyl state. Then I will show our quantum oscillation studies on two new Dirac nodal line semimetals - ZrSiSe and ZrSiTe. We have not only revealed their signatures of nodal-line fermions, but also demonstrated that their atomically thin crystals are accessible via mechanical exfoliation, raising the possibility of realizing the theoretically predicted 2D topological insulators. Finally I will discuss exotic quantum transport behavior arising from the zeroth Landau level in Weyl semimetal YbMnBi2. This work is supported by the U.S. DOE under Grant No. DE-SC0014208 (support for the work on ZrSiSe and ZrSiTe) and DOE-EPSCoR Grant No. DE-SC0012432 with additional support from the Louisiana BoR (support for the work on (Sr/Ba)MnSb2 and YbMnBi2).

Corrections to hyperfine splitting and Lamb shift induced by diagrams with second order radiative insertions in the electron line

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eides, M.I.; Karshenboim, S.G.; Shelyuto, V.A.

1994-12-31

Contributions to HFS and to the Lamb shift intervals of order a{sup 2}(Za){sup 5} induced by gauge invariant set of nineteen topologically different graphs with two radiative photons inserted in the electron line are considered. Corrections both to HFS and Lamb shift induced by nine diagrams are calculated in the Fried-Yennie gauge.

Search for Violations of Lorentz Invariance and CPT Symmetry in B_{(s)}^{0} Mixing.

PubMed

Aaij, R; Abellán Beteta, C; Adeva, B; Adinolfi, M; Ajaltouni, Z; Akar, S; Albrecht, J; Alessio, F; Alexander, M; Ali, S; Alkhazov, G; Alvarez Cartelle, P; Alves, A A; Amato, S; Amerio, S; Amhis, Y; An, L; Anderlini, L; Andreassi, G; Andreotti, M; Andrews, J E; Appleby, R B; Aquines Gutierrez, O; Archilli, F; d'Argent, P; Artamonov, A; Artuso, M; Aslanides, E; Auriemma, G; Baalouch, M; Bachmann, S; Back, J J; Badalov, A; Baesso, C; Baker, S; Baldini, W; Barlow, R J; Barschel, C; Barsuk, S; Barter, W; Batozskaya, V; Battista, V; Bay, A; Beaucourt, L; Beddow, J; Bedeschi, F; Bediaga, I; Bel, L J; Bellee, V; Belloli, N; Belyaev, I; Ben-Haim, E; Bencivenni, G; Benson, S; Benton, J; Berezhnoy, A; Bernet, R; Bertolin, A; Betti, F; Bettler, M-O; van Beuzekom, M; Bifani, S; Billoir, P; Bird, T; Birnkraut, A; Bizzeti, A; Blake, T; Blanc, F; Blouw, J; Blusk, S; Bocci, V; Bondar, A; Bondar, N; Bonivento, W; Borgheresi, A; Borghi, S; Borisyak, M; Borsato, M; Boubdir, M; Bowcock, T J V; Bowen, E; Bozzi, C; Braun, S; Britsch, M; Britton, T; Brodzicka, J; Buchanan, E; Burr, C; Bursche, A; Buytaert, J; Cadeddu, S; Calabrese, R; Calvi, M; Calvo Gomez, M; Campana, P; Campora Perez, D; Capriotti, L; Carbone, A; Carboni, G; Cardinale, R; Cardini, A; Carniti, P; Carson, L; Carvalho Akiba, K; Casse, G; Cassina, L; Castillo Garcia, L; Cattaneo, M; Cauet, Ch; Cavallero, G; Cenci, R; Charles, M; Charpentier, Ph; Chatzikonstantinidis, G; Chefdeville, M; Chen, S; Cheung, S-F; Chrzaszcz, M; Cid Vidal, X; Ciezarek, G; Clarke, P E L; Clemencic, M; Cliff, H V; Closier, J; Coco, V; Cogan, J; Cogneras, E; Cogoni, V; Cojocariu, L; Collazuol, G; Collins, P; Comerma-Montells, A; Contu, A; Cook, A; Coombes, M; Coquereau, S; Corti, G; Corvo, M; Couturier, B; Cowan, G A; Craik, D C; Crocombe, A; Cruz Torres, M; Cunliffe, S; Currie, R; D'Ambrosio, C; Dall'Occo, E; Dalseno, J; David, P N Y; Davis, A; De Aguiar Francisco, O; De Bruyn, K; De Capua, S; De Cian, M; De Miranda, J M; De Paula, L; De Simone, P; Dean, C-T; Decamp, D; Deckenhoff, M; Del Buono, L; Déléage, N; Demmer, M; Derkach, D; Deschamps, O; Dettori, F; Dey, B; Di Canto, A; Di Ruscio, F; Dijkstra, H; Dordei, F; Dorigo, M; Dosil Suárez, A; Dovbnya, A; Dreimanis, K; Dufour, L; Dujany, G; Dungs, K; Durante, P; Dzhelyadin, R; Dziurda, A; Dzyuba, A; Easo, S; Egede, U; Egorychev, V; Eidelman, S; Eisenhardt, S; Eitschberger, U; Ekelhof, R; Eklund, L; El Rifai, I; Elsasser, Ch; Ely, S; Esen, S; Evans, H M; Evans, T; Falabella, A; Färber, C; Farley, N; Farry, S; Fay, R; Fazzini, D; Ferguson, D; Fernandez Albor, V; Ferrari, F; Ferreira Rodrigues, F; Ferro-Luzzi, M; Filippov, S; Fiore, M; Fiorini, M; Firlej, M; Fitzpatrick, C; Fiutowski, T; Fleuret, F; Fohl, K; Fontana, M; Fontanelli, F; Forshaw, D C; Forty, R; Frank, M; Frei, C; Frosini, M; Fu, J; Furfaro, E; Gallas Torreira, A; Galli, D; Gallorini, S; Gambetta, S; Gandelman, M; Gandini, P; Gao, Y; García Pardiñas, J; Garra Tico, J; Garrido, L; Garsed, P J; Gascon, D; Gaspar, C; Gavardi, L; Gazzoni, G; Gerick, D; Gersabeck, E; Gersabeck, M; Gershon, T; Ghez, Ph; Gianì, S; Gibson, V; Girard, O G; Giubega, L; Gligorov, V V; Göbel, C; Golubkov, D; Golutvin, A; Gomes, A; Gotti, C; Grabalosa Gándara, M; Graciani Diaz, R; Granado Cardoso, L A; Graugés, E; Graverini, E; Graziani, G; Grecu, A; Griffith, P; Grillo, L; Grünberg, O; Gushchin, E; Guz, Yu; Gys, T; Hadavizadeh, T; Hadjivasiliou, C; Haefeli, G; Haen, C; Haines, S C; Hall, S; Hamilton, B; Han, X; Hansmann-Menzemer, S; Harnew, N; Harnew, S T; Harrison, J; He, J; Head, T; Heister, A; Hennessy, K; Henrard, P; Henry, L; Hernando Morata, J A; van Herwijnen, E; Heß, M; Hicheur, A; Hill, D; Hoballah, M; Hombach, C; Hongming, L; Hulsbergen, W; Humair, T; Hushchyn, M; Hussain, N; Hutchcroft, D; Idzik, M; Ilten, P; Jacobsson, R; Jaeger, A; Jalocha, J; Jans, E; Jawahery, A; John, M; Johnson, D; Jones, C R; Joram, C; Jost, B; Jurik, N; Kandybei, S; Kanso, W; Karacson, M; Karbach, T M; Karodia, S; Kecke, M; Kelsey, M; Kenyon, I R; Kenzie, M; Ketel, T; Khairullin, E; Khanji, B; Khurewathanakul, C; Kirn, T; Klaver, S; Klimaszewski, K; Kolpin, M; Komarov, I; Koopman, R F; Koppenburg, P; Kozeiha, M; Kravchuk, L; Kreplin, K; Kreps, M; Krokovny, P; Kruse, F; Krzemien, W; Kucewicz, W; Kucharczyk, M; Kudryavtsev, V; Kuonen, A K; Kurek, K; Kvaratskheliya, T; Lacarrere, D; Lafferty, G; Lai, A; Lambert, D; Lanfranchi, G; Langenbruch, C; Langhans, B; Latham, T; Lazzeroni, C; Le Gac, R; van Leerdam, J; Lees, J-P; Lefèvre, R; Leflat, A; Lefrançois, J; Lemos Cid, E; Leroy, O; Lesiak, T; Leverington, B; Li, Y; Likhomanenko, T; Lindner, R; Linn, C; Lionetto, F; Liu, B; Liu, X; Loh, D; Longstaff, I; Lopes, J H; Lucchesi, D; Lucio Martinez, M; Luo, H; Lupato, A; Luppi, E; Lupton, O; Lusardi, N; Lusiani, A; Lyu, X; Machefert, F; Maciuc, F; Maev, O; Maguire, K; Malde, S; Malinin, A; Manca, G; Mancinelli, G; Manning, P; Mapelli, A; Maratas, J; Marchand, J F; Marconi, U; Marin Benito, C; Marino, P; Marks, J; Martellotti, G; Martin, M; Martinelli, M; Martinez Santos, D; Martinez Vidal, F; Martins Tostes, D; Massacrier, L M; Massafferri, A; Matev, R; Mathad, A; Mathe, Z; Matteuzzi, C; Mauri, A; Maurin, B; Mazurov, A; McCann, M; McCarthy, J; McNab, A; McNulty, R; Meadows, B; Meier, F; Meissner, M; Melnychuk, D; Merk, M; Merli, A; Michielin, E; Milanes, D A; Minard, M-N; Mitzel, D S; Molina Rodriguez, J; Monroy, I A; Monteil, S; Morandin, M; Morawski, P; Mordà, A; Morello, M J; Moron, J; Morris, A B; Mountain, R; Muheim, F; Müller, D; Müller, J; Müller, K; Müller, V; Mussini, M; Muster, B; Naik, P; Nakada, T; Nandakumar, R; Nandi, A; Nasteva, I; Needham, M; Neri, N; Neubert, S; Neufeld, N; Neuner, M; Nguyen, A D; Nguyen-Mau, C; Niess, V; Nieswand, S; Niet, R; Nikitin, N; Nikodem, T; Novoselov, A; O'Hanlon, D P; Oblakowska-Mucha, A; Obraztsov, V; Ogilvy, S; Okhrimenko, O; Oldeman, R; Onderwater, C J G; Osorio Rodrigues, B; Otalora Goicochea, J M; Otto, A; Owen, P; Oyanguren, A; Palano, A; Palombo, F; Palutan, M; Panman, J; Papanestis, A; Pappagallo, M; Pappalardo, L L; Pappenheimer, C; Parker, W; Parkes, C; Passaleva, G; Patel, G D; Patel, M; Patrignani, C; Pearce, A; Pellegrino, A; Penso, G; Pepe Altarelli, M; Perazzini, S; Perret, P; Pescatore, L; Petridis, K; Petrolini, A; Petruzzo, M; Picatoste Olloqui, E; Pietrzyk, B; Pikies, M; Pinci, D; Pistone, A; Piucci, A; Playfer, S; Plo Casasus, M; Poikela, T; Polci, F; Poluektov, A; Polyakov, I; Polycarpo, E; Popov, A; Popov, D; Popovici, B; Potterat, C; Price, E; Price, J D; Prisciandaro, J; Pritchard, A; Prouve, C; Pugatch, V; Puig Navarro, A; Punzi, G; Qian, W; Quagliani, R; Rachwal, B; Rademacker, J H; Rama, M; Ramos Pernas, M; Rangel, M S; Raniuk, I; Raven, G; Redi, F; Reichert, S; Dos Reis, A C; Renaudin, V; Ricciardi, S; Richards, S; Rihl, M; Rinnert, K; Rives Molina, V; Robbe, P; Rodrigues, A B; Rodrigues, E; Rodriguez Lopez, J A; Rodriguez Perez, P; Rogozhnikov, A; Roiser, S; Romanovsky, V; Romero Vidal, A; Ronayne, J W; Rotondo, M; Ruf, T; Ruiz Valls, P; Saborido Silva, J J; Sagidova, N; Saitta, B; Salustino Guimaraes, V; Sanchez Mayordomo, C; Sanmartin Sedes, B; Santacesaria, R; Santamarina Rios, C; Santimaria, M; Santovetti, E; Sarti, A; Satriano, C; Satta, A; Saunders, D M; Savrina, D; Schael, S; Schiller, M; Schindler, H; Schlupp, M; Schmelling, M; Schmelzer, T; Schmidt, B; Schneider, O; Schopper, A; Schubiger, M; Schune, M-H; Schwemmer, R; Sciascia, B; Sciubba, A; Semennikov, A; Sergi, A; Serra, N; Serrano, J; Sestini, L; Seyfert, P; Shapkin, M; Shapoval, I; Shcheglov, Y; Shears, T; Shekhtman, L; Shevchenko, V; Shires, A; Siddi, B G; Silva Coutinho, R; Silva de Oliveira, L; Simi, G; Sirendi, M; Skidmore, N; Skwarnicki, T; Smith, E; Smith, I T; Smith, J; Smith, M; Snoek, H; Sokoloff, M D; Soler, F J P; Soomro, F; Souza, D; Souza De Paula, B; Spaan, B; Spradlin, P; Sridharan, S; Stagni, F; Stahl, M; Stahl, S; Stefkova, S; Steinkamp, O; Stenyakin, O; Stevenson, S; Stoica, S; Stone, S; Storaci, B; Stracka, S; Straticiuc, M; Straumann, U; Sun, L; Sutcliffe, W; Swientek, K; Swientek, S; Syropoulos, V; Szczekowski, M; Szumlak, T; T'Jampens, S; Tayduganov, A; Tekampe, T; Tellarini, G; Teubert, F; Thomas, C; Thomas, E; van Tilburg, J; Tisserand, V; Tobin, M; Tolk, S; Tomassetti, L; Tonelli, D; Topp-Joergensen, S; Tournefier, E; Tourneur, S; Trabelsi, K; Traill, M; Tran, M T; Tresch, M; Trisovic, A; Tsaregorodtsev, A; Tsopelas, P; Tuning, N; Ukleja, A; Ustyuzhanin, A; Uwer, U; Vacca, C; Vagnoni, V; Valat, S; Valenti, G; Vallier, A; Vazquez Gomez, R; Vazquez Regueiro, P; Vázquez Sierra, C; Vecchi, S; van Veghel, M; Velthuis, J J; Veltri, M; Veneziano, G; Vesterinen, M; Viaud, B; Vieira, D; Vieites Diaz, M; Vilasis-Cardona, X; Volkov, V; Vollhardt, A; Voong, D; Vorobyev, A; Vorobyev, V; Voß, C; de Vries, J A; Waldi, R; Wallace, C; Wallace, R; Walsh, J; Wang, J; Ward, D R; Watson, N K; Websdale, D; Weiden, A; Whitehead, M; Wicht, J; Wilkinson, G; Wilkinson, M; Williams, M; Williams, M P; Williams, M; Williams, T; Wilson, F F; Wimberley, J; Wishahi, J; Wislicki, W; Witek, M; Wormser, G; Wotton, S A; Wraight, K; Wright, S; Wyllie, K; Xie, Y; Xu, Z; Yang, Z; Yin, H; Yu, J; Yuan, X; Yushchenko, O; Zangoli, M; Zavertyaev, M; Zhang, L; Zhang, Y; Zhelezov, A; Zheng, Y; Zhokhov, A; Zhong, L; Zhukov, V; Zucchelli, S

2016-06-17

Violations of CPT symmetry and Lorentz invariance are searched for by studying interference effects in B^{0} mixing and in B_{s}^{0} mixing. Samples of B^{0}→J/ψK_{S}^{0} and B_{s}^{0}→J/ψK^{+}K^{-} decays are recorded by the LHCb detector in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3  fb^{-1}. No periodic variations of the particle-antiparticle mass differences are found, consistent with Lorentz invariance and CPT symmetry. Results are expressed in terms of the standard model extension parameter Δa_{μ} with precisions of O(10^{-15}) and O(10^{-14})  GeV for the B^{0} and B_{s}^{0} systems, respectively. With no assumption on Lorentz (non)invariance, the CPT-violating parameter z in the B_{s}^{0} system is measured for the first time and found to be Re(z)=-0.022±0.033±0.005 and Im(z)=0.004±0.011±0.002, where the first uncertainties are statistical and the second systematic.

Topology, Geometry, and Mechanics of Z -Plasty

NASA Astrophysics Data System (ADS)

Matsumoto, Elisabetta A.; Liang, Haiyi; Mahadevan, L.

2018-02-01

Reconstructive surgeries often use topological manipulation of tissue to minimize postoperative scarring. The most common version of this, Z -plasty, involves modifying a straight line cut into a Z shape, followed by a rotational transposition of the resulting triangular pedicle flaps, and a final restitching of the wound. This locally reorients the anisotropic stress field and reduces the potential for scarring. We analyze the planar geometry and mechanics of the Z -plasty to quantify the rotation of the overall stress field and the local forces on the restitched cut using theory, simulations, and simple physical Z -plasty experiments with foam sheets that corroborate each other. Our study rationalizes the most typical surgical choice of this angle, and opens the way for a range of surgical decisions by characterizing the stresses along the cut.

Singular trajectories: space-time domain topology of developing speckle fields

NASA Astrophysics Data System (ADS)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

Analysis of Extended Z-source Inverter for Photovoltaic System

NASA Astrophysics Data System (ADS)

Prakash, G.; Subramani, C.; Dhineshkumar, K.; Rayavel, P.

2018-04-01

The Z-source inverter has picked up prominence as a solitary stage buck-support inverter topology among numerous specialists. Notwithstanding, its boosting capacity could be constrained, and in this manner, it may not be reasonable for a few applications requiring high lift request of falling other dc-dc help converters. The Z-source inverter is a recent converter topology that exhibits both voltage-buck and voltage-boost capability This could lose the effectiveness and request all the more detecting for controlling the additional new stages. This paper is proposing another group of broadened help semi Z - source inverter (ZSI) to fill the exploration hole left in the improvement of ZSI. These new topologies can be worked with same regulation strategies that were produced for unique ZSI. Likewise, they have a similar number of dynamic switches as unique ZSI saving the single-organize nature of ZSI. Proposed topologies are dissected in the enduring state and their exhibitions are approved utilizing recreated comes about acquired in MATLAB/Simulink. Besides, they are tentatively approved with comes about acquired from a model created in the research facility. The trend of fast increase of the PV energy use is related to the increasing efficiency of solar cells as well as the improvements of manufacturing technology of solar panels.

Robustness of topological Hall effect of nontrivial spin textures

NASA Astrophysics Data System (ADS)

Jalil, Mansoor B. A.; Tan, Seng Ghee

2014-05-01

We analyze the topological Hall conductivity (THC) of topologically nontrivial spin textures like magnetic vortices and skyrmions and investigate its possible application in the readback for magnetic memory based on those spin textures. Under adiabatic conditions, such spin textures would theoretically yield quantized THC values, which are related to topological invariants such as the winding number and polarity, and as such are insensitive to fluctuations and smooth deformations. However, in a practical setting, the finite size of spin texture elements and the influence of edges may cause them to deviate from their ideal configurations. We calculate the degree of robustness of the THC output in practical magnetic memories in the presence of edge and finite size effects.

Topological acoustic polaritons: robust sound manipulation at the subwavelength scale

NASA Astrophysics Data System (ADS)

Yves, Simon; Fleury, Romain; Lemoult, Fabrice; Fink, Mathias; Lerosey, Geoffroy

2017-07-01

Topological insulators, a hallmark of condensed matter physics, have recently reached the classical realm of acoustic waves. A remarkable property of time-reversal invariant topological insulators is the presence of unidirectional spin-polarized propagation along their edges, a property that could lead to a wealth of new opportunities in the ability to guide and manipulate sound. Here, we demonstrate and study the possibility to induce topologically non-trivial acoustic states at the deep subwavelength scale, in a structured two-dimensional metamaterial composed of Helmholtz resonators. Radically different from previous designs based on non-resonant sonic crystals, our proposal enables robust sound manipulation on a surface along predefined, subwavelength pathways of arbitrary shapes.

A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikolaenko, S S

2014-02-28

The paper is concerned with the topological analysis of the Chaplygin integrable case in the dynamics of a rigid body in a fluid. A full list of the topological types of Chaplygin systems in their dependence on the energy level is compiled on the basis of the Fomenko-Zieschang theory. An effective description of the topology of the Liouville foliation in terms of natural coordinate variables is also presented, which opens a direct way to calculating topological invariants. It turns out that on all nonsingular energy levels Chaplygin systems are Liouville equivalent to the well-known Euler case in the dynamics of a rigid body withmore » fixed point. Bibliography: 23 titles.« less

Machine Learning Topological Invariants with Neural Networks

NASA Astrophysics Data System (ADS)

Zhang, Pengfei; Shen, Huitao; Zhai, Hui

2018-02-01

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.

Symmetry Enriched Topological Phases and Their Edge Theories

NASA Astrophysics Data System (ADS)

Heinrich, Christopher

In this thesis we investigate topological phases of matter that have a global, unbroken symmetry group--also known as symmetry enriched topological (SET) phases. We address three questions about these phases: (1) how can we build exactly solvable models that realize them? (2) how can we determine if their edge theories can be gapped without breaking the symmetry? and (3) how do we understand the phenomenon of decoupled charge and neutral modes which occurs in certain fractional quantum Hall states? More specifically, we address the first question by constructing exactly solvable models for a wide class of symmetry enriched topological (SET) phases, which we call symmetry-enriched string nets. The construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group G, and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. As an example, we present a model for a phase with the same anyon excitations as the toric code and with a Z2 symmetry which exchanges the e and m type anyons. We further illustrate our construction with a number of additional examples. For the second question, we focus on the edge theories of 2D SET phases with Z2 symmetry. The central problem we seek to solve is to determine which edge theories can be gapped without breaking the symmetry. Previous attempts to answer this question in special cases relied on constructing perturbations of a particular type to gap the edge. This method proves the edge can be gapped when the appropriate perturbations can be found, but is inconclusive if they cannot be found. We build on this previous work by deriving a necessary and sufficient algebraic condition for when the edge can be gapped. Our results apply to Z2 symmetry protected topological phases as well as Abelian Z2 SET phases. Finally, in the fourth chapter, we describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode--i.e. an edge mode that does not carry electric charge. These models consist of two counter-propagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the nu = 2/3 state is the most prominent example.

Measurements of the pp →ZZ production cross section and the Z→4ℓ branching fraction, and constraints on anomalous triple gauge couplings at $$\\sqrt{s}$$ = 13 TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sirunyan, A. M.; Tumasyan, A.; Adam, W.

Four-lepton production in proton-proton collisions,more » $$\\mathrm {p}\\mathrm {p}\\rightarrow (\\mathrm{Z}/ \\gamma ^*)(\\mathrm{Z}/\\gamma ^*) \\rightarrow 4\\ell $$ , where $$\\ell = \\mathrm {e}$$ or $$\\mu $$ , is studied at a center-of-mass energy of 13 $$\\,\\text {TeV}$$ with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 35.9 $$\\,\\text {fb}^{-1}$$ . The ZZ production cross section, $$\\sigma (\\mathrm {p}\\mathrm {p}\\rightarrow \\mathrm{Z}\\mathrm{Z}) = 17.2 \\pm 0.5\\,\\text {(stat)} \\pm 0.7\\,\\text {(syst)} \\pm 0.4\\,\\text {(theo)} \\pm 0.4\\,\\text {(lumi)} \\text { pb} $$ , measured using events with two opposite-sign, same-flavor lepton pairs produced in the mass region $$60< m_{\\ell ^+\\ell ^-} < 120\\,\\text {GeV} $$ , is consistent with standard model predictions. Differential cross sections are measured and are well described by the theoretical predictions. The Z boson branching fraction to four leptons is measured to be $$\\mathcal {B}(\\mathrm{Z}\\rightarrow 4\\ell ) = 4.8 \\pm 0.2\\,\\text {(stat)} \\pm 0.2\\,\\text {(syst)} \\pm 0.1\\,\\text {(theo)} \\pm 0.1\\,\\text {(lumi)} \\times 10^{-6}$$ for events with a four-lepton invariant mass in the range $$80< m_{4\\ell } < 100\\,\\text {GeV} $$ and a dilepton mass $$m_{\\ell \\ell } > 4\\,\\text {GeV} $$ for all opposite-sign, same-flavor lepton pairs. Finally, the results agree with standard model predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZ $$\\gamma $$ couplings at 95% confidence level: $$-0.0012 < f_4^\\mathrm{Z}<0.0010$$ , $$-0.0010 < f_5^\\mathrm{Z} < 0.0013$$ , $$-0.0012 < f_4^{\\gamma }<0.0013$$ , $$-0.0012 < f_5^{\\gamma } < 0.0013$$ .« less

Measurements of the pp →ZZ production cross section and the Z→4ℓ branching fraction, and constraints on anomalous triple gauge couplings at $$\\sqrt{s}$$ = 13 TeV

DOE PAGES

Sirunyan, A. M.; Tumasyan, A.; Adam, W.; ...

2018-02-24

Four-lepton production in proton-proton collisions,more » $$\\mathrm {p}\\mathrm {p}\\rightarrow (\\mathrm{Z}/ \\gamma ^*)(\\mathrm{Z}/\\gamma ^*) \\rightarrow 4\\ell $$ , where $$\\ell = \\mathrm {e}$$ or $$\\mu $$ , is studied at a center-of-mass energy of 13 $$\\,\\text {TeV}$$ with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 35.9 $$\\,\\text {fb}^{-1}$$ . The ZZ production cross section, $$\\sigma (\\mathrm {p}\\mathrm {p}\\rightarrow \\mathrm{Z}\\mathrm{Z}) = 17.2 \\pm 0.5\\,\\text {(stat)} \\pm 0.7\\,\\text {(syst)} \\pm 0.4\\,\\text {(theo)} \\pm 0.4\\,\\text {(lumi)} \\text { pb} $$ , measured using events with two opposite-sign, same-flavor lepton pairs produced in the mass region $$60< m_{\\ell ^+\\ell ^-} < 120\\,\\text {GeV} $$ , is consistent with standard model predictions. Differential cross sections are measured and are well described by the theoretical predictions. The Z boson branching fraction to four leptons is measured to be $$\\mathcal {B}(\\mathrm{Z}\\rightarrow 4\\ell ) = 4.8 \\pm 0.2\\,\\text {(stat)} \\pm 0.2\\,\\text {(syst)} \\pm 0.1\\,\\text {(theo)} \\pm 0.1\\,\\text {(lumi)} \\times 10^{-6}$$ for events with a four-lepton invariant mass in the range $$80< m_{4\\ell } < 100\\,\\text {GeV} $$ and a dilepton mass $$m_{\\ell \\ell } > 4\\,\\text {GeV} $$ for all opposite-sign, same-flavor lepton pairs. Finally, the results agree with standard model predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZ $$\\gamma $$ couplings at 95% confidence level: $$-0.0012 < f_4^\\mathrm{Z}<0.0010$$ , $$-0.0010 < f_5^\\mathrm{Z} < 0.0013$$ , $$-0.0012 < f_4^{\\gamma }<0.0013$$ , $$-0.0012 < f_5^{\\gamma } < 0.0013$$ .« less

Observation of topological states in an optical Raman lattice with ultracold fermions

NASA Astrophysics Data System (ADS)

Song, Bo; He, Chengdong; Zhang, Long; Poon, Ting Fung Jeffrey; Hajiyev, Elnur; Ren, Zejian; Seo, Bojeong; Zhang, Shanchao; Liu, Xiong-Jun; Jo, Gyu-Boong

2017-04-01

The spin-orbit coupling with cold atoms, especially in optical lattices, provides a versatile platform to investigate the intriguing topological matters. In this talk, we will present the realization of one-dimensional spin-dependent lattice dressed by the periodic Raman field. Ultracold 173Yb fermions loaded into an optical Raman lattice reveal non-trivial spin textures due to the band topology, by which we measured topological invariants and determined a topological phase transition. In addition, we explored the non-equilibrium quench dynamics between the topological and the trivial states by suddenly changing the band topology of the optical Raman lattice. The optical Raman lattice demonstrated here opens a new avenue to study the spin-orbit coupling physics and furthermore to realize novel quantum matters such as symmetry-protected topological states. Funded by Croucher Foundation and Research Grants Council (RGC) of Hong Kong (Project ECS26300014, GRF16300215, GRF16311516, and Croucher Innovation Grants); MOST (Grant No. 2016YFA0301604) and NSFC (No. 11574008).

Observation of symmetry-protected topological band with ultracold fermions

PubMed Central

Song, Bo; Zhang, Long; He, Chengdong; Poon, Ting Fung Jeffrey; Hajiyev, Elnur; Zhang, Shanchao; Liu, Xiong-Jun; Jo, Gyu-Boong

2018-01-01

Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal invariant topological insulator, a symmetry-protected topological (SPT) phase in the symplectic class of the Altland-Zirnbauer classification. We report the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and study quench dynamics between topologically distinct regimes. The observed SPT band can be protected by a magnetic group and a nonlocal chiral symmetry, with the band topology being measured via Bloch states at symmetric momenta. The topology also resides in far-from-equilibrium spin dynamics, which are predicted and observed in experiment to exhibit qualitatively distinct behaviors in quenching to trivial and nontrivial regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology. This work opens the way to expanding the scope of SPT physics with ultracold atoms and studying nonequilibrium quantum dynamics in these exotic systems. PMID:29492457

Exact phase boundaries and topological phase transitions of the X Y Z spin chain

NASA Astrophysics Data System (ADS)

Jafari, S. A.

2017-07-01

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Topological Gyroscopic Metamaterials

NASA Astrophysics Data System (ADS)

Nash, Lisa Michelle

Topological materials are generally insulating in their bulk, with protected conducting states on their boundaries that are robust against disorder and perturbation of material property. The existence of these conducting edge states is characterized by an integer topological invariant. Though the phenomenon was first discovered in electronic systems, recent years have shown that topological states exist in classical systems as well. In this thesis we are primarily concerned with the topological properties of gyroscopic materials, which are created by coupling networks of fast-spinning objects. Through a series of simulations, numerical calculations, and experiments, we show that these materials can support topological edge states. We find that edge states in these gyroscopic metamaterials bear the hallmarks of topology related to broken time reversal symmetry: they transmit excitations unidirectionally and are extremely robust against experimental disorder. We also explore requirements for topology by studying several lattice configurations and find that topology emerges naturally in gyroscopic systems.A simple prescription can be used to create many gyroscopic lattices. Though many of our gyroscopic networks are periodic, we explore amorphous point-sets and find that topology also emerges in these networks.

Bottom-quark forward-backward asymmetry, dark matter, and the LHC

NASA Astrophysics Data System (ADS)

Liu, Da; Liu, Jia; Wagner, Carlos E. M.; Wang, Xiao-Ping

2018-03-01

The LEP experiment at CERN provided accurate measurements of the Z neutral gauge boson properties. Although all measurements agree well with the standard model (SM) predictions, the forward backward asymmetry of the bottom-quark remains almost 3 σ away from the SM value. We proposed that this anomaly may be explained by the existence of a new U (1 )D gauge boson, which couples with opposite charges to the right-handed components of the bottom and charm quarks. Cancellation of gauge anomalies demands the presence of a vector-like singlet charged lepton as well as a neutral Dirac (or Majorana) particle that provides a dark matter candidate. Constraints from precision measurements imply that the mass of the new gauge boson should be around 115 GeV. We discuss the experimental constraints on this scenario, including the existence of a di-jet resonance excess at an invariant mass similar to the mass of this new gauge boson, observed in boosted topologies at the CMS experiment.

Lasing in topological edge states of a one-dimensional lattice

NASA Astrophysics Data System (ADS)

St-Jean, P.; Goblot, V.; Galopin, E.; Lemaître, A.; Ozawa, T.; Le Gratiet, L.; Sagnes, I.; Bloch, J.; Amo, A.

2017-10-01

Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. Because their properties are inherited from the topology of the bulk, these edge states present a strong immunity to distortions of the underlying architecture. This feature offers new opportunities for robust trapping of light in nano- and micrometre-scale systems subject to fabrication imperfections and environmentally induced deformations. Here, we report lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su-Schrieffer-Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear phenomena in topological photonics.

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

NASA Astrophysics Data System (ADS)

Wang, Tenghui; Zhang, Zhenxing; Xiang, Liang; Gong, Zhihao; Wu, Jianlan; Yin, Yi

2018-04-01

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the "shortcut to adiabaticity" (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.

Topological Mechanics of Origami and Kirigami

NASA Astrophysics Data System (ADS)

Chen, Bryan Gin-ge; Liu, Bin; Evans, Arthur A.; Paulose, Jayson; Cohen, Itai; Vitelli, Vincenzo; Santangelo, C. D.

2016-04-01

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.

Exploring photonic topological insulator states in a circuit-QED lattice

NASA Astrophysics Data System (ADS)

Li, Jing-Ling; Shan, Chuan-Jia; Zhao, Feng

2018-04-01

We propose a simple protocol to explore the topological properties of photonic integer quantum Hall states in a one-dimensional circiut-QED lattice. By periodically modulating the on-site photonic energies in such a lattice, we demonstrate that this one-dimensional lattice model can be mapped into a two-dimensional integer quantum Hall insulator model. Based on the lattice-based cavity input-output theory, we show that both the photonic topological protected edge states and topological invariants can be clearly measured from the final steady state of the resonator lattice after taking into account cavity dissipation. Interestingly, we also find that the measurement signals associated with the above topological features are quite unambitious even in five coupled dissipative resonators. Our work opens up a new prospect of exploring topological states with a small-size dissipative quantum artificial lattice, which is quite attractive to the current quantum optics community.

On the Periodic Solutions of the Five-Dimensional Lorenz Equation Modeling Coupled Rosby Waves and Gravity Waves

NASA Astrophysics Data System (ADS)

Carvalho, Tiago; Llibre, Jaume

2017-06-01

Lorenz studied the coupled Rosby waves and gravity waves using the differential system U˙ = -VW + bVZ,V˙ = UW - bUZ,Ẇ = -UV,Ẋ = -Z,Ż = bUV + X. This system has the two first integrals H1 = U2 + V2,H 2 = V2 + W2 + X2 + Z2. Our main result shows that in each invariant set {H1 = h1 > 0}∩{H2 = h2 > 0} there are at least four (resp., 2) periodic solutions of the differential system with b≠0 and h2 > h1 (resp., h2 < h1).

The phase topology of a special case of Goryachev integrability in rigid body dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryabov, P. E., E-mail: orelryabov@mail.ru

2014-07-31

The phase topology of a special case of Goryachev integrability in the problem of motion of a rigid body in a fluid is investigated using the method of Boolean functions, which was developed by Kharlamov for algebraically separated systems. The bifurcation diagram of the moment map is found and the Fomenko invariant, which classifies the systems up to rough Liouville equivalence, is specified. Bibliography: 15 titles. (paper)

Deformations, moduli stabilisation and gauge couplings at one-loop

NASA Astrophysics Data System (ADS)

Honecker, Gabriele; Koltermann, Isabel; Staessens, Wieland

2017-04-01

We investigate deformations of Z_2 orbifold singularities on the toroidal orbifold {T}^6/(Z_2× Z_6) with discrete torsion in the framework of Type IIA orientifold model building with intersecting D6-branes wrapping special Lagrangian cycles. To this aim, we employ the hypersurface formalism developed previously for the orbifold {T}^6/(Z_2× Z_6) with discrete torsion and adapt it to the (Z_2× Z_6× Ω R) point group by modding out the remaining Z_3 subsymmetry and the orientifold projection Ω R. We first study the local behaviour of the Z_3× Ω R invariant deformation orbits under non-zero deformation and then develop methods to assess the deformation effects on the fractional three-cycle volumes globally. We confirm that D6-branes supporting USp(2 N) or SO(2 N) gauge groups do not constrain any deformation, while deformation parameters associated to cycles wrapped by D6-branes with U( N) gauge groups are constrained by D-term supersymmetry breaking. These features are exposed in global prototype MSSM, Left-Right symmetric and Pati-Salam models first constructed in [1, 2], for which we here count the number of stabilised moduli and study flat directions changing the values of some gauge couplings.

The uniformity and time-invariance of the intra-cluster metal distribution in galaxy clusters from the IllustrisTNG simulations

NASA Astrophysics Data System (ADS)

Vogelsberger, Mark; Marinacci, Federico; Torrey, Paul; Genel, Shy; Springel, Volker; Weinberger, Rainer; Pakmor, Rüdiger; Hernquist, Lars; Naiman, Jill; Pillepich, Annalisa; Nelson, Dylan

2018-02-01

The distribution of metals in the intra-cluster medium (ICM) encodes important information about the enrichment history and formation of galaxy clusters. Here, we explore the metal content of clusters in IllustrisTNG - a new suite of galaxy formation simulations building on the Illustris project. Our cluster sample contains 20 objects in TNG100 - a ˜(100 Mpc)3 volume simulation with 2 × 18203 resolution elements, and 370 objects in TNG300 - a ˜(300 Mpc)3 volume simulation with 2 × 25003 resolution elements. The z = 0 metallicity profiles agree with observations, and the enrichment history is consistent with observational data going beyond z ˜ 1, showing nearly no metallicity evolution. The abundance profiles vary only minimally within the cluster samples, especially in the outskirts with a relative scatter of ˜ 15 per cent. The average metallicity profile flattens towards the centre, where we find a logarithmic slope of -0.1 compared to -0.5 in the outskirts. Cool core clusters have more centrally peaked metallicity profiles (˜0.8 solar) compared to non-cool core systems (˜0.5 solar), similar to observational trends. Si/Fe and O/Fe radial profiles follow positive gradients. The outer abundance profiles do not evolve below z ˜ 2, whereas the inner profiles flatten towards z = 0. More than ˜ 80 per cent of the metals in the ICM have been accreted from the proto-cluster environment, which has been enriched to ˜0.1 solar already at z ˜ 2. We conclude that the intra-cluster metal distribution is uniform among our cluster sample, nearly time-invariant in the outskirts for more than 10 Gyr, and forms through a universal enrichment history.

Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator

NASA Astrophysics Data System (ADS)

Zhang, Zhiwang; Tian, Ye; Cheng, Ying; Liu, Xiaojun; Christensen, Johan

2017-12-01

Topologically protected wave engineering in artificially structured media resides at the frontier of ongoing metamaterials research, which is inspired by quantum mechanics. Acoustic analogs of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation by means of robust edge mode excitations through analogies drawn to exotic quantum states. A variety of artificial acoustic systems hosting topological edge states have been proposed analogous to the quantum Hall effect, topological insulators, and Floquet topological insulators in electronic systems. However, those systems were characterized by a fixed geometry and a very narrow frequency response, which severely hinders the exploration and design of useful applications. Here we establish acoustic multipolar pseudospin states as an engineering degree of freedom in time-reversal invariant flow-free phononic crystals and develop reconfigurable topological insulators through rotation of their meta-atoms and reshaping of the metamolecules. Specifically, we show how rotation forms man-made snowflakelike molecules, whose topological phase mimics pseudospin-down (pseudospin-up) dipolar and quadrupolar states, which are responsible for a plethora of robust edge confined properties and topological controlled refraction disobeying Snell's law.

Topologically nontrivial Fermi regions and their novel electromagnetic response properties

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Zhang, Xiao

In the last decade, there has been a surge of interest in the application of topology to condensed matter physics. So far, most studies have been concerned with the novel properties that arise due to nontrivial band topology, i.e Quantum Anomalous Hall and Z2 topological insulators (TIs). In this talk, I shall describe another context where nontrivial topology also leads to interesting, measurable effects. Within the semi-classical Boltzmann approach, it can be shown that a topologically nontrivial Fermi sea region generically exhibits a non-monotonic nonlinear electromagnetic response in the limit of low chemical potential. Such topologically nontrivial regions of filled states can arise in experimentally realized TI heterostructures or materials with large Rashba splitting, i.e. BiTeI, where the Fermi sea is not simply connected. A non-monotonic electromagnetic response implies regimes of negative differential resistance, which have important applications in technologies involving microwave generation, like motion sensing and radio astronomy. We hope that nontrivial Fermi sea topology will hence provide another route for the realization of such technologies.

Protein structure similarity from Principle Component Correlation analysis.

PubMed

Zhou, Xiaobo; Chou, James; Wong, Stephen T C

2006-01-25

Owing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology. Currently, the structural similarity between two proteins is measured by the root-mean-square-deviation (RMSD) in their best-superimposed atomic coordinates. RMSD is the golden rule of measuring structural similarity when the structures are nearly identical; it, however, fails to detect the higher order topological similarities in proteins evolved into different shapes. We propose new algorithms for extracting geometrical invariants of proteins that can be effectively used to identify homologous protein structures or topologies in order to quantify both close and remote structural similarities. We measure structural similarity between proteins by correlating the principle components of their secondary structure interaction matrix. In our approach, the Principle Component Correlation (PCC) analysis, a symmetric interaction matrix for a protein structure is constructed with relationship parameters between secondary elements that can take the form of distance, orientation, or other relevant structural invariants. When using a distance-based construction in the presence or absence of encoded N to C terminal sense, there are strong correlations between the principle components of interaction matrices of structurally or topologically similar proteins. The PCC method is extensively tested for protein structures that belong to the same topological class but are significantly different by RMSD measure. The PCC analysis can also differentiate proteins having similar shapes but different topological arrangements. Additionally, we demonstrate that when using two independently defined interaction matrices, comparison of their maximum eigenvalues can be highly effective in clustering structurally or topologically similar proteins. We believe that the PCC analysis of interaction matrix is highly flexible in adopting various structural parameters for protein structure comparison.

Unique topological characterization of braided magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yeates, A. R.; Hornig, G.

We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a cross-section of the magnetic field, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the cross-section yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove thatmore » it uniquely characterizes the field line mapping and hence the magnetic topology.« less

Topological superconductivity in the extended Kitaev-Heisenberg model

NASA Astrophysics Data System (ADS)

Schmidt, Johann; Scherer, Daniel D.; Black-Schaffer, Annica M.

2018-01-01

We study superconducting pairing in the doped Kitaev-Heisenberg model by taking into account the recently proposed symmetric off-diagonal exchange Γ . By performing a mean-field analysis, we classify all possible superconducting phases in terms of symmetry, explicitly taking into account effects of spin-orbit coupling. Solving the resulting gap equations self-consistently, we map out a phase diagram that involves several topologically nontrivial states. For Γ <0 , we find a competition between a time-reversal symmetry-breaking chiral phase with Chern number ±1 and a time-reversal symmetric nematic phase that breaks the rotational symmetry of the lattice. On the other hand, for Γ ≥0 we find a time-reversal symmetric phase that preserves all the lattice symmetries, thus yielding clearly distinguishable experimental signatures for all superconducting phases. Both of the time-reversal symmetric phases display a transition to a Z2 nontrivial phase at high doping levels. Finally, we also include a symmetry-allowed spin-orbit coupling kinetic energy and show that it destroys a tentative symmetry-protected topological order at lower doping levels. However, it can be used to tune the time-reversal symmetric phases into a Z2 nontrivial phase even at lower doping.

Disorder enabled band structure engineering of a topological insulator surface

DOE PAGES

Xu, Yishuai; Chiu, Janet; Miao, Lin; ...

2017-02-03

Three-dimensional topological insulators are bulk insulators with Z 2 topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numerical simulations and scanning tunnelling microscopy data to show that these resonance states have significance well beyond themore » localized regime usually associated with impurity bands. Lastly, at native densities in the model Bi 2X 3 (X=Bi, Te) compounds, defect resonance states are predicted to generate a new quantum basis for an emergent electron gas that supports diffusive electrical transport.« less

Topological photonic crystals with zero Berry curvature

NASA Astrophysics Data System (ADS)

Liu, Feng; Deng, Hai-Yao; Wakabayashi, Katsunori

2018-02-01

Topological photonic crystals are designed based on the concept of Zak's phase rather than the topological invariants such as the Chern number and spin Chern number, which rely on the existence of a nonvanishing Berry curvature. Our photonic crystals (PCs) are made of pure dielectrics and sit on a square lattice obeying the C4 v point-group symmetry. Two varieties of PCs are considered: one closely resembles the electronic two-dimensional Su-Schrieffer-Heeger model, and the other continues as an extension of this analogy. In both cases, the topological transitions are induced by adjusting the lattice constants. Topological edge modes (TEMs) are shown to exist within the nontrivial photonic band gaps on the termination of those PCs. The high efficiency of these TEMs transferring electromagnetic energy against several types of disorders has been demonstrated using the finite-element method.

Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Chandran, Anushya; Burnell, F. J.; Sondhi, S. L.

2013-03-01

We consider the non-equilibrium dynamics of topologically ordered systems, such as spin liquids, driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now without the presence of symmetry breaking and a local order parameter. The non-equilibrium dynamics near the critical point is universal in a particular scaling limit. The late stages of the process are seen to exhibit slow, quantum coarsening dynamics for the extended string-nets characterizing the topological phase, a potentially interesting signature of topological order. Certain gapped degrees of freedom that could potentially destroy coarsening are, at worst, dangerously irrelevant in the scaling limit. We also note a time dependent amplification of the energy splitting between topologically degenerate states on closed manifolds. We illustrate these phenomena in the context of particular phase transitions out of the abelian Z2 topologically ordered phase of the toric code, and the non-abelian SU(2)k ordered phases of the relevant Levin-Wen models. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915 and DMR 10-06608.

Saddle-like topological surface states on the T T'X family of compounds (T , T' = Transition metal, X =Si , Ge)

NASA Astrophysics Data System (ADS)

Singh, Bahadur; Zhou, Xiaoting; Lin, Hsin; Bansil, Arun

2018-02-01

Topological nodal-line semimetals are exotic conductors that host symmetry-protected conducting nodal lines in their bulk electronic spectrum and nontrivial drumhead states on the surface. Based on first-principles calculations and an effective model analysis, we identify the presence of topological nodal-line semimetal states in the low crystalline symmetric T T'X family of compounds (T ,T' = transition metal, X = Si or Ge) in the absence of spin-orbit coupling (SOC). Taking ZrPtGe as an exemplar system, we show that owing to small lattice symmetry this material harbors a single nodal line on the ky=0 plane with large energy dispersion and unique drumhead surface state with a saddlelike energy dispersion. When the SOC is included, the nodal line gaps out and the system transitions to a strong topological insulator state with Z2=(1 ;000 ) . The topological surface state evolves from the drumhead surface state via the sharing of its saddlelike energy dispersion within the bulk energy gap. These features differ remarkably from those of the currently known topological surface states in topological insulators such as Bi2Se3 with Dirac-cone-like energy dispersions.

Singularity and stability in a periodic system of particle accelerators

NASA Astrophysics Data System (ADS)

Cai, Yunhai

2018-05-01

We study the single-particle dynamics in a general and parametrized alternating-gradient cell with zero chromaticity using the Lie algebra method. To our surprise, the first-order perturbation of the sextupoles largely determines the dynamics away from the major resonances. The dynamic aperture can be estimated from the topology and geometry of the phase space. In the linearly normalized phase space, it is scaled according to A ¯ ∝ϕ √{L } , where ϕ is the bending angle and L the length of the cell. For the 2 degrees of freedom with equal betatron tunes, the analytical perturbation theory leads us to the invariant or quasi-invariant tori, which play an important role in determining the stable volume in the four-dimensional phase space.

Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1

NASA Astrophysics Data System (ADS)

Dalmazi, Denis; dos Santos, A. L. R.; Ghosh, Subir; Mendonça, E. L.

2017-09-01

There are two covariant descriptions of massless spin-2 particles in D=3+1 via a symmetric rank-2 tensor: the linearized Einstein-Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized new massive gravity (NMG) in D=2+1 via Kaluza-Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the WTDIFF model to a linearized scalar-tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 self-dual models. Moreover, we examine the singular replacement h_{μ ν } → h_{μ ν } - η _{μ ν }h/D and prove that it leads to consistent massive spin-2 models in D=2+1. They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern-Simons term (in TMG) are invariant under longitudinal reparametrizations δ h_{μ ν } = partial _{μ }partial _{ν }ζ , which is not a symmetry of the WTDIFF Einstein-Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like 1/p^2 for large momentum.

Application of modern tensor calculus to engineered domain structures. 1. Calculation of tensorial covariants.

PubMed

Kopský, Vojtech

2006-03-01

This article is a roadmap to a systematic calculation and tabulation of tensorial covariants for the point groups of material physics. The following are the essential steps in the described approach to tensor calculus. (i) An exact specification of the considered point groups by their embellished Hermann-Mauguin and Schoenflies symbols. (ii) Introduction of oriented Laue classes of magnetic point groups. (iii) An exact specification of matrix ireps (irreducible representations). (iv) Introduction of so-called typical (standard) bases and variables -- typical invariants, relative invariants or components of the typical covariants. (v) Introduction of Clebsch-Gordan products of the typical variables. (vi) Calculation of tensorial covariants of ascending ranks with consecutive use of tables of Clebsch-Gordan products. (vii) Opechowski's magic relations between tensorial decompositions. These steps are illustrated for groups of the tetragonal oriented Laue class D(4z) -- 4(z)2(x)2(xy) of magnetic point groups and for tensors up to fourth rank.

Dichromatic State Sum Models for Four-Manifolds from Pivotal Functors

NASA Astrophysics Data System (ADS)

Bärenz, Manuel; Barrett, John

2017-11-01

A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed.

Dichromatic State Sum Models for Four-Manifolds from Pivotal Functors

NASA Astrophysics Data System (ADS)

Bärenz, Manuel; Barrett, John

2018-06-01

A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed.

SL(2,R) duality-symmetric action for electromagnetic theory with electric and magnetic sources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Choonkyu, E-mail: cklee@phya.snu.ac.kr; School of Physics, Korea Institute for Advanced Study, Seoul 130-722; Min, Hyunsoo, E-mail: hsmin@dirac.uos.ac.kr

2013-12-15

For the SL(2,R) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials A{sup μ} and B{sup μ} in a judicious way. On the two potentials A{sup μ} and B{sup μ} the SL(2,R) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,Z)-invariant action. Also given is a Zwanziger-type action for SL(2,R) duality-invariant Born–Infeld electrodynamics which can be important for D-brane dynamics in string theory. -- Highlights: •We formulatemore » a local, manifestly duality-symmetric, Zwanziger-type action. •Maxwell electrodynamics is generalized to include dilaton and axion fields. •SL(2,R) symmetry is manifest. •We formulate a local, manifestly duality-symmetric, nonlinear Born–Infeld action with SL(2,R) symmetry.« less

Persistent homology analysis of ion aggregations and hydrogen-bonding networks.

PubMed

Xia, Kelin

2018-05-16

Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and their associated water hydrogen-bonding networks still remains a challenging problem. In this paper, a newly-invented mathematical method called persistent homology is introduced, for the first time, to quantitatively analyze the intrinsic topological properties of ion aggregation systems and hydrogen-bonding networks. The two most distinguishable properties of persistent homology analysis of assembly systems are as follows. First, it does not require a predefined bond length to construct the ion or hydrogen-bonding network. Persistent homology results are determined by the morphological structure of the data only. Second, it can directly measure the size of circles or holes in ion aggregates and hydrogen-bonding networks. To validate our model, we consider two well-studied systems, i.e., NaCl and KSCN solutions, generated from molecular dynamics simulations. They are believed to represent two morphological types of aggregation, i.e., local clusters and extended ion networks. It has been found that the two aggregation types have distinguishable topological features and can be characterized by our topological model very well. Further, we construct two types of networks, i.e., O-networks and H2O-networks, for analyzing the topological properties of hydrogen-bonding networks. It is found that for both models, KSCN systems demonstrate much more dramatic variations in their local circle structures with a concentration increase. A consistent increase of large-sized local circle structures is observed and the sizes of these circles become more and more diverse. In contrast, NaCl systems show no obvious increase of large-sized circles. Instead a consistent decline of the average size of the circle structures is observed and the sizes of these circles become more and more uniform with a concentration increase. As far as we know, these unique intrinsic topological features in ion aggregation systems have never been pointed out before. More importantly, our models can be directly used to quantitatively analyze the intrinsic topological invariants, including circles, loops, holes, and cavities, of any network-like structures, such as nanomaterials, colloidal systems, biomolecular assemblies, among others. These topological invariants cannot be described by traditional graph and network models.

Symmetry breaking: a tool to unveil the topology of chaotic scattering with three degrees of freedom

NASA Astrophysics Data System (ADS)

Jung, Christof; Zapfe, W. P. Karel; Merlo, Olivier; Seligman, T. H.

2010-12-01

We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.

Symmetry breaking: a tool to unveil the topology of chaotic scattering with three degrees of freedom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jung, Christof; Zapfe, W. P. Karel; Seligman, T. H.

2010-12-23

We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.

z -Weyl gravity in higher dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moon, Taeyoon; Oh, Phillial, E-mail: dpproject@skku.edu, E-mail: ploh@skku.edu

We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the foliation preserving diffeomorphism invariance adapted to the extra dimensions, thus keeping the general covariance only for the four dimensional spacetime. The conformally invariant gravity can be constructed with an extra (Weyl) scalar field and a real parameter z which describes the degree of anisotropy of conformal transformation between the spacetime and extra dimensional metrics. In the zero mode effective 4D action, it reduces tomore » four-dimensional scalar-tensor theory coupled with nonlinear sigma model described by extra dimensional metrics. There are no restrictions on the value of z at the classical level and possible applications to the cosmological constant problem with a specific choice of z are discussed.« less

First observation of forward Z → b b bar production in pp collisions at √{ s } = 8 TeV

NASA Astrophysics Data System (ADS)

Aaij, R.; Adeva, B.; Adinolfi, M.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Alfonso Albero, A.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Andreassi, G.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Archilli, F.; d'Argent, P.; Arnau Romeu, J.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Babuschkin, I.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baker, S.; Balagura, V.; Baldini, W.; Baranov, A.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Baryshnikov, F.; Batozskaya, V.; Battista, V.; Bay, A.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Beiter, A.; Bel, L. J.; Beliy, N.; Bellee, V.; Belloli, N.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Beranek, S.; Berezhnoy, A.; Bernet, R.; Berninghoff, D.; Bertholet, E.; Bertolin, A.; Betancourt, C.; Betti, F.; Bettler, M.-O.; van Beuzekom, M.; Bezshyiko, Ia.; Bifani, S.; Billoir, P.; Birnkraut, A.; Bitadze, A.; Bizzeti, A.; Bjørn, M.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Boettcher, T.; Bondar, A.; Bondar, N.; Bonivento, W.; Bordyuzhin, I.; Borgheresi, A.; Borghi, S.; Borisyak, M.; Borsato, M.; Bossu, F.; Boubdir, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Braun, S.; Britton, T.; Brodzicka, J.; Brundu, D.; Buchanan, E.; Burr, C.; Bursche, A.; Buytaert, J.; Byczynski, W.; Cadeddu, S.; Cai, H.; Calabrese, R.; Calladine, R.; Calvi, M.; Calvo Gomez, M.; Camboni, A.; Campana, P.; Campora Perez, D. H.; Capriotti, L.; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carniti, P.; Carson, L.; Carvalho Akiba, K.; Casse, G.; Cassina, L.; Castillo Garcia, L.; Cattaneo, M.; Cavallero, G.; Cenci, R.; Chamont, D.; Chapman, M. G.; Charles, M.; Charpentier, Ph.; Chatzikonstantinidis, G.; Chefdeville, M.; Chen, S.; Cheung, S. F.; Chitic, S.-G.; Chobanova, V.; Chrzaszcz, M.; Chubykin, A.; Ciambrone, P.; Cid Vidal, X.; Ciezarek, G.; Clarke, P. E. L.; Clemencic, M.; Cliff, H. V.; Closier, J.; Cogan, J.; Cogneras, E.; Cogoni, V.; Cojocariu, L.; Collins, P.; Colombo, T.; Comerma-Montells, A.; Contu, A.; Cook, A.; Coombs, G.; Coquereau, S.; Corti, G.; Corvo, M.; Costa Sobral, C. M.; Couturier, B.; Cowan, G. A.; Craik, D. C.; Crocombe, A.; Cruz Torres, M.; Currie, R.; D'Ambrosio, C.; Da Cunha Marinho, F.; Dall'Occo, E.; Dalseno, J.; Davis, A.; De Aguiar Francisco, O.; De Capua, S.; De Cian, M.; De Miranda, J. M.; De Paula, L.; De Serio, M.; De Simone, P.; Dean, C. T.; Decamp, D.; Del Buono, L.; Dembinski, H.-P.; Demmer, M.; Dendek, A.; Derkach, D.; Deschamps, O.; Dettori, F.; Dey, B.; Di Canto, A.; Di Nezza, P.; Dijkstra, H.; Dordei, F.; Dorigo, M.; Dosil Suárez, A.; Douglas, L.; Dovbnya, A.; Dreimanis, K.; Dufour, L.; Dujany, G.; Durante, P.; Dzhelyadin, R.; Dziewiecki, M.; Dziurda, A.; Dzyuba, A.; Easo, S.; Ebert, M.; Egede, U.; Egorychev, V.; Eidelman, S.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; Ely, S.; Esen, S.; Evans, H. M.; Evans, T.; Falabella, A.; Farley, N.; Farry, S.; Fazzini, D.; Federici, L.; Ferguson, D.; Fernandez, G.; Fernandez Declara, P.; Fernandez Prieto, A.; Ferrari, F.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fini, R. A.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fleuret, F.; Fohl, K.; Fontana, M.; Fontanelli, F.; Forshaw, D. C.; Forty, R.; Franco Lima, V.; Frank, M.; Frei, C.; Fu, J.; Funk, W.; Furfaro, E.; Färber, C.; Gabriel, E.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; Garcia Martin, L. M.; García Pardiñas, J.; Garra Tico, J.; Garrido, L.; Garsed, P. J.; Gascon, D.; Gaspar, C.; Gavardi, L.; Gazzoni, G.; Gerick, D.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianì, S.; Gibson, V.; Girard, O. G.; Giubega, L.; Gizdov, K.; Gligorov, V. V.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gorelov, I. V.; Gotti, C.; Govorkova, E.; Grabowski, J. P.; Graciani Diaz, R.; Granado Cardoso, L. A.; Graugés, E.; Graverini, E.; Graziani, G.; Grecu, A.; Greim, R.; Griffith, P.; Grillo, L.; Gruber, L.; Gruberg Cazon, B. R.; Grünberg, O.; Gushchin, E.; Guz, Yu.; Gys, T.; Göbel, C.; Hadavizadeh, T.; Hadjivasiliou, C.; Haefeli, G.; Haen, C.; Haines, S. C.; Hamilton, B.; Han, X.; Hancock, T. H.; Hansmann-Menzemer, S.; Harnew, N.; Harnew, S. T.; Harrison, J.; Hasse, C.; Hatch, M.; He, J.; Hecker, M.; Heinicke, K.; Heister, A.; Hennessy, K.; Henrard, P.; Henry, L.; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hombach, C.; Hopchev, P. H.; Huard, Z. C.; Hulsbergen, W.; Humair, T.; Hushchyn, M.; Hutchcroft, D.; Ibis, P.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jalocha, J.; Jans, E.; Jawahery, A.; Jiang, F.; John, M.; Johnson, D.; Jones, C. R.; Joram, C.; Jost, B.; Jurik, N.; Kandybei, S.; Karacson, M.; Kariuki, J. M.; Karodia, S.; Kazeev, N.; Kecke, M.; Kelsey, M.; Kenzie, M.; Ketel, T.; Khairullin, E.; Khanji, B.; Khurewathanakul, C.; Kirn, T.; Klaver, S.; Klimaszewski, K.; Klimkovich, T.; Koliiev, S.; Kolpin, M.; Komarov, I.; Kopecna, R.; Koppenburg, P.; Kosmyntseva, A.; Kotriakhova, S.; Kozeiha, M.; Kravchuk, L.; Kreps, M.; Krokovny, P.; Kruse, F.; Krzemien, W.; Kucewicz, W.; Kucharczyk, M.; Kudryavtsev, V.; Kuonen, A. K.; Kurek, K.; Kvaratskheliya, T.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lanfranchi, G.; Langenbruch, C.; Latham, T.; Lazzeroni, C.; Le Gac, R.; Leflat, A.; Lefrançois, J.; Lefèvre, R.; Lemaitre, F.; Lemos Cid, E.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, P.-R.; Li, T.; Li, Y.; Li, Z.; Likhomanenko, T.; Lindner, R.; Lionetto, F.; Lisovskyi, V.; Liu, X.; Loh, D.; Loi, A.; Longstaff, I.; Lopes, J. H.; Lucchesi, D.; Lucio Martinez, M.; Luo, H.; Lupato, A.; Luppi, E.; Lupton, O.; Lusiani, A.; Lyu, X.; Machefert, F.; Maciuc, F.; Macko, V.; Mackowiak, P.; Maddrell-Mander, S.; Maev, O.; Maguire, K.; Maisuzenko, D.; Majewski, M. W.; Malde, S.; Malinin, A.; Maltsev, T.; Manca, G.; Mancinelli, G.; Manning, P.; Marangotto, D.; Maratas, J.; Marchand, J. F.; Marconi, U.; Marin Benito, C.; Marinangeli, M.; Marino, P.; Marks, J.; Martellotti, G.; Martin, M.; Martinelli, M.; Martinez Santos, D.; Martinez Vidal, F.; Martins Tostes, D.; Massacrier, L. M.; Massafferri, A.; Matev, R.; Mathad, A.; Mathe, Z.; Matteuzzi, C.; Mauri, A.; Maurice, E.; Maurin, B.; Mazurov, A.; McCann, M.; McNab, A.; McNulty, R.; Mead, J. V.; Meadows, B.; Meaux, C.; Meier, F.; Meinert, N.; Melnychuk, D.; Merk, M.; Merli, A.; Michielin, E.; Milanes, D. A.; Millard, E.; Minard, M.-N.; Minzoni, L.; Mitzel, D. S.; Mogini, A.; Molina Rodriguez, J.; Mombächer, T.; Monroy, I. A.; Monteil, S.; Morandin, M.; Morello, M. J.; Morgunova, O.; Moron, J.; Morris, A. B.; Mountain, R.; Muheim, F.; Mulder, M.; Müller, D.; Müller, J.; Müller, K.; Müller, V.; Naik, P.; Nakada, T.; Nandakumar, R.; Nandi, A.; Nasteva, I.; Needham, M.; Neri, N.; Neubert, S.; Neufeld, N.; Neuner, M.; Nguyen, T. D.; Nguyen-Mau, C.; Nieswand, S.; Niet, R.; Nikitin, N.; Nikodem, T.; Nogay, A.; O'Hanlon, D. P.; Oblakowska-Mucha, A.; Obraztsov, V.; Ogilvy, S.; Oldeman, R.; Onderwater, C. J. G.; Ossowska, A.; Otalora Goicochea, J. M.; Owen, P.; Oyanguren, A.; Pais, P. R.; Palano, A.; Palutan, M.; Papanestis, A.; Pappagallo, M.; Pappalardo, L. L.; Parker, W.; Parkes, C.; Passaleva, G.; Pastore, A.; Patel, M.; Patrignani, C.; Pearce, A.; Pellegrino, A.; Penso, G.; Pepe Altarelli, M.; Perazzini, S.; Perret, P.; Pescatore, L.; Petridis, K.; Petrolini, A.; Petrov, A.; Petruzzo, M.; Picatoste Olloqui, E.; Pietrzyk, B.; Pikies, M.; Pinci, D.; Pisani, F.; Pistone, A.; Piucci, A.; Placinta, V.; Playfer, S.; Plo Casasus, M.; Polci, F.; Poli Lener, M.; Poluektov, A.; Polyakov, I.; Polycarpo, E.; Pomery, G. J.; Ponce, S.; Popov, A.; Popov, D.; Poslavskii, S.; Potterat, C.; Price, E.; Prisciandaro, J.; Prouve, C.; Pugatch, V.; Puig Navarro, A.; Pullen, H.; Punzi, G.; Qian, W.; Quagliani, R.; Quintana, B.; Rachwal, B.; Rademacker, J. H.; Rama, M.; Ramos Pernas, M.; Rangel, M. S.; Raniuk, I.; Ratnikov, F.; Raven, G.; Ravonel Salzgeber, M.; Reboud, M.; Redi, F.; Reichert, S.; dos Reis, A. C.; Remon Alepuz, C.; Renaudin, V.; Ricciardi, S.; Richards, S.; Rihl, M.; Rinnert, K.; Rives Molina, V.; Robbe, P.; Robert, A.; Rodrigues, A. B.; Rodrigues, E.; Rodriguez Lopez, J. A.; Rodriguez Perez, P.; Rogozhnikov, A.; Roiser, S.; Rollings, A.; Romanovskiy, V.; Romero Vidal, A.; Ronayne, J. W.; Rotondo, M.; Rudolph, M. S.; Ruf, T.; Ruiz Valls, P.; Ruiz Vidal, J.; Saborido Silva, J. J.; Sadykhov, E.; Sagidova, N.; Saitta, B.; Salustino Guimaraes, V.; Sanchez Mayordomo, C.; Sanmartin Sedes, B.; Santacesaria, R.; Santamarina Rios, C.; Santimaria, M.; Santovetti, E.; Sarpis, G.; Sarti, A.; Satriano, C.; Satta, A.; Saunders, D. M.; Savrina, D.; Schael, S.; Schellenberg, M.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmelzer, T.; Schmidt, B.; Schneider, O.; Schopper, A.; Schreiner, H. F.; Schubert, K.; Schubiger, M.; Schune, M.-H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Semennikov, A.; Sepulveda, E. S.; Sergi, A.; Serra, N.; Serrano, J.; Sestini, L.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, V.; Siddi, B. G.; Silva Coutinho, R.; Silva de Oliveira, L.; Simi, G.; Simone, S.; Sirendi, M.; Skidmore, N.; Skwarnicki, T.; Smith, E.; Smith, I. T.; Smith, J.; Smith, M.; Soares Lavra, l.; Sokoloff, M. D.; Soler, F. J. P.; Souza De Paula, B.; Spaan, B.; Spradlin, P.; Sridharan, S.; Stagni, F.; Stahl, M.; Stahl, S.; Stefko, P.; Stefkova, S.; Steinkamp, O.; Stemmle, S.; Stenyakin, O.; Stepanova, M.; Stevens, H.; Stone, S.; Storaci, B.; Stracka, S.; Stramaglia, M. E.; Straticiuc, M.; Straumann, U.; Sun, J.; Sun, L.; Sutcliffe, W.; Swientek, K.; Syropoulos, V.; Szczekowski, M.; Szumlak, T.; Szymanski, M.; T'Jampens, S.; Tayduganov, A.; Tekampe, T.; Tellarini, G.; Teubert, F.; Thomas, E.; van Tilburg, J.; Tilley, M. J.; Tisserand, V.; Tobin, M.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Toriello, F.; Tourinho Jadallah Aoude, R.; Tournefier, E.; Traill, M.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tully, A.; Tuning, N.; Ukleja, A.; Usachov, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagner, A.; Vagnoni, V.; Valassi, A.; Valat, S.; Valenti, G.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vecchi, S.; van Veghel, M.; Velthuis, J. J.; Veltri, M.; Veneziano, G.; Venkateswaran, A.; Verlage, T. A.; Vernet, M.; Vesterinen, M.; Viana Barbosa, J. V.; Viaud, B.; Vieira, D.; Vieites Diaz, M.; Viemann, H.; Vilasis-Cardona, X.; Vitti, M.; Volkov, V.; Vollhardt, A.; Voneki, B.; Vorobyev, A.; Vorobyev, V.; Voß, C.; de Vries, J. A.; Vázquez Sierra, C.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wang, J.; Ward, D. R.; Wark, H. M.; Watson, N. K.; Websdale, D.; Weiden, A.; Whitehead, M.; Wicht, J.; Wilkinson, G.; Wilkinson, M.; Williams, M.; Williams, M. P.; Williams, M.; Williams, T.; Wilson, F. F.; Wimberley, J.; Winn, M.; Wishahi, J.; Wislicki, W.; Witek, M.; Wormser, G.; Wotton, S. A.; Wraight, K.; Wyllie, K.; Xie, Y.; Xu, Z.; Yang, Z.; Yang, Z.; Yao, Y.; Yin, H.; Yu, J.; Yuan, X.; Yushchenko, O.; Zarebski, K. A.; Zavertyaev, M.; Zhang, L.; Zhang, Y.; Zhelezov, A.; Zheng, Y.; Zhu, X.; Zhukov, V.; Zonneveld, J. B.; Zucchelli, S.; LHCb Collaboration

2018-01-01

The decay Z → b b bar is reconstructed in pp collision data, corresponding to 2 fb-1 of integrated luminosity, collected by the LHCb experiment at a centre-of-mass energy of √{ s } = 8 TeV. The product of the Z production cross-section and the Z → b b bar branching fraction is measured for candidates in the fiducial region defined by two particle-level b-quark jets with pseudorapidities in the range 2.2 < η < 4.2, with transverse momenta pT > 20 GeV and dijet invariant mass in the range 45

Godbillon Vey Helicity and Magnetic Helicity in Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Webb, G. M.; Hu, Q.; Anco, S.; Zank, G. P.

2017-12-01

The Godbillon-Vey invariant arises in homology theory, and algebraic topology, where conditions for a layered family of 2D surfaces forms a 3D manifold were elucidated. The magnetic Godbillon-Vey helicity invariant in magnetohydrodynamics (MHD) is a helicity invariant that occurs for flows, in which the magnetic helicity density hm= A\\cdotB=0 where A is the magnetic vector potential and B is the magnetic induction. Our purpose is to elucidate the evolution of the magnetic Godbillon-Vey field η =A×B/|A|2 and the Godbillon-Vey helicity hgv}= η \\cdot∇ × η in general MHD flows in which the magnetic helicity hm≠q 0. It is shown that hm acts as a source term in the Godbillon-Vey helicity transport equation, in which hm is coupled to hgv via the shear tensor of the background flow. The transport equation for hgv depends on the electric field potential ψ , which is related to the gauge for A, which takes its simplest form for the advected A gauge in which ψ =A\\cdot u where u is the fluid velocity.

Topology determines force distributions in one-dimensional random spring networks.

PubMed

Heidemann, Knut M; Sageman-Furnas, Andrew O; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F; Wardetzky, Max

2018-02-01

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

Topology determines force distributions in one-dimensional random spring networks

NASA Astrophysics Data System (ADS)

Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max

2018-02-01

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N ,z ) . Despite the universal properties of such (N ,z ) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

Geometry and physics

PubMed Central

Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel

2010-01-01

We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740

Measures for brain connectivity analysis: nodes centrality and their invariant patterns

NASA Astrophysics Data System (ADS)

da Silva, Laysa Mayra Uchôa; Baltazar, Carlos Arruda; Silva, Camila Aquemi; Ribeiro, Mauricio Watanabe; de Aratanha, Maria Adelia Albano; Deolindo, Camila Sardeto; Rodrigues, Abner Cardoso; Machado, Birajara Soares

2017-07-01

The high dynamical complexity of the brain is related to its small-world topology, which enable both segregated and integrated information processing capabilities. Several measures of connectivity estimation have already been employed to characterize functional brain networks from multivariate electrophysiological data. However, understanding the properties of each measure that lead to a better description of the real topology and capture the complex phenomena present in the brain remains challenging. In this work we compared four nonlinear connectivity measures and show that each method characterizes distinct features of brain interactions. The results suggest an invariance of global network parameters from different behavioral states and that more complete description may be reached considering local features, independently of the connectivity measure employed. Our findings also point to future perspectives in connectivity studies that combine distinct and complementary dependence measures in assembling higher dimensions manifolds.

Measurements of the p p→ ZZ production cross section and the Z→ 4ℓ branching fraction, and constraints on anomalous triple gauge couplings at √{s} = 13 {TeV}

NASA Astrophysics Data System (ADS)

Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Ambrogi, F.; Asilar, E.; Bergauer, T.; Brandstetter, J.; Brondolin, E.; Dragicevic, M.; Erö, J.; Flechl, M.; Friedl, M.; Frühwirth, R.; Ghete, V. M.; Grossmann, J.; Hrubec, J.; Jeitler, M.; König, A.; Krammer, N.; Krätschmer, I.; Liko, D.; Madlener, T.; Mikulec, I.; Pree, E.; Rabady, D.; Rad, N.; Rohringer, H.; Schieck, J.; Schöfbeck, R.; Spanring, M.; Spitzbart, D.; Waltenberger, W.; Wittmann, J.; Wulz, C.-E.; Zarucki, M.; Chekhovsky, V.; Mossolov, V.; Gonzalez, J. Suarez; De Wolf, E. A.; Di Croce, D.; Janssen, X.; Lauwers, J.; Van De Klundert, M.; Van Haevermaet, H.; Van Mechelen, P.; Van Remortel, N.; Zeid, S. Abu; Blekman, F.; D'Hondt, J.; De Bruyn, I.; De Clercq, J.; Deroover, K.; Flouris, G.; Lontkovskyi, D.; Lowette, S.; Moortgat, S.; Moreels, L.; Python, Q.; Skovpen, K.; Tavernier, S.; Van Doninck, W.; Van Mulders, P.; Van Parijs, I.; Brun, H.; Clerbaux, B.; De Lentdecker, G.; Delannoy, H.; Fasanella, G.; Favart, L.; Goldouzian, R.; Grebenyuk, A.; Karapostoli, G.; Lenzi, T.; Luetic, J.; Maerschalk, T.; Marinov, A.; Randle-conde, A.; Seva, T.; Velde, C. Vander; Vanlaer, P.; Vannerom, D.; Yonamine, R.; Zenoni, F.; Zhang, F.; Cimmino, A.; Cornelis, T.; Dobur, D.; Fagot, A.; Gul, M.; Khvastunov, I.; Poyraz, D.; Roskas, C.; Salva, S.; Tytgat, M.; Verbeke, W.; Zaganidis, N.; Bakhshiansohi, H.; Bondu, O.; Brochet, S.; Bruno, G.; Caputo, C.; Caudron, A.; De Visscher, S.; Delaere, C.; Delcourt, M.; Francois, B.; Giammanco, A.; Jafari, A.; Komm, M.; Krintiras, G.; Lemaitre, V.; Magitteri, A.; Mertens, A.; Musich, M.; Piotrzkowski, K.; Quertenmont, L.; Marono, M. Vidal; Wertz, S.; Beliy, N.; Aldá Júnior, W. L.; Alves, F. L.; Alves, G. A.; Brito, L.; Martins Junior, M. Correa; Hensel, C.; Moraes, A.; Pol, M. E.; Rebello Teles, P.; Das Chagas, E. Belchior Batista; Carvalho, W.; Chinellato, J.; Custódio, A.; Da Costa, E. M.; Da Silveira, G. G.; De Jesus Damiao, D.; De Souza, S. Fonseca; Guativa, L. M. Huertas; Malbouisson, H.; De Almeida, M. Melo; Herrera, C. Mora; Mundim, L.; Nogima, H.; Santoro, A.; Sznajder, A.; Tonelli Manganote, E. J.; Da Silva De Araujo, F. Torres; Pereira, A. Vilela; Ahuja, S.; Bernardes, C. A.; Tomei, T. R. Fernandez Perez; Gregores, E. M.; Mercadante, P. G.; Novaes, S. F.; Padula, Sandra S.; Abad, D. Romero; Vargas, J. C. Ruiz; Aleksandrov, A.; Hadjiiska, R.; Iaydjiev, P.; Misheva, M.; Rodozov, M.; Shopova, M.; Stoykova, S.; Sultanov, G.; Dimitrov, A.; Glushkov, I.; Litov, L.; Pavlov, B.; Petkov, P.; Fang, W.; Gao, X.; Ahmad, M.; Bian, J. G.; Chen, G. M.; Chen, H. S.; Chen, M.; Chen, Y.; Jiang, C. H.; Leggat, D.; Liao, H.; Liu, Z.; Romeo, F.; Shaheen, S. M.; Spiezia, A.; Tao, J.; Wang, C.; Wang, Z.; Yazgan, E.; Zhang, H.; Zhao, J.; Ban, Y.; Chen, G.; Li, Q.; Liu, S.; Mao, Y.; Qian, S. J.; Wang, D.; Xu, Z.; Avila, C.; Cabrera, A.; Sierra, L. F. Chaparro; Florez, C.; Hernández, C. F. González; Alvarez, J. D. Ruiz; Courbon, B.; Godinovic, N.; Lelas, D.; Puljak, I.; Cipriano, P. M. Ribeiro; Sculac, T.; Antunovic, Z.; Kovac, M.; Brigljevic, V.; Ferencek, D.; Kadija, K.; Mesic, B.; Starodumov, A.; Susa, T.; Ather, M. W.; Attikis, A.; Mavromanolakis, G.; Mousa, J.; Nicolaou, C.; Ptochos, F.; Razis, P. A.; Rykaczewski, H.; Finger, M.; Finger, M.; Jarrin, E. Carrera; Assran, Y.; Mahmoud, M. A.; Mahrous, A.; Dewanjee, R. K.; Kadastik, M.; Perrini, L.; Raidal, M.; Tiko, A.; Veelken, C.; Eerola, P.; Pekkanen, J.; Voutilainen, M.; Härkönen, J.; Järvinen, T.; Karimäki, V.; Kinnunen, R.; Lampén, T.; Lassila-Perini, K.; Lehti, S.; Lindén, T.; Luukka, P.; Tuominen, E.; Tuominiemi, J.; Tuovinen, E.; Talvitie, J.; Tuuva, T.; Besancon, M.; Couderc, F.; Dejardin, M.; Denegri, D.; Faure, J. L.; Ferri, F.; Ganjour, S.; Ghosh, S.; Givernaud, A.; Gras, P.; de Monchenault, G. Hamel; Jarry, P.; Kucher, I.; Locci, E.; Machet, M.; Malcles, J.; Negro, G.; Rander, J.; Rosowsky, A.; Sahin, M. Ö.; Titov, M.; Abdulsalam, A.; Antropov, I.; Baffioni, S.; Beaudette, F.; Busson, P.; Cadamuro, L.; Charlot, C.; de Cassagnac, R. Granier; Jo, M.; Lisniak, S.; Lobanov, A.; Blanco, J. Martin; Nguyen, M.; Ochando, C.; Ortona, G.; Paganini, P.; Pigard, P.; Regnard, S.; Salerno, R.; Sauvan, J. B.; Sirois, Y.; Leiton, A. G. Stahl; Strebler, T.; Yilmaz, Y.; Zabi, A.; Zghiche, A.; Agram, J.-L.; Andrea, J.; Bloch, D.; Brom, J.-M.; Buttignol, M.; Chabert, E. C.; Chanon, N.; Collard, C.; Conte, E.; Coubez, X.; Fontaine, J.-C.; Gelé, D.; Goerlach, U.; Jansová, M.; Bihan, A.-C. Le; Tonon, N.; Van Hove, P.; Gadrat, S.; Beauceron, S.; Bernet, C.; Boudoul, G.; Chierici, R.; Contardo, D.; Depasse, P.; El Mamouni, H.; Fay, J.; Finco, L.; Gascon, S.; Gouzevitch, M.; Grenier, G.; Ille, B.; Lagarde, F.; Laktineh, I. B.; Lethuillier, M.; Mirabito, L.; Pequegnot, A. L.; Perries, S.; Popov, A.; Sordini, V.; Vander Donckt, M.; Viret, S.; Khvedelidze, A.; Tsamalaidze, Z.; Autermann, C.; Beranek, S.; Feld, L.; Kiesel, M. 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T.; Meister, D.; Micheli, F.; Musella, P.; Nessi-Tedaldi, F.; Pandolfi, F.; Pata, J.; Pauss, F.; Perrin, G.; Perrozzi, L.; Quittnat, M.; Reichmann, M.; Schönenberger, M.; Shchutska, L.; Tavolaro, V. R.; Theofilatos, K.; Olsson, M. L. Vesterbacka; Wallny, R.; Zhu, D. H.; Aarrestad, T. K.; Amsler, C.; Canelli, M. F.; De Cosa, A.; Del Burgo, R.; Donato, S.; Galloni, C.; Hreus, T.; Kilminster, B.; Ngadiuba, J.; Pinna, D.; Rauco, G.; Robmann, P.; Salerno, D.; Seitz, C.; Takahashi, Y.; Zucchetta, A.; Candelise, V.; Doan, T. H.; Jain, Sh.; Khurana, R.; Kuo, C. M.; Lin, W.; Pozdnyakov, A.; Yu, S. S.; Kumar, Arun; Chang, P.; Chao, Y.; Chen, K. F.; Chen, P. H.; Fiori, F.; Hou, W.-S.; Hsiung, Y.; Liu, Y. F.; Lu, R.-S.; Paganis, E.; Psallidas, A.; Steen, A.; Tsai, J. f.; Asavapibhop, B.; Kovitanggoon, K.; Singh, G.; Srimanobhas, N.; Boran, F.; Cerci, S.; Damarseckin, S.; Demiroglu, Z. S.; Dozen, C.; Dumanoglu, I.; Girgis, S.; Gokbulut, G.; Guler, Y.; Hos, I.; Kangal, E. E.; Kara, O.; Topaksu, A. Kayis; Kiminsu, U.; Oglakci, M.; Onengut, G.; Ozdemir, K.; Cerci, D. Sunar; Tali, B.; Turkcapar, S.; Zorbakir, I. S.; Zorbilmez, C.; Bilin, B.; Karapinar, G.; Ocalan, K.; Yalvac, M.; Zeyrek, M.; Gülmez, E.; Kaya, M.; Kaya, O.; Tekten, S.; Yetkin, E. A.; Agaras, M. N.; Atay, S.; Cakir, A.; Cankocak, K.; Grynyov, B.; Levchuk, L.; Sorokin, P.; Aggleton, R.; Ball, F.; Beck, L.; Brooke, J. J.; Burns, D.; Clement, E.; Cussans, D.; Davignon, O.; Flacher, H.; Goldstein, J.; Grimes, M.; Heath, G. P.; Heath, H. F.; Jacob, J.; Kreczko, L.; Lucas, C.; Newbold, D. M.; Paramesvaran, S.; Poll, A.; Sakuma, T.; El Nasr-storey, S. Seif; Smith, D.; Smith, V. J.; Bell, K. W.; Belyaev, A.; Brew, C.; Brown, R. M.; Calligaris, L.; Cieri, D.; Cockerill, D. J. A.; Coughlan, J. A.; Harder, K.; Harper, S.; Olaiya, E.; Petyt, D.; Shepherd-Themistocleous, C. H.; Thea, A.; Tomalin, I. R.; Williams, T.; Auzinger, G.; Bainbridge, R.; Breeze, S.; Buchmuller, O.; Bundock, A.; Casasso, S.; Citron, M.; Colling, D.; Corpe, L.; Dauncey, P.; Davies, G.; De Wit, A.; Della Negra, M.; Di Maria, R.; Elwood, A.; Haddad, Y.; Hall, G.; Iles, G.; James, T.; Lane, R.; Laner, C.; Lyons, L.; Magnan, A.-M.; Malik, S.; Mastrolorenzo, L.; Matsushita, T.; Nash, J.; Nikitenko, A.; Palladino, V.; Pesaresi, M.; Raymond, D. M.; Richards, A.; Rose, A.; Scott, E.; Seez, C.; Shtipliyski, A.; Summers, S.; Tapper, A.; Uchida, K.; Vazquez Acosta, M.; Virdee, T.; Wardle, N.; Winterbottom, D.; Wright, J.; Zenz, S. C.; Cole, J. E.; Hobson, P. R.; Khan, A.; Kyberd, P.; Reid, I. D.; Symonds, P.; Teodorescu, L.; Turner, M.; Borzou, A.; Call, K.; Dittmann, J.; Hatakeyama, K.; Liu, H.; Pastika, N.; Smith, C.; Bartek, R.; Dominguez, A.; Buccilli, A.; Cooper, S. I.; Henderson, C.; Rumerio, P.; West, C.; Arcaro, D.; Avetisyan, A.; Bose, T.; Gastler, D.; Rankin, D.; Richardson, C.; Rohlf, J.; Sulak, L.; Zou, D.; Benelli, G.; Cutts, D.; Garabedian, A.; Hakala, J.; Heintz, U.; Hogan, J. M.; Kwok, K. H. M.; Laird, E.; Landsberg, G.; Mao, Z.; Narain, M.; Pazzini, J.; Piperov, S.; Sagir, S.; Syarif, R.; Yu, D.; Band, R.; Brainerd, C.; Burns, D.; De La Barca Sanchez, M. Calderon; Chertok, M.; Conway, J.; Conway, R.; Cox, P. T.; Erbacher, R.; Flores, C.; Funk, G.; Gardner, M.; Ko, W.; Lander, R.; Mclean, C.; Mulhearn, M.; Pellett, D.; Pilot, J.; Shalhout, S.; Shi, M.; Smith, J.; Squires, M.; Stolp, D.; Tos, K.; Tripathi, M.; Wang, Z.; Bachtis, M.; Bravo, C.; Cousins, R.; Dasgupta, A.; Florent, A.; Hauser, J.; Ignatenko, M.; Mccoll, N.; Saltzberg, D.; Schnaible, C.; Valuev, V.; Bouvier, E.; Burt, K.; Clare, R.; Ellison, J.; Gary, J. W.; Shirazi, S. M. A. Ghiasi; Hanson, G.; Heilman, J.; Jandir, P.; Kennedy, E.; Lacroix, F.; Long, O. R.; Negrete, M. Olmedo; Paneva, M. I.; Shrinivas, A.; Si, W.; Wang, L.; Wei, H.; Wimpenny, S.; Yates, B. R.; Branson, J. G.; Cittolin, S.; Derdzinski, M.; Gerosa, R.; Hashemi, B.; Holzner, A.; Klein, D.; Kole, G.; Krutelyov, V.; Letts, J.; Macneill, I.; Masciovecchio, M.; Olivito, D.; Padhi, S.; Pieri, M.; Sani, M.; Sharma, V.; Simon, S.; Tadel, M.; Vartak, A.; Wasserbaech, S.; Wood, J.; Würthwein, F.; Yagil, A.; Della Porta, G. Zevi; Amin, N.; Bhandari, R.; Bradmiller-Feld, J.; Campagnari, C.; Dishaw, A.; Dutta, V.; Franco Sevilla, M.; George, C.; Golf, F.; Gouskos, L.; Gran, J.; Heller, R.; Incandela, J.; Mullin, S. D.; Ovcharova, A.; Qu, H.; Richman, J.; Stuart, D.; Suarez, I.; Yoo, J.; Anderson, D.; Bendavid, J.; Bornheim, A.; Lawhorn, J. M.; Newman, H. B.; Nguyen, T.; Pena, C.; Spiropulu, M.; Vlimant, J. R.; Xie, S.; Zhang, Z.; Zhu, R. Y.; Andrews, M. B.; Ferguson, T.; Mudholkar, T.; Paulini, M.; Russ, J.; Sun, M.; Vogel, H.; Vorobiev, I.; Weinberg, M.; Cumalat, J. P.; Ford, W. T.; Jensen, F.; Johnson, A.; Krohn, M.; Leontsinis, S.; Mulholland, T.; Stenson, K.; Wagner, S. R.; Alexander, J.; Chaves, J.; Chu, J.; Dittmer, S.; Mcdermott, K.; Mirman, N.; Patterson, J. R.; Rinkevicius, A.; Ryd, A.; Skinnari, L.; Soffi, L.; Tan, S. M.; Tao, Z.; Thom, J.; Tucker, J.; Wittich, P.; Zientek, M.; Abdullin, S.; Albrow, M.; Apollinari, G.; Apresyan, A.; Apyan, A.; Banerjee, S.; Bauerdick, L. A. T.; Beretvas, A.; Berryhill, J.; Bhat, P. C.; Bolla, G.; Burkett, K.; Butler, J. N.; Canepa, A.; Cerati, G. B.; Cheung, H. W. K.; Chlebana, F.; Cremonesi, M.; Duarte, J.; Elvira, V. D.; Freeman, J.; Gecse, Z.; Gottschalk, E.; Gray, L.; Green, D.; Grünendahl, S.; Gutsche, O.; Harris, R. M.; Hasegawa, S.; Hirschauer, J.; Hu, Z.; Jayatilaka, B.; Jindariani, S.; Johnson, M.; Joshi, U.; Klima, B.; Kreis, B.; Lammel, S.; Lincoln, D.; Lipton, R.; Liu, M.; Liu, T.; De Sá, R. Lopes; Lykken, J.; Maeshima, K.; Magini, N.; Marraffino, J. M.; Maruyama, S.; Mason, D.; McBride, P.; Merkel, P.; Mrenna, S.; Nahn, S.; O'Dell, V.; Pedro, K.; Prokofyev, O.; Rakness, G.; Ristori, L.; Schneider, B.; Sexton-Kennedy, E.; Soha, A.; Spalding, W. J.; Spiegel, L.; Stoynev, S.; Strait, J.; Strobbe, N.; Taylor, L.; Tkaczyk, S.; Tran, N. V.; Uplegger, L.; Vaandering, E. W.; Vernieri, C.; Verzocchi, M.; Vidal, R.; Wang, M.; Weber, H. A.; Whitbeck, A.; Acosta, D.; Avery, P.; Bortignon, P.; Bourilkov, D.; Brinkerhoff, A.; Carnes, A.; Carver, M.; Curry, D.; Field, R. D.; Furic, I. K.; Konigsberg, J.; Korytov, A.; Kotov, K.; Ma, P.; Matchev, K.; Mei, H.; Mitselmakher, G.; Rank, D.; Sperka, D.; Terentyev, N.; Thomas, L.; Wang, J.; Wang, S.; Yelton, J.; Joshi, Y. R.; Linn, S.; Markowitz, P.; Rodriguez, J. L.; Ackert, A.; Adams, T.; Askew, A.; Hagopian, S.; Hagopian, V.; Johnson, K. F.; Kolberg, T.; Martinez, G.; Perry, T.; Prosper, H.; Saha, A.; Santra, A.; Sharma, V.; Yohay, R.; Baarmand, M. M.; Bhopatkar, V.; Colafranceschi, S.; Hohlmann, M.; Noonan, D.; Roy, T.; Yumiceva, F.; Adams, M. R.; Apanasevich, L.; Berry, D.; Betts, R. R.; Cavanaugh, R.; Chen, X.; Evdokimov, O.; Gerber, C. E.; Hangal, D. A.; Hofman, D. J.; Jung, K.; Kamin, J.; Gonzalez, I. D. Sandoval; Tonjes, M. B.; Trauger, H.; Varelas, N.; Wang, H.; Wu, Z.; Zhang, J.; Bilki, B.; Clarida, W.; Dilsiz, K.; Durgut, S.; Gandrajula, R. P.; Haytmyradov, M.; Khristenko, V.; Merlo, J.-P.; Mermerkaya, H.; Mestvirishvili, A.; Moeller, A.; Nachtman, J.; Ogul, H.; Onel, Y.; Ozok, F.; Penzo, A.; Snyder, C.; Tiras, E.; Wetzel, J.; Yi, K.; Blumenfeld, B.; Cocoros, A.; Eminizer, N.; Fehling, D.; Feng, L.; Gritsan, A. V.; Maksimovic, P.; Roskes, J.; Sarica, U.; Swartz, M.; Xiao, M.; You, C.; Al-bataineh, A.; Baringer, P.; Bean, A.; Boren, S.; Bowen, J.; Castle, J.; Khalil, S.; Kropivnitskaya, A.; Majumder, D.; Mcbrayer, W.; Murray, M.; Royon, C.; Sanders, S.; Schmitz, E.; Stringer, R.; Takaki, J. D. Tapia; Wang, Q.; Ivanov, A.; Kaadze, K.; Maravin, Y.; Mohammadi, A.; Saini, L. K.; Skhirtladze, N.; Toda, S.; Rebassoo, F.; Wright, D.; Anelli, C.; Baden, A.; Baron, O.; Belloni, A.; Calvert, B.; Eno, S. C.; Ferraioli, C.; Hadley, N. J.; Jabeen, S.; Jeng, G. Y.; Kellogg, R. G.; Kunkle, J.; Mignerey, A. C.; Ricci-Tam, F.; Shin, Y. H.; Skuja, A.; Tonwar, S. C.; Abercrombie, D.; Allen, B.; Azzolini, V.; Barbieri, R.; Baty, A.; Bi, R.; Brandt, S.; Busza, W.; Cali, I. A.; D'Alfonso, M.; Demiragli, Z.; Ceballos, G. Gomez; Goncharov, M.; Hsu, D.; Iiyama, Y.; Innocenti, G. M.; Klute, M.; Kovalskyi, D.; Lai, Y. S.; Lee, Y.-J.; Levin, A.; Luckey, P. D.; Maier, B.; Marini, A. C.; Mcginn, C.; Mironov, C.; Narayanan, S.; Niu, X.; Paus, C.; Roland, C.; Roland, G.; Salfeld-Nebgen, J.; Stephans, G. S. F.; Tatar, K.; Velicanu, D.; Wang, J.; Wang, T. W.; Wyslouch, B.; Benvenuti, A. C.; Chatterjee, R. M.; Evans, A.; Hansen, P.; Kalafut, S.; Kubota, Y.; Lesko, Z.; Mans, J.; Nourbakhsh, S.; Ruckstuhl, N.; Rusack, R.; Turkewitz, J.; Acosta, J. G.; Oliveros, S.; Avdeeva, E.; Bloom, K.; Claes, D. R.; Fangmeier, C.; Gonzalez Suarez, R.; Kamalieddin, R.; Kravchenko, I.; Monroy, J.; Siado, J. E.; Snow, G. R.; Stieger, B.; Alyari, M.; Dolen, J.; Godshalk, A.; Harrington, C.; Iashvili, I.; Nguyen, D.; Parker, A.; Rappoccio, S.; Roozbahani, B.; Alverson, G.; Barberis, E.; Hortiangtham, A.; Massironi, A.; Morse, D. M.; Nash, D.; Orimoto, T.; De Lima, R. Teixeira; Trocino, D.; Wood, D.; Bhattacharya, S.; Charaf, O.; Hahn, K. A.; Mucia, N.; Odell, N.; Pollack, B.; Schmitt, M. H.; Sung, K.; Trovato, M.; Velasco, M.; Dev, N.; Hildreth, M.; Anampa, K. Hurtado; Jessop, C.; Karmgard, D. J.; Kellams, N.; Lannon, K.; Loukas, N.; Marinelli, N.; Meng, F.; Mueller, C.; Musienko, Y.; Planer, M.; Reinsvold, A.; Ruchti, R.; Smith, G.; Taroni, S.; Wayne, M.; Wolf, M.; Woodard, A.; Alimena, J.; Antonelli, L.; Bylsma, B.; Durkin, L. S.; Flowers, S.; Francis, B.; Hart, A.; Hill, C.; Ji, W.; Liu, B.; Luo, W.; Puigh, D.; Winer, B. L.; Wulsin, H. W.; Cooperstein, S.; Driga, O.; Elmer, P.; Hardenbrook, J.; Hebda, P.; Higginbotham, S.; Lange, D.; Luo, J.; Marlow, D.; Mei, K.; Ojalvo, I.; Olsen, J.; Palmer, C.; Piroué, P.; Stickland, D.; Tully, C.; Malik, S.; Norberg, S.; Barker, A.; Barnes, V. E.; Das, S.; Folgueras, S.; Gutay, L.; Jha, M. K.; Jones, M.; Jung, A. W.; Khatiwada, A.; Miller, D. H.; Neumeister, N.; Peng, C. C.; Schulte, J. F.; Sun, J.; Wang, F.; Xie, W.; Cheng, T.; Parashar, N.; Stupak, J.; Adair, A.; Akgun, B.; Chen, Z.; Ecklund, K. M.; Geurts, F. J. M.; Guilbaud, M.; Li, W.; Michlin, B.; Northup, M.; Padley, B. P.; Roberts, J.; Rorie, J.; Tu, Z.; Zabel, J.; Bodek, A.; de Barbaro, P.; Demina, R.; Duh, Y. t.; Ferbel, T.; Galanti, M.; Garcia-Bellido, A.; Han, J.; Hindrichs, O.; Khukhunaishvili, A.; Lo, K. H.; Tan, P.; Verzetti, M.; Ciesielski, R.; Goulianos, K.; Mesropian, C.; Agapitos, A.; Chou, J. P.; Gershtein, Y.; Espinosa, T. A. Gómez; Halkiadakis, E.; Heindl, M.; Hughes, E.; Kaplan, S.; Elayavalli, R. Kunnawalkam; Kyriacou, S.; Lath, A.; Montalvo, R.; Nash, K.; Osherson, M.; Saka, H.; Salur, S.; Schnetzer, S.; Sheffield, D.; Somalwar, S.; Stone, R.; Thomas, S.; Thomassen, P.; Walker, M.; Delannoy, A. G.; Foerster, M.; Heideman, J.; Riley, G.; Rose, K.; Spanier, S.; Thapa, K.; Bouhali, O.; Hernandez, A. Castaneda; Celik, A.; Dalchenko, M.; De Mattia, M.; Delgado, A.; Dildick, S.; Eusebi, R.; Gilmore, J.; Huang, T.; Kamon, T.; Mueller, R.; Pakhotin, Y.; Patel, R.; Perloff, A.; Perniè, L.; Rathjens, D.; Safonov, A.; Tatarinov, A.; Ulmer, K. A.; Akchurin, N.; Damgov, J.; De Guio, F.; Dudero, P. R.; Faulkner, J.; Gurpinar, E.; Kunori, S.; Lamichhane, K.; Lee, S. W.; Libeiro, T.; Peltola, T.; Undleeb, S.; Volobouev, I.; Wang, Z.; Greene, S.; Gurrola, A.; Janjam, R.; Johns, W.; Maguire, C.; Melo, A.; Ni, H.; Sheldon, P.; Tuo, S.; Velkovska, J.; Xu, Q.; Arenton, M. W.; Barria, P.; Cox, B.; Hirosky, R.; Ledovskoy, A.; Li, H.; Neu, C.; Sinthuprasith, T.; Wang, Y.; Wolfe, E.; Xia, F.; Harr, R.; Karchin, P. E.; Sturdy, J.; Zaleski, S.; Brodski, M.; Buchanan, J.; Caillol, C.; Dasu, S.; Dodd, L.; Duric, S.; Gomber, B.; Grothe, M.; Herndon, M.; Hervé, A.; Hussain, U.; Klabbers, P.; Lanaro, A.; Levine, A.; Long, K.; Loveless, R.; Pierro, G. A.; Polese, G.; Ruggles, T.; Savin, A.; Smith, N.; Smith, W. H.; Taylor, D.; Woods, N.

2018-02-01

Four-lepton production in proton-proton collisions, p p→ (Z/ γ ^*)(Z/γ ^*) → 4ℓ , where ℓ = e or μ , is studied at a center-of-mass energy of 13 {TeV} with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 35.9 {fb}^{-1}. The ZZ production cross section, σ (p p→ ZZ) = 17.2 ± 0.5 {(stat)} ± 0.7 {(syst)} ± 0.4 {(theo)} ± 0.4 {(lumi)} { pb} , measured using events with two opposite-sign, same-flavor lepton pairs produced in the mass region 60< m_{ℓ ^+ℓ ^-} < 120 {GeV} , is consistent with standard model predictions. Differential cross sections are measured and are well described by the theoretical predictions. The Z boson branching fraction to four leptons is measured to be B(Z→ 4ℓ) = 4.8 ± 0.2 {(stat)} ± 0.2 {(syst)} ± 0.1 {(theo)} ± 0.1 {(lumi)} × 10^{-6} for events with a four-lepton invariant mass in the range 80< m_{4ℓ } < 100 {GeV} and a dilepton mass m_{ℓ ℓ } > 4 {GeV} for all opposite-sign, same-flavor lepton pairs. The results agree with standard model predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZγ couplings at 95% confidence level: -0.0012

HORIZON RUN 3: TOPOLOGY AS A STANDARD RULER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Speare, Robert; Gott, J. Richard; Kim, Juhan

2015-02-01

We study the physically self-bound cold dark matter halo distribution, which we associate with the massive galaxies within Horizon Run 3, to estimate the accuracy of the determination of the cosmological distance scale measured by the topology analysis. We apply the routine '''Contour 3D''' to the 108 Mock Survey of π steradians out to redshift z = 0.6, which effectively corresponds to the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) survey, and compare the topology with that of a Gaussian random phase field. We find that given three separate smoothing lengths λ = 15, 21, and 34 h {sup –1} Mpc,more » the least χ{sup 2} fit genus per unit volume (g) yields a 1.7% fractional uncertainty in smoothing length and angular diameter distance to z = 0.6. This is an improvement on former calibrations and presents an error estimate competitive with baryon acoustic oscillation scale techniques. We also present three-dimensional graphics of the Horizon Run 3 spherical mock survey to show a wealth of large-scale structures of the universe that are expected for surveys like BOSS.« less

Bifurcation and Hysteresis of the Magnetospheric Structure with a varying Southward IMF: Field Topology and Global Three-dimensional Full Particle Simulations

NASA Technical Reports Server (NTRS)

Cai, DongSheng; Tao, Weinfeng; Yan, Xiaoyang; Lembege, Bertrand; Nishikawa, Ken-Ichi

2007-01-01

Using a three-dimensional full electromagnetic particle model (EMPM), we have performed global simulations of the interaction between the solar wind and the terrestrial magnetosphere, and have investigated its asymptotic stability. The distance between the dayside magnetopause subsolar point and the Earth center, R(sub mp) is measured, as the intensity of southward IMF |B(sub z)| is slowly varying. Based on the field topology theory, one analyzes the variation of R(sub mp) as a reference index of the dynamics of this interaction, when IMF |B(sub z)| successively increases and decreases to its original value. Two striking results are observed. First, as the IMF |B(sub z)| increases above a critical value, the variation of R(sub mp) suddenly changes (so called 'bifurcation' process in field topology). Above this critical value, the overall magnetic field topology changes drastically and is identified as being the signature of magnetic reconnection at the subsolar point on the magnetopause. Second, this subsolar point recovers its original location R(sub mp) by following different paths as the IMF |B(sub z)| value increases (from zero to a maximum fixed value) and decreases (from this maximum to zero) passing through some critical values. These different paths are the signature of 'hysteresis' effect, and are characteristic of the so-called 'subcritical-type' bifurcation. This hysteresis signature indicates that dissipation processes take place via an energy transfer from the solar wind to the magnetosphere by some irreversible way, which leads to a drastic change in the magnetospheric field topology. This hysteresis is interpreted herein as a consequence of the magnetic reconnection taking place at the dayside magnetopause. The field topology reveals to be a very powerful tool to analyze the signatures of three-dimensional magnetic reconnection without the obligation for determining the mechanisms responsible for, and the consequences of the reconnection on the overall magnetospheric dynamics.

Observation of the {chi}{sub c2}(2P) meson in the reaction {gamma}{gamma}{yields}DD at BABAR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aubert, B.; Karyotakis, Y.; Lees, J. P.

2010-05-01

A search for the Z(3930) resonance in {gamma}{gamma} production of the DD system has been performed using a data sample corresponding to an integrated luminosity of 384 fb{sup -1} recorded by the BABAR experiment at the PEP-II asymmetric-energy electron-positron collider. The DD invariant mass distribution shows clear evidence of the Z(3930) state with a significance of 5.8{sigma}. We determine mass and width values of (3926.7{+-}2.7{+-}1.1) MeV/c{sup 2} and (21.3{+-}6.8{+-}3.6) MeV, respectively. A decay angular analysis provides evidence that the Z(3930) is a tensor state with positive parity and C parity (J{sup PC}=2{sup ++}); therefore we identify the Z(3930) state asmore » the {chi}{sub c2}(2P) meson. The value of the partial width {Gamma}{sub {gamma}{gamma}x}B(Z(3930){yields}DD) is found to be (0.24{+-}0.05{+-}0.04) keV.« less

The invariant of the stiffness filter function with the weight filter function of the power function form

NASA Astrophysics Data System (ADS)

Shang, Zhen; Sui, Yun-Kang

2012-12-01

Based on the independent, continuous and mapping (ICM) method and homogenization method, a research model is constructed to propose and deduce a theorem and corollary from the invariant between the weight filter function and the corresponding stiffness filter function of the form of power function. The efficiency in searching for optimum solution will be raised via the choice of rational filter functions, so the above mentioned results are very important to the further study of structural topology optimization.

Morse homotopy and Chern-Simons perturbation theory

NASA Astrophysics Data System (ADS)

Fukaya, Kenji

1996-11-01

We define and invariant of a three manifold equipped with a flat bundle with vanishing homology. The construction is based on Morse theory using several Morse functions simultaneously and is regarded as a higher loop analogue of various product operations in algebraic topology. There is a heuristic argument that this invariant is related to perturbative Chern-Simons Gauge theory by Axelrod-Singer, etc. There is also a theorem which gives a relation of the construction to open string theory on the cotangent bundle.

Are there p-adic knot invariants?

NASA Astrophysics Data System (ADS)

Morozov, A. Yu.

2016-04-01

We suggest using the Hall-Littlewood version of the Rosso-Jones formula to define the germs of p-adic HOMFLY-PT polynomials for torus knots [ m, n] as coefficients of superpolynomials in a q-expansion. In this form, they have at least the [ m, n] ↔ [ n, m] topological invariance. This opens a new possibility to interpret superpolynomials as p-adic deformations of HOMFLY polynomials and poses a question of generalizing to other knot families, which is a substantial problem for several branches of modern theory.

The Differential cross section distribution of Drell-Yan dielectron pairs in the z boson mass region

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Jiyeon

We report on a measurement of the rapidity distribution, dσ/dy, for Z=Drell-Yan → ee events produced in pmore » $$\\bar{p}$$ collisions at √s = 1.96 TeV. The data sample consists of 2.13 fb -1 corresponding to about 160,000 Z/Drell-Yan → ee candidates in the Z boson mass region collected by the Collider Detector at Fermilab. The dσ/dy distribution, which is measured over the full kinematic range for e +e - pairs in the invariant mass range 66 < M ee < 116 GeV/c 2, is compared with theory predictions. There is good agreement between the data and predictions of Quantum Chromodynamics in Next to Leading Order with the CTEQ6.1M Parton Distribution Functions.« less

Topological energy conversion through the bulk or the boundary of driven systems

NASA Astrophysics Data System (ADS)

Peng, Yang; Refael, Gil

2018-04-01

Combining physical and synthetic dimensions allows a controllable realization and manipulation of high-dimensional topological states. In our work, we introduce two quasiperiodically driven one-dimensional systems which enable tunable topological energy conversion between different driving sources. Using three drives, we realize a four-dimensional quantum Hall state which allows energy conversion between two of the drives within the bulk of the one-dimensional system. With only two drives, we achieve energy conversion between the two at the edge of the chain. Both effects are a manifestation of the effective axion electrodynamics in a three-dimensional time-reversal-invariant topological insulator. Furthermore, we explore the effects of disorder and commensurability of the driving frequencies, and show the phenomena are robust. We propose two experimental platforms, based on semiconductor heterostructures and ultracold atoms in optical lattices, in order to observe the topological energy conversion.

Topological phases in the Haldane model with spin–spin on-site interactions

NASA Astrophysics Data System (ADS)

Rubio-García, A.; García-Ripoll, J. J.

2018-04-01

Ultracold atom experiments allow the study of topological insulators, such as the non-interacting Haldane model. In this work we study a generalization of the Haldane model with spin–spin on-site interactions that can be implemented on such experiments. We focus on measuring the winding number, a topological invariant, of the ground state, which we compute using a mean-field calculation that effectively captures long-range correlations and a matrix product state computation in a lattice with 64 sites. Our main result is that we show how the topological phases present in the non-interacting model survive until the interactions are comparable to the kinetic energy. We also demonstrate the accuracy of our mean-field approach in efficiently capturing long-range correlations. Based on state-of-the-art ultracold atom experiments, we propose an implementation of our model that can give information about the topological phases.

Decentralised fixed modes of networked MIMO systems

NASA Astrophysics Data System (ADS)

Hao, Yuqing; Duan, Zhisheng; Chen, Guanrong

2018-04-01

In this paper, decentralised fixed modes (DFMs) of a networked system are studied. The network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. The effects of the network topology, the node-system dynamics, the external control inputs, and the inner interactions on the existence of DFMs for the whole networked system are investigated. A necessary and sufficient condition for networked multi-input/multi-output (MIMO) systems in a general topology to possess no DFMs is derived. For networked single-input/single-output (SISO) LTI systems in general as well as some typical topologies, some specific conditions for having no DFMs are established. It is shown that the existence of DFMs is an integrated result of the aforementioned relevant factors which cannot be decoupled into individual DFMs of the node-systems and the properties solely determined by the network topology.

Phase diagram of the isotropic spin-(3)/(2) model on the z=3 Bethe lattice

NASA Astrophysics Data System (ADS)

Depenbrock, Stefan; Pollmann, Frank

2013-07-01

We study an SU(2) symmetric spin-3/2 model on the z=3 Bethe lattice using the infinite time evolving block decimation (iTEBD) method. This model is shown to exhibit a rich phase diagram. We compute several order parameters which allow us to identify a ferromagnetic, a ferrimagnetic, an antiferromagnetic, as well as a dimerized phase. We calculate the entanglement spectra from which we conclude the existence of a symmetry protected topological phase that is characterized by S=1/2 edge spins. Details of the iTEBD algorithm used for the simulations are included.

Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms

USGS Publications Warehouse

Love, Jeffrey J.

2012-01-01

Statistical analysis is made of rare, extreme geophysical events recorded in historical data -- counting the number of events $k$ with sizes that exceed chosen thresholds during specific durations of time $\\tau$. Under transformations that stabilize data and model-parameter variances, the most likely Poisson-event occurrence rate, $k/\\tau$, applies for frequentist inference and, also, for Bayesian inference with a Jeffreys prior that ensures posterior invariance under changes of variables. Frequentist confidence intervals and Bayesian (Jeffreys) credibility intervals are approximately the same and easy to calculate: $(1/\\tau)[(\\sqrt{k} - z/2)^{2},(\\sqrt{k} + z/2)^{2}]$, where $z$ is a parameter that specifies the width, $z=1$ ($z=2$) corresponding to $1\\sigma$, $68.3\\%$ ($2\\sigma$, $95.4\\%$). If only a few events have been observed, as is usually the case for extreme events, then these "error-bar" intervals might be considered to be relatively wide. From historical records, we estimate most likely long-term occurrence rates, 10-yr occurrence probabilities, and intervals of frequentist confidence and Bayesian credibility for large earthquakes, explosive volcanic eruptions, and magnetic storms.

Hidden landscapes in thin film topological insulators: between order and disorder, 2D and 3D, normal and topological phases

NASA Astrophysics Data System (ADS)

Oh, Seongshik

Topological insulator (TI) is one of the rare systems in the history of condensed matter physics that is initiated by theories and followed by experiments. Although this theory-driven advance helped move the field quite fast despite its short history, apparently there exist significant gaps between theories and experiments. Many of these discrepancies originate from the very fact that the worlds readily accessible to theories are often far from the real worlds that are available in experiments. For example, the very paradigm of topological protection of the surface states on Z2 TIs such as Bi2Se3, Bi2Te3, Sb2Te3, etc, is in fact valid only if the sample size is infinite and the crystal momentum is well-defined in all three dimensions. On the other hand, many widely studied forms of TIs such as thin films and nano-wires have significant confinement in one or more of the dimensions with varying level of disorders. In other words, many of the real world topological systems have some important parameters that are not readily captured by theories, and thus it is often questionable how far the topological theories are valid to real systems. Interestingly, it turns out that this very uncertainty of the theories provides additional control knobs that allow us to explore hidden topological territories. In this talk, I will discuss how these additional knobs in thin film topological insulators reveal surprising, at times beautiful, landscapes at the boundaries between order and disorder, 2D and 3D, normal and topological phases. This work is supported by Gordon and Betty Moore Foundation's EPiQS Initiative (GBMF4418).

Dynamic surface electronic reconstruction as symmetry-protected topological orders in topological insulator Bi2Se3

NASA Astrophysics Data System (ADS)

Shu, G. J.; Liou, S. C.; Karna, S. K.; Sankar, R.; Hayashi, M.; Chou, F. C.

2018-04-01

The layered narrow-band-gap semiconductor Bi2Se3 is composed of heavy elements with strong spin-orbital coupling, which has been identified both as a good candidate for a thermoelectric material with high thermoelectric figure of merit (Z T ) and as a topological insulator of the Z2 type with a gapless surface band in a Dirac-cone shape. The existence of a conjugated π -bond system on the surface of each Bi2Se3 quintuple layer is proposed based on an extended valence bond model with valence electrons distributed in the hybridized orbitals. Supporting experimental evidence of a two-dimensional (2D) conjugated π -bond system on each quintuple layer of Bi2Se3 is provided using electron energy-loss spectroscopy and electron density mapping through inverse Fourier transform of x-ray diffraction data. Quantum chemistry calculations support the π -bond existence between partially filled 4 pz orbitals of Se via side-to-side orbital overlap positively. The conjugated π -bond system on the surface of each quintuple Bi2Se3 layer is proposed to be similar to that found in graphite (graphene) and responsible for the unique 2D conduction mechanism. The van der Waals (vdW) attractive force between quintuple layers is interpreted to be coming from the antiferroelectrically ordered effective electric dipoles, which are constructed with π -bond trimer pairs on Se layers across the vdW gap of minimized Coulomb repulsion.

Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence

NASA Astrophysics Data System (ADS)

Danish, Mohammad; Meneveau, Charles

2018-04-01

Knowledge of local flow-topology, the patterns of streamlines around a moving fluid element as described by the velocity-gradient tensor, is useful for developing insights into turbulence processes, such as energy cascade, material element deformation, or scalar mixing. Much has been learned in the recent past about flow topology at the smallest (viscous) scales of turbulence. However, less is known at larger scales, for instance, at the inertial scales of turbulence. In this work, we present a detailed study on the scale dependence of various quantities of interest, such as the population fraction of different types of flow-topologies, the joint probability distribution of the second and third invariants of the velocity gradient tensor, and the geometrical alignment of vorticity with strain-rate eigenvectors. We perform the analysis on a simulation dataset of isotropic turbulence at Reλ=433 . While quantities appear close to scale invariant in the inertial range, we observe a "bump" in several quantities at length scales between the inertial and viscous ranges. For instance, the population fraction of unstable node-saddle-saddle flow topology shows an increase when reducing the scale from the inertial entering the viscous range. A similar bump is observed for the vorticity-strain-rate alignment. In order to document possible dynamical causes for the different trends in the viscous and inertial ranges, we examine the probability fluxes appearing in the Fokker-Plank equation governing the velocity gradient invariants. Specifically, we aim to understand whether the differences observed between the viscous and inertial range statistics are due to effects caused by pressure, subgrid-scale, or viscous stresses or various combinations of these terms. To decompose the flow into small and large scales, we mainly use a spectrally compact non-negative filter with good spatial localization properties (Eyink-Aluie filter). The analysis shows that when going from the inertial range into the viscous range, the subgrid-stress effect decreases more rapidly as a function of scale than the viscous effects increase. To make up for the difference, the pressure Hessian also behaves somewhat differently in the viscous than in the inertial range. The results have implications for models for the velocity gradient tensor showing that the effects of subgrid scales may not be simply modeled via a constant eddy viscosity in the inertial range if one wishes to reproduce the observed trends.

Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets

NASA Astrophysics Data System (ADS)

Zhu, Guo-Yi; Wang, Ziqiang; Zhang, Guang-Ming

2017-05-01

Motivated by the recent observations of nodeless superconductivity in the monolayer CuO2 grown on the Bi2Sr2CaCu2O8+δ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional t\\text-J model in proximity to an antiferromagnetic (AF) insulator. We found that i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity-induced AF field. ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodeless. iii) Between the pure d-wave and s-wave paired phases, there emerge two topologically distinct SC phases with (s+\\text{i}d) symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a Z 2 topological superconductor protected by valley symmetry, exhibiting robust gapless nonchiral edge modes. These findings strongly suggest that the high-T c superconductors in proximity to antiferromagnets can realize fully gapped symmetry-protected topological SC.

The non-commutative topology of two-dimensional dirty superconductors

NASA Astrophysics Data System (ADS)

De Nittis, Giuseppe; Schulz-Baldes, Hermann

2018-01-01

Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence. In this work, these techniques are implemented to study two-dimensional dirty superconductors described by Bogoliubov-de Gennes Hamiltonians. After a thorough presentation of the basic framework and the topological invariants, Kubo formulas for the thermal, thermoelectric and spin Hall conductance are analyzed together with the corresponding edge currents.

A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fokicheva, V V

2015-10-31

A new class of integrable billiard systems, called generalized billiards, is discovered. These are billiards in domains formed by gluing classical billiard domains along pieces of their boundaries. (A classical billiard domain is a part of the plane bounded by arcs of confocal quadrics.) On the basis of the Fomenko-Zieschang theory of invariants of integrable systems, a full topological classification of generalized billiards is obtained, up to Liouville equivalence. Bibliography: 18 titles.

Identification of functional modules that correlate with phenotypic difference: the influence of network topology

PubMed Central

2010-01-01

One of the important challenges to post-genomic biology is relating observed phenotypic alterations to the underlying collective alterations in genes. Current inferential methods, however, invariably omit large bodies of information on the relationships between genes. We present a method that takes account of such information - expressed in terms of the topology of a correlation network - and we apply the method in the context of current procedures for gene set enrichment analysis. PMID:20187943

Topological crystalline materials: General formulation, module structure, and wallpaper groups

NASA Astrophysics Data System (ADS)

Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori

2017-06-01

We formulate topological crystalline materials on the basis of the twisted equivariant K theory. Basic ideas of the twisted equivariant K theory are explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk gapless topological materials such as Weyl and Dirac semimetals, and nodal superconductors. As an application of our formulation, we present a complete classification of topological crystalline surface states, in the absence of time-reversal invariance. The classification works for gapless surface states of three-dimensional insulators, as well as full gapped two-dimensional insulators. Such surface states and two-dimensional insulators are classified in a unified way by 17 wallpaper groups, together with the presence or the absence of (sublattice) chiral symmetry. We identify the topological numbers and their representations under the wallpaper group operation. We also exemplify the usefulness of our formulation in the classification of bulk gapless phases. We present a class of Weyl semimetals and Weyl superconductors that are topologically protected by inversion symmetry.

Face Centered Cubic SnSe as a Z2 Trivial Dirac Nodal Line Material

NASA Astrophysics Data System (ADS)

Tateishi, Ikuma; Matsuura, Hiroyasu

2018-07-01

The presence of a Dirac nodal line in a time-reversal and inversion symmetric system is dictated by the Z2 index when spin-orbit interaction is absent. In a first principles calculation, we show that a Dirac nodal line can emerge in Z2 trivial material by calculating the band structure of SnSe in a face centered cubic lattice as an example. We qualitatively show that it becomes a topological crystalline insulator when spin-orbit interaction is taken into account. We clarify the origin of the Dirac nodal line by obtaining irreducible representations corresponding to bands and explain the triviality of the Z2 index. We construct an effective model representing the Dirac nodal line using the k · p method, and discuss the Berry phase and a surface state expected from the Dirac nodal line.

Pressure evolution of electrical transport in the 3D topological insulator (Bi,Sb)2(Te,Se)3

NASA Astrophysics Data System (ADS)

Jeffries, Jason; Butch, N. P.; Vohra, Y. K.; Weir, S. T.

2014-03-01

The group V-VI compounds--like Bi2Se3, Sb2Te3, or Bi2Te3--have been widely studied in recent years for their bulk topological properties. The high-Z members of this series form with the same crystal structure, and are therefore amenable to isostructural substitution studies. It is possible to tune the Bi-Sb and Te-Se ratios such that the material exhibits insulating behavior, thus providing an excellent platform for understanding how a topological insulator evolves with applied pressure. We report our observations of the pressure-dependent electrical transport and compare that behavior with other binary V-VI compounds under pressure. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344.

The embedding problem in topological dynamics and Takens’ theorem

NASA Astrophysics Data System (ADS)

Gutman, Yonatan; Qiao, Yixiao; Szabó, Gábor

2018-02-01

We prove that every {Z}k -action (X, {Z}k, T) of mean dimension less than D/2 admitting a factor (Y, {Z}k, S) of Rokhlin dimension not greater than L embeds in (([0, 1](L+1)D){\\hspace{0pt}}{Zk}× Y, σ× S) , where D\\in{N} , L\\in{N}\\cup\\{0\\} and σ is the shift on the Hilbert cube ([0, 1](L+1)D){\\hspace{0pt}}{Zk} ; in particular, when (Y, {Z}k, S) is an irrational {Z}k -rotation on the k-torus, (X, {Z}k, T) embeds in (([0, 1]2^kD+1){\\hspace{0pt}}{Z^k}, σ) , which is compared to a previous result in Gutman, Lindenstrauss and Tsukamoto (2016 Geom. Funct. Anal. 3 778-817). Moreover, we give a complete and detailed proof of Takens’ embedding theorem with a continuous observable for {Z} -actions and deduce the analogous result for {Z}k -actions. Lastly, we show that the Lindenstrauss-Tsukamoto conjecture for {Z} -actions holds generically, discuss an analogous conjecture for {Z}k -actions in Gutman, Qiao and Tsukamoto (2017 arXiv:1709.00125) and verify it for {Z}k -actions on finite dimensional spaces.

Realization of space-time inversion-invariant topological semimetal-bands in superconducting quantum circuits.

NASA Astrophysics Data System (ADS)

Yu, Y.; Tan, X.; Liu, Q.; Xue, G.; Yu, H.; Zhao, Y.; Wang, Z.

Topological band theory has attracted much attention since several types of topological metals and semimetals have been explored. These robustness of nodal band structures are symmetry-protected, whose topological features have deepened and widened the understandings of condensed matter physics. Meanwhile, as artificial quantum systems superconducting circuits possess high controllability, supplying a powerful approach to investigate topological properties of condensed matter systems. We realize a Hamiltonian with space-time (PT) symmetry by mapping momentum space of nodal band structure to parameter space in a superconducting quantum circuit. By measuring energy spectrum of the system, we observe the gapless band structure of topological semimetals, shown as Dirac points in momentum space. The phase transition from topological semimetal to topological insulator can be realized by continuously tuning the parameter in Hamiltonian. We add perturbation to broken time reversal symmetry. As long as the combined PT symmetry is preserved, the Dirac points of the topological semimetal are still observable, suggesting the robustness of the topological protection of the gapless energy band. Our work open a platform to simulate the relation between the symmetry and topological stability in condensed matter systems. Supported by the NKRDP of China (2016YFA0301802) and the GRF of Hong Kong (HKU173051/14P&HKU173055/15P).

Rooting gene trees without outgroups: EP rooting.

PubMed

Sinsheimer, Janet S; Little, Roderick J A; Lake, James A

2012-01-01

Gene sequences are routinely used to determine the topologies of unrooted phylogenetic trees, but many of the most important questions in evolution require knowing both the topologies and the roots of trees. However, general algorithms for calculating rooted trees from gene and genomic sequences in the absence of gene paralogs are few. Using the principles of evolutionary parsimony (EP) (Lake JA. 1987a. A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony. Mol Biol Evol. 4:167-181) and its extensions (Cavender, J. 1989. Mechanized derivation of linear invariants. Mol Biol Evol. 6:301-316; Nguyen T, Speed TP. 1992. A derivation of all linear invariants for a nonbalanced transversion model. J Mol Evol. 35:60-76), we explicitly enumerate all linear invariants that solely contain rooting information and derive algorithms for rooting gene trees directly from gene and genomic sequences. These new EP linear rooting invariants allow one to determine rooted trees, even in the complete absence of outgroups and gene paralogs. EP rooting invariants are explicitly derived for three taxon trees, and rules for their extension to four or more taxa are provided. The method is demonstrated using 18S ribosomal DNA to illustrate how the new animal phylogeny (Aguinaldo AMA et al. 1997. Evidence for a clade of nematodes, arthropods, and other moulting animals. Nature 387:489-493; Lake JA. 1990. Origin of the metazoa. Proc Natl Acad Sci USA 87:763-766) may be rooted directly from sequences, even when they are short and paralogs are unavailable. These results are consistent with the current root (Philippe H et al. 2011. Acoelomorph flatworms are deuterostomes related to Xenoturbella. Nature 470:255-260).

Rooting Gene Trees without Outgroups: EP Rooting

PubMed Central

Sinsheimer, Janet S.; Little, Roderick J. A.; Lake, James A.

2012-01-01

Gene sequences are routinely used to determine the topologies of unrooted phylogenetic trees, but many of the most important questions in evolution require knowing both the topologies and the roots of trees. However, general algorithms for calculating rooted trees from gene and genomic sequences in the absence of gene paralogs are few. Using the principles of evolutionary parsimony (EP) (Lake JA. 1987a. A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony. Mol Biol Evol. 4:167–181) and its extensions (Cavender, J. 1989. Mechanized derivation of linear invariants. Mol Biol Evol. 6:301–316; Nguyen T, Speed TP. 1992. A derivation of all linear invariants for a nonbalanced transversion model. J Mol Evol. 35:60–76), we explicitly enumerate all linear invariants that solely contain rooting information and derive algorithms for rooting gene trees directly from gene and genomic sequences. These new EP linear rooting invariants allow one to determine rooted trees, even in the complete absence of outgroups and gene paralogs. EP rooting invariants are explicitly derived for three taxon trees, and rules for their extension to four or more taxa are provided. The method is demonstrated using 18S ribosomal DNA to illustrate how the new animal phylogeny (Aguinaldo AMA et al. 1997. Evidence for a clade of nematodes, arthropods, and other moulting animals. Nature 387:489–493; Lake JA. 1990. Origin of the metazoa. Proc Natl Acad Sci USA 87:763–766) may be rooted directly from sequences, even when they are short and paralogs are unavailable. These results are consistent with the current root (Philippe H et al. 2011. Acoelomorph flatworms are deuterostomes related to Xenoturbella. Nature 470:255–260). PMID:22593551

Quantum Hall effect with small numbers of vortices in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Byrnes, Tim; Dowling, Jonathan P.

2015-08-01

When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of 2 π . In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of m /2 h , where m is the mass of the atoms and h is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.

Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis

PubMed Central

Reuter, Martin; Wolter, Franz-Erich; Shenton, Martha; Niethammer, Marc

2009-01-01

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel. PMID:20161035

Renormalization of quark propagators from twisted-mass lattice QCD at N{sub f}=2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blossier, B.; Boucaud, Ph.; Pene, O.

2011-04-01

We present results concerning the nonperturbative evaluation of the renormalization constant for the quark field, Z{sub q}, from lattice simulations with twisted-mass quarks and three values of the lattice spacing. We use the regularization-invariant momentum-subtraction (RI'-MOM) scheme. Z{sub q} has very large lattice spacing artefacts; it is considered here as a test bed to elaborate accurate methods which will be used for other renormalization constants. We recall and develop the nonperturbative correction methods and propose tools to test the quality of the correction. These tests are also applied to the perturbative correction method. We check that the lattice-spacing artefacts indeedmore » scale as a{sup 2}p{sup 2}. We then study the running of Z{sub q} with particular attention to the nonperturbative effects, presumably dominated by the dimension-two gluon condensate in Landau gauge. We show indeed that this effect is present, and not small. We check its scaling in physical units, confirming that it is a continuum effect. It gives a {approx}4% contribution at 2 GeV. Different variants are used in order to test the reliability of our result and estimate the systematic uncertainties. Finally, combining all our results and using the known Wilson coefficient of , we find g{sup 2}({mu}{sup 2}){sub {mu}}{sup 2}{sub CM}=2.01(11)({sub -0.73}{sup +0.61})GeV{sup 2} at {mu}=10 GeV, the local operator A{sup 2} being renormalized in the MS scheme. This last result is in fair agreement within uncertainties with the value independently extracted from the strong coupling constant. We convert the nonperturbative part of Z{sub q} from the regularization-invariant momentum-subtraction (RI'-MOM) scheme to MS. Our result for the quark field renormalization constant in the MS scheme is Z{sub q} {sup MS} {sup pert}((2 GeV){sup 2},g{sub bare}{sup 2})=0.750(3)(7)-0.313(20)(g{sub bare}{sup 2}-1.5) for the perturbative contribution and Z{sub q}{sup MSnonperturbative}((2 GeV){sup 2},g{sub bare}{sup 2})=0.781(6)(21)-0.313(20)(g{sub bare}{sup 2}-1.5) when the nonperturbative contribution is included.« less

Gauging Spatial Symmetries and the Classification of Topological Crystalline Phases

NASA Astrophysics Data System (ADS)

Thorngren, Ryan; Else, Dominic V.

2018-01-01

We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We introduce the notion of a crystalline topological liquid and argue that most (and perhaps all) phases of interest are likely to satisfy this criterion. We prove a crystalline equivalence principle, which states that in Euclidean space, crystalline topological liquids with symmetry group G are in one-to-one correspondence with topological phases protected by the same symmetry G , but acting internally, where if an element of G is orientation reversing, it is realized as an antiunitary symmetry in the internal symmetry group. As an example, we explicitly compute, using group cohomology, a partial classification of bosonic symmetry-protected topological phases protected by crystalline symmetries in (3 +1 ) dimensions for 227 of the 230 space groups. For the 65 space groups not containing orientation-reversing elements (Sohncke groups), there are no cobordism invariants that may contribute phases beyond group cohomology, so we conjecture that our classification is complete.

Engineering three-dimensional topological insulators in Rashba-type spin-orbit coupled heterostructures

PubMed Central

Das, Tanmoy; Balatsky, A. V.

2013-01-01

Topological insulators represent a new class of quantum phase defined by invariant symmetries and spin-orbit coupling that guarantees metallic Dirac excitations at its surface. The discoveries of these states have sparked the hope of realizing non-trivial excitations and novel effects such as a magnetoelectric effect and topological Majorana excitations. Here we develop a theoretical formalism to show that a three-dimensional topological insulator can be designed artificially via stacking bilayers of two-dimensional Fermi gases with opposite Rashba-type spin-orbit coupling on adjacent layers, and with interlayer quantum tunneling. We demonstrate that in the stack of bilayers grown along a (001)-direction, a non-trivial topological phase transition occurs above a critical number of Rashba bilayers. In the topological phase, we find the formation of a single spin-polarized Dirac cone at the -point. This approach offers an accessible way to design artificial topological insulators in a set up that takes full advantage of the atomic layer deposition approach. This design principle is tunable and also allows us to bypass limitations imposed by bulk crystal geometry. PMID:23739724

TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions

PubMed Central

2017-01-01

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/ PMID:28749969

Spin and chirality effects in antler-topology processes at high energy $${e^+e^-}$$ colliders

DOE PAGES

Choi, S. Y.; Christensen, N. D.; Salmon, D.; ...

2015-10-01

We perform a model-independent investigation of spin and chirality correlation effects in the antler-topology processes e +e -→P +P -→(ℓ+D0)(ℓ-D¯0) at high-energy e +e - colliders with polarized beams. Generally the production process e +e -→P +P - can occur not only through the s-channel exchange of vector bosons, V0 , including the neutral Standard Model (SM) gauge bosons, γ and Z, but also through the s- and t-channel exchanges of new neutral states, S0 and T0 , and the u-channel exchange of new doubly charged states, U-- . The general set of (non-chiral) three-point couplings of the new particlesmore » and leptons allowed in a renormalizable quantum field theory is considered. The general spin and chirality analysis is based on the threshold behavior of the excitation curves for P +P - pair production in e +e - collisions with longitudinal- and transverse-polarized beams, the angular distributions in the production process and also the production-decay angular correlations. In the first step, we present the observables in the helicity formalism. Subsequently, we show how a set of observables can be designed for determining the spins and chiral structures of the new particles without any model assumptions. Finally, taking into account a typical set of approximately chiral invariant scenarios, we demonstrate how the spin and chirality effects can be probed experimentally at a high-energy e +e - collider.« less

Spin and chirality effects in antler-topology processes at high energy $$\\varvec{e^+e^-}$$ e + e - colliders

DOE PAGES

Choi, S. Y.; Christensen, N. D.; Salmon, D.; ...

2015-10-01

We perform a model-independent investigation of spin and chirality correlation effects in the antler-topology processes e+e−→P+P−→(ℓ+D0)(ℓ−D¯0) at high-energy e+e− colliders with polarized beams. Generally the production process e+e−→P+P− can occur not only through the s-channel exchange of vector bosons, V0 , including the neutral Standard Model (SM) gauge bosons, γ and Z, but also through the s- and t-channel exchanges of new neutral states, S0 and T0 , and the u-channel exchange of new doubly charged states, U−− . The general set of (non-chiral) three-point couplings of the new particles and leptons allowed in a renormalizable quantum field theory ismore » considered. The general spin and chirality analysis is based on the threshold behavior of the excitation curves for P+P− pair production in e+e− collisions with longitudinal- and transverse-polarized beams, the angular distributions in the production process and also the production-decay angular correlations. In the first step, we present the observables in the helicity formalism. Subsequently, we show how a set of observables can be designed for determining the spins and chiral structures of the new particles without any model assumptions. Finally, taking into account a typical set of approximately chiral invariant scenarios, we demonstrate how the spin and chirality effects can be probed experimentally at a high-energy e+e− collider.« less

Spin and chirality effects in antler-topology processes at high energy $${e^+e^-}$$ colliders

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, S. Y.; Christensen, N. D.; Salmon, D.

We perform a model-independent investigation of spin and chirality correlation effects in the antler-topology processes e +e -→P +P -→(ℓ+D0)(ℓ-D¯0) at high-energy e +e - colliders with polarized beams. Generally the production process e +e -→P +P - can occur not only through the s-channel exchange of vector bosons, V0 , including the neutral Standard Model (SM) gauge bosons, γ and Z, but also through the s- and t-channel exchanges of new neutral states, S0 and T0 , and the u-channel exchange of new doubly charged states, U-- . The general set of (non-chiral) three-point couplings of the new particlesmore » and leptons allowed in a renormalizable quantum field theory is considered. The general spin and chirality analysis is based on the threshold behavior of the excitation curves for P +P - pair production in e +e - collisions with longitudinal- and transverse-polarized beams, the angular distributions in the production process and also the production-decay angular correlations. In the first step, we present the observables in the helicity formalism. Subsequently, we show how a set of observables can be designed for determining the spins and chiral structures of the new particles without any model assumptions. Finally, taking into account a typical set of approximately chiral invariant scenarios, we demonstrate how the spin and chirality effects can be probed experimentally at a high-energy e +e - collider.« less

Donaldson-Witten theory and indefinite theta functions

NASA Astrophysics Data System (ADS)

Korpas, Georgios; Manschot, Jan

2017-11-01

We consider partition functions with insertions of surface operators of topologically twisted N=2 , SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter a, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a \\overlineQ -exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate ā using Zwegers' indefinite theta functions. In this way, we reproduce Göttsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions.

PubMed

Medhi, Amal; Shenoy, Vijay B

2012-09-05

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Topological phases in a Kitaev chain with imbalanced pairing

NASA Astrophysics Data System (ADS)

Li, C.; Zhang, X. Z.; Zhang, G.; Song, Z.

2018-03-01

We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. An exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of ground states occurs, associated with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist in an open chain in the time-reversal symmetry-unbroken region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.

On supersymmetric AdS6 solutions in 10 and 11 dimensions

NASA Astrophysics Data System (ADS)

Gutowski, J.; Papadopoulos, G.

2017-12-01

We prove a non-existence theorem for smooth, supersymmetric, warped AdS 6 solutions with connected, compact without boundary internal space in D = 11 and (massive) IIA supergravities. In IIB supergravity we show that if such AdS 6 solutions exist, then the NSNS and RR 3-form fluxes must be linearly independent and certain spinor bilinears must be appropriately restricted. Moreover we demonstrate that the internal space admits an so(3) action which leaves all the fields invariant and for smooth solutions the principal orbits must have co-dimension two. We also describe the topology and geometry of internal spaces that admit such a so(3) action and show that there are no solutions for which the internal space has topology F × S 2, where F is an oriented surface.

Local and gauge invariant observables in gravity

NASA Astrophysics Data System (ADS)

Khavkine, Igor

2015-09-01

It is well known that general relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observable. We propose a generalized notion of local observables, which retain the most important properties that follow from the standard definition of locality, yet is flexible enough to admit a large class of diffeomorphism invariant observables in GR. The generalization comes at a small price—that the domain of definition of a generalized local observable may not cover the entire phase space of GR and two such observables may have distinct domains. However, the subset of metrics on which generalized local observables can be defined is in a sense generic (its open interior is non-empty in the Whitney strong topology). Moreover, generalized local gauge invariant observables are sufficient to separate diffeomorphism orbits on this admissible subset of the phase space. Connecting the construction with the notion of differential invariants gives a general scheme for defining generalized local gauge invariant observables in arbitrary gauge theories, which happens to agree with well-known results for Maxwell and Yang-Mills theories.

Search for resonant production of tt decaying to jets in pp collisions at √{s}=1.96 TeV

DOE PAGES

Aaltonen, T.

2011-10-11

This Letter reports a search for non-standard model topquark resonances, Z', decaying to ttMs; →W +bW -b , where both W decay to quarks. We examine the top-antitop quark invariant mass spectrum for the presence of narrow resonant states. The search uses a data sample of p{bar p} collisions at a center of mass energy of 1.96 TeV collected by the CDF II detector at the Fermilab Tevatron, with an integrated luminosity of 2.8 fb -1. No evidence for top-antitop quark resonant production is found. We place upper limits on the production cross section times branching ratio for a specificmore » topcolor assisted technicolor model with width of λ Z' = 0.012 M Z'. Within this model, we exclude Z' boson with masses below 805 GeV/c 2 at the 95% confidence level.« less

Spin-Caloritronic Batteries

NASA Astrophysics Data System (ADS)

Yu, Xiao-Qin; Zhu, Zhen-Gang; Su, Gang; Jauho, A.-P.

2017-11-01

The thermoelectric performance of a topological energy converter is analyzed. The H -shaped device is based on a combination of transverse topological effects involving the spin: the inverse spin Hall effect and the spin Nernst effect. The device can convert a temperature drop in one arm into an electric power output in the other arm. Analytical expressions for the output voltage, the figure of merit (Z T ), and energy-converting efficiency are reported. We show that the output voltage and the Z T can be tuned by the geometry of the device and the physical properties of the material. Importantly, contrary to a conventional thermoelectric device, here a low electric conductivity may, in fact, enhance the Z T value, thereby opening a path to strategies in optimizing the figure of merit.

Persistent topological features of dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maletić, Slobodan, E-mail: slobodan@hitsz.edu.cn; Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade; Zhao, Yi, E-mail: zhao.yi@hitsz.edu.cn

Inspired by an early work of Muldoon et al., Physica D 65, 1–16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examinedmore » by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.« less

A magnetic topological semimetal Sr 1-yMn 1-zSb2 (y, z < 0.10)

DOE PAGES

Liu, J. Y.; Hu, J.; Zhang, Qiang; ...

2017-07-24

Weyl (WSMs) evolve from Dirac semimetals in the presence of broken time-reversal symmetry (TRS) or space-inversion symmetry. The WSM phases in TaAs-class materials and photonic crystals are due to the loss of space-inversion symmetry. For TRS-breaking WSMs, despite numerous theoretical and experimental efforts, few examples have been reported. Here in this paper, we report a new type of magnetic semimetal Sr 1-yMn 1-zSb 2 (y, z < 0.1) with nearly massless relativistic fermion behaviour (m* = 0.04 - 0.05m 0, where m 0 is the free-electron mass). This material exhibits a ferromagnetic order for 304 K < T < 565more » K, but a canted antiferromagnetic order with a ferromagnetic component for T < 304 K. The combination of relativistic fermion behaviour and ferromagnetism in Sr 1-yMn 1-zSb2 offers a rare opportunity to investigate the interplay between relativistic fermions and spontaneous TRS breaking.« less

A magnetic topological semimetal Sr 1-yMn 1-zSb2 (y, z < 0.10)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, J. Y.; Hu, J.; Zhang, Qiang

Weyl (WSMs) evolve from Dirac semimetals in the presence of broken time-reversal symmetry (TRS) or space-inversion symmetry. The WSM phases in TaAs-class materials and photonic crystals are due to the loss of space-inversion symmetry. For TRS-breaking WSMs, despite numerous theoretical and experimental efforts, few examples have been reported. Here in this paper, we report a new type of magnetic semimetal Sr 1-yMn 1-zSb 2 (y, z < 0.1) with nearly massless relativistic fermion behaviour (m* = 0.04 - 0.05m 0, where m 0 is the free-electron mass). This material exhibits a ferromagnetic order for 304 K < T < 565more » K, but a canted antiferromagnetic order with a ferromagnetic component for T < 304 K. The combination of relativistic fermion behaviour and ferromagnetism in Sr 1-yMn 1-zSb2 offers a rare opportunity to investigate the interplay between relativistic fermions and spontaneous TRS breaking.« less

THE SMALLEST FIELD OF DEFINITION OF A SUBGROUP OF THE GROUP \\mathrm{PSL}_2

NASA Astrophysics Data System (ADS)

Vinberg, È. B.

1995-02-01

As previously proved by the author, for each semisimple algebraic group of adjoint type that is dense in the Zariski topology there exists a smallest field of definition which is an invariant of the class of commensurable subgroups. In the present paper an algorithm is given for finding the smallest field of definition of a dense finitely generated subgroup of the group \\mathrm{PSL}_2(\\mathbb{C}). A criterion for arithmeticity of a lattice in \\mathrm{PSL}_2(\\mathbb{R}) or \\mathrm{PSL}_2(\\mathbb{C}) in terms of this field is presented.Bibliography: 7 titles.

On a canonical quantization of 3D Anti de Sitter pure gravity

NASA Astrophysics Data System (ADS)

Kim, Jihun; Porrati, Massimo

2015-10-01

We perform a canonical quantization of pure gravity on AdS 3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,{R})× SL(2,{R}) . We first quantize the theory canonically on an asymptotically AdS space -which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,{R}) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS 3.

Pressure-induced organic topological nodal-line semimetal in the three-dimensional molecular crystal Pd (dddt) 2

NASA Astrophysics Data System (ADS)

Liu, Zhao; Wang, Haidi; Wang, Z. F.; Yang, Jinlong; Liu, Feng

2018-04-01

The nodal-line semimetal represents a class of topological materials characterized with highest band degeneracy. It is usually found in inorganic materials of high crystal symmetry or a minimum symmetry of inversion aided with accidental band degeneracy [Phys. Rev. Lett. 118, 176402 (2017), 10.1103/PhysRevLett.118.176402]. Based on first-principles band structure, Wannier charge center, and topological surface state calculations, here we predict a pressure-induced topological nodal-line semimetal in the absence of spin-orbit coupling (SOC) in the synthesized single-component 3D molecular crystal Pd (dddt) 2 . We show a Γ -centered single nodal line undulating within a narrow energy window across the Fermi level. This intriguing nodal line is generated by pressure-induced accidental band degeneracy, without protection from any crystal symmetry. When SOC is included, the fourfold degenerated nodal line is gapped and Pd (dddt) 2 becomes a strong 3D topological metal with an Z2 index of (1;000). However, the tiny SOC gap makes it still possible to detect the nodal-line properties experimentally. Our findings afford an attractive route for designing and realizing topological states in 3D molecular crystals, as they are weakly bonded through van der Waals forces with a low crystal symmetry so that their electronic structures can be easily tuned by pressure.

Symmetry protected topological Luttinger liquids and the phase transition between them

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

2018-01-01

We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singletmore » $$d_{xy}$$ in the non-trivial phase and triplet $$S_z=0$$ in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Yishuai; Chiu, Janet; Miao, Lin

Three-dimensional topological insulators are bulk insulators with Z 2 topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numerical simulations and scanning tunnelling microscopy data to show that these resonance states have significance well beyond themore » localized regime usually associated with impurity bands. Lastly, at native densities in the model Bi 2X 3 (X=Bi, Te) compounds, defect resonance states are predicted to generate a new quantum basis for an emergent electron gas that supports diffusive electrical transport.« less

Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

NASA Astrophysics Data System (ADS)

Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

2018-03-01

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

Linear response and Berry curvature in two-dimensional topological phases

NASA Astrophysics Data System (ADS)

Bradlyn, Barry J.

In this thesis we examine the viscous and thermal transport properties of chiral topological phases, and their relationship to topological invariants. We start by developing a Kubo formalism for calculating the frequency dependent viscosity tensor of a general quantum system, both with and without a uniform external magnetic field. The importance of contact terms is emphasized. We apply this formalism to the study of integer and fractional quantum Hall states, as well as p + ip paired superfluids, and verify the relationship between the Hall viscosity and the mean orbital spin density. We also elucidate the connection between our Kubo formulas and prior adiabatic transport calculations of the Hall viscosity. Additionally, we derive a general relationship between the frequency dependent viscosity and conductivity tensors for Galilean-invariant systems. We comment on the implications of this relationship towards the measurement of Hall viscosity in solid-state systems. To address the question of thermal transport, we first review the standard Kubo formalism of Luttinger for computing thermoelectric coefficients. We apply this to the specific case of non-interacting electrons in the integer quantum Hall regime, paying careful attention to the roles of bulk and edge effects. In order to generalize our discussion to interacting systems, we construct a low-energy effective action for a two-dimensional non-relativistic topological phase of matter in a continuum, which completely describes all of its bulk thermoelectric and visco-elastic properties in the limit of low frequencies, long distances, and zero temperature, without assuming either Lorentz or Galilean invariance, by coupling the microscopic degrees of freedom to the background spacetime geometry. We derive the most general form of a local bulk induced action to first order in derivatives of the background fields, from which thermodynamic and transport properties can be obtained. We show that the gapped bulk cannot contribute to low-temperature thermoelectric transport other than the ordinary Hall conductivity; the other thermoelectric effects (if they occur) are thus purely edge effects. The stress response to time-dependent strains is given by the Hall viscosity, which is robust against perturbations and related to the spin current. Finally, we address the issue of calculating the topological central charge from bulk wavefunctions for a topological phase. Using the form of the topological terms in the induced action, we show that we can calculate the various coefficients of these terms as Berry curvatures associated to certain metric and electromagnetic vector potential perturbations. We carry out this computation explicitly for quantum Hall trial wavefunctions that can be represented as conformal blocks in a chiral conformal field theory (CFT). These calculations make use of the gauge and gravitational anomalies in the underlying chiral CFT.

Using sorted invariant mass variables to evade combinatorial ambiguities in cascade decays

DOE PAGES

Kim, Doojin; Matchev, Konstantin T.; Park, Myeonghun

2016-02-19

The classic method for mass determination in a SUSY-like cascade decay chain relies on measurements of the kinematic endpoints in the invariant mass distributions of suitable collections of visible decay products. However, the procedure is complicated by combinatorial ambiguities: e.g., the visible final state particles may be indistinguishable (as in the case of QCD jets), or one may not know the exact order in which they are emitted along the decay chain. In order to avoid such combinatorial ambiguities, we propose to treat the nal state particles fully democratically and consider the sorted set of the invariant masses of allmore » possible partitions of the visible particles in the decay chain. In particular, for a decay to N visible particles, one considers the sorted sets of all possible n-body invariant mass combinations (2≤ n≤ N) and determines the kinematic endpoint m (n,r) max of the distribution of the r-th largest n-body invariant mass m (n,r) for each possible value of n and r. For the classic example of a squark decay in supersymmetry, we provide analytical formulas for the interpretation of these endpoints in terms of the underlying physical masses. We point out that these measurements can be used to determine the structure of the decay topology, e.g., the number and position of intermediate on-shell resonances.« less

Using sorted invariant mass variables to evade combinatorial ambiguities in cascade decays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Doojin; Matchev, Konstantin T.; Park, Myeonghun

The classic method for mass determination in a SUSY-like cascade decay chain relies on measurements of the kinematic endpoints in the invariant mass distributions of suitable collections of visible decay products. However, the procedure is complicated by combinatorial ambiguities: e.g., the visible final state particles may be indistinguishable (as in the case of QCD jets), or one may not know the exact order in which they are emitted along the decay chain. In order to avoid such combinatorial ambiguities, we propose to treat the nal state particles fully democratically and consider the sorted set of the invariant masses of allmore » possible partitions of the visible particles in the decay chain. In particular, for a decay to N visible particles, one considers the sorted sets of all possible n-body invariant mass combinations (2≤ n≤ N) and determines the kinematic endpoint m (n,r) max of the distribution of the r-th largest n-body invariant mass m (n,r) for each possible value of n and r. For the classic example of a squark decay in supersymmetry, we provide analytical formulas for the interpretation of these endpoints in terms of the underlying physical masses. We point out that these measurements can be used to determine the structure of the decay topology, e.g., the number and position of intermediate on-shell resonances.« less

Electrically tunable robust edge states in graphene-based topological photonic crystal slabs

NASA Astrophysics Data System (ADS)

Song, Zidong; Liu, HongJun; Huang, Nan; Wang, ZhaoLu

2018-03-01

Topological photonic crystals are optical structures supporting topologically protected unidirectional edge states that exhibit robustness against defects. Here, we propose a graphene-based all-dielectric photonic crystal slab structure that supports two-dimensionally confined topological edge states. These topological edge states can be confined in the out-of-plane direction by two parallel graphene sheets. In the structure, the excitation frequency range of topological edge states can be dynamically and continuously tuned by varying bias voltage across the two parallel graphene sheets. Utilizing this kind of architecture, we construct Z-shaped channels to realize topological edge transmission with diffrerent frequencies. The proposal provides a new degree of freedom to dynamically control topological edge states and potential applications for robust integrated photonic devices and optical communication systems.

Pressure evolution of electrical transport in the 3D topological insulator (Bi,Sb) 2 (Se,Te) 3

DOE PAGES

Jeffries, J. R.; Butch, N. P.; Vohra, Y. K.; ...

2015-03-18

The group V-VI compounds|like Bi 2Se 3, Sb 2Te 3, or Bi 2Te 3|have been widely studied in recent years for their bulk topological properties. The high-Z members of this series form with the same crystal structure, and are therefore amenable to isostructural substitution studies. It is possible to tune the Bi-Sb and Te-Se ratios such that the material exhibits insulating behavior, thus providing an excellent platform for understanding how a topological insulator evolves with applied pressure. We report our observations of the pressure-dependent electrical transport and crystal structure of a pseudobinary (Bi,Sb) 2(Te,Se) 3 compound. Similar to some ofmore » its sister compounds, the (Bi,Sb) 2(Te,Se) 3 pseudobinary compound undergoes multiple, pressure-induced phase transformations that result in metallization, the onset of a close-packed crystal structure, and the development of distinct superconducting phases.« less

Charged bottomoniumlike states Z{sub b}(10610) and Z{sub b}(10650) and the {Upsilon}(5S){yields}{Upsilon}(2S){pi}{sup +}{pi}{sup -} decay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Dianyong; Nuclear Theory Group, Institute of Modern Physics of CAS, Lanzhou 730000; Liu Xiang

2011-10-01

Inspired by the newly observed two charged bottomoniumlike states, we consider the possible contribution from the intermediate Z{sub b}(10610) and Z{sub b}(10650) states to the {Upsilon}(5S){yields}{Upsilon}(2S){pi}{sup +}{pi}{sup -} decay process, which naturally explains Belle's previous observation of the anomalous {Upsilon}(2S){pi}{sup +}{pi}{sup -} production near the peak of {Upsilon}(5S) at {radical}(s)=10.87 GeV [K. F. Chen et al. (Belle Collaboration), Phys. Rev. Lett. 100, 112001 (2008)]. The resulting d{Gamma}({Upsilon}(5S){yields}{Upsilon}(2S){pi}{sup +}{pi}{sup -})/dm{sub {pi}}{sup +}{sub {pi}}{sup -} and d{Gamma}({Upsilon}(5S){yields}{Upsilon}(2S){pi}{sup +}{pi}{sup -})/dcos{theta} distributions agree with Belle's measurement after inclusion of these Z{sub b} states. This formalism also reproduces the Belle observation of the double-peak structuremore » and its reflection in the {Upsilon}(2S){pi}{sup +} invariant mass spectrum of the {Upsilon}(5S){yields}{Upsilon}(2S){pi}{sup +}{pi}{sup -} decay.« less

Complex Critical Exponents for Percolation Transitions in Josephson-Junction Arrays, Antiferromagnets, and Interacting Bosons

NASA Astrophysics Data System (ADS)

Fernandes, Rafael M.; Schmalian, Jörg

2011-02-01

We show that the critical behavior of the XY quantum-rotor model undergoing a percolation transition is dramatically affected by its topological Berry phase 2πρ. In particular, for irrational ρ, its low-energy excitations emerge as spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions arise, such as complex critical exponents, log-periodic oscillations and dynamically broken scale invariance.

Electronic structure and Fermi surface topology of WTe2 in a magnetic field

NASA Astrophysics Data System (ADS)

Krishna, Jyoti; Maitra, T.

2018-05-01

Two dimensional (2D) layered transition metal dichalcogenides (TMDs) have recently become the foremost candidate for future electronic device applications overcoming graphene as latter has no bandgap which limits some of the applications. WTe2 is one such TMD whose magnetoresistance (MR) continue to increase with magnetic field without any indication of saturation. Inspired by this, we have theoretically investigated the material using first principle density functional theory (DFT) approach to study the effect of magnetic field on electronic structure of the compound. The magnetic field is seen to enhance the hole pockets' size along Γ-Z direction, which brings in significant change in the Fermi surface topology.

Dual-scale topology optoelectronic processor.

PubMed

Marsden, G C; Krishnamoorthy, A V; Esener, S C; Lee, S H

1991-12-15

The dual-scale topology optoelectronic processor (D-STOP) is a parallel optoelectronic architecture for matrix algebraic processing. The architecture can be used for matrix-vector multiplication and two types of vector outer product. The computations are performed electronically, which allows multiplication and summation concepts in linear algebra to be generalized to various nonlinear or symbolic operations. This generalization permits the application of D-STOP to many computational problems. The architecture uses a minimum number of optical transmitters, which thereby reduces fabrication requirements while maintaining area-efficient electronics. The necessary optical interconnections are space invariant, minimizing space-bandwidth requirements.

Broadband and stable acoustic vortex emitter with multi-arm coiling slits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Xue; Liang, Bin, E-mail: liangbin@nju.edu.cn, E-mail: eleqc@nus.edu.sg, E-mail: jccheng@nju.edu.cn; Zou, Xin-ye

2016-05-16

We present the analytical design and experimental realization of a scheme based on multi-arm coiling slits to generate the stable acoustic vortices in a broadband. The proposed structure is able to spiral the acoustic wave spatially and generate the twisted acoustic vortices with invariant topological charge for a long propagation distance. Compared with conventional methods which require the electronic control of a bulky loudspeaker, this scheme provides an effective and compact solution to generate acoustic vortices with controllable topological charge in the broadband, which offers more initiatives in the demanding applications.

Numerical grid generation techniques. [conference

NASA Technical Reports Server (NTRS)

1980-01-01

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Topological string, supersymmetric gauge theory and bps counting

NASA Astrophysics Data System (ADS)

Pan, Guang

In this thesis we study the Donaldson-Thomas theory on the local curve geometry, which arises in the context of geometric engineering of supersymmetric gauge theory from type IIA string compactification. The topological A-model amplitude gives the F-term interaction of the compactified theory. In particular, it is related to the instanton partition function via Nekrasov conjecture. We will introduce ADHM sheaves on curve, as an alternative description of local Donaldson-Thomas theory. We derive the wallcrossing of ADHM invariants and their refinements. We show that it is equivalent to the semi-primitive wallcrossing from supergravity, and the Kontsevich-Soibelman wallcrossing formula. As an application, we discuss the connection between ADHM moduli space with Hitchin system. In particular we give a recursive formula for the Poincare polynomial of Hitchin system in terms of instanton partition function, from refined wallcrossing. We also introduce higher rank generalization of Donaldson-Thomas invariant in the context of ADHM sheaves. We study their wallcrossing and discuss their physical interpretation via string duality.

Topological analysis of metabolic networks based on petri net theory.

PubMed

Zevedei-Oancea, Ionela; Schuster, Stefan

2011-01-01

Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.

Topological analysis of metabolic networks based on Petri net theory.

PubMed

Zevedei-Oancea, Ionela; Schuster, Stefan

2003-01-01

Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.

Measurement of Z0-boson production at large rapidities in Pb-Pb collisions at √{sNN } = 5.02TeV

NASA Astrophysics Data System (ADS)

Acharya, S.; Adamová, D.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Al-Turany, M.; Alam, S. N.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alfaro Molina, R.; Ali, Y.; Alici, A.; Alkin, A.; Alme, J.; Alt, T.; Altenkamper, L.; Altsybeev, I.; Andrei, C.; Andreou, D.; Andrews, H. A.; Andronic, A.; Angeletti, M.; Anguelov, V.; Anson, C.; Antičić, T.; Antinori, F.; Antonioli, P.; Apadula, N.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Baldisseri, A.; Ball, M.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barioglio, L.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartsch, E.; Bastid, N.; Basu, S.; Batigne, G.; Batyunya, B.; Batzing, P. C.; Bazo Alba, J. L.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Beltran, L. G. E.; Belyaev, V.; Bencedi, G.; Beole, S.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhaduri, P. P.; Bhasin, A.; Bhat, I. R.; Bhattacharjee, B.; Bhom, J.; Bianchi, A.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Blair, J. T.; Blau, D.; Blume, C.; Boca, G.; Bock, F.; Bogdanov, A.; Boldizsár, L.; Bombara, M.; Bonomi, G.; Bonora, M.; Borel, H.; Borissov, A.; Borri, M.; Botta, E.; Bourjau, C.; Bratrud, L.; Braun-Munzinger, P.; Bregant, M.; Broker, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buhler, P.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Caines, H.; Caliva, A.; Calvo Villar, E.; Camacho, R. S.; Camerini, P.; Capon, A. A.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Chandra, S.; Chang, B.; Chang, W.; Chapeland, S.; Chartier, M.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Chojnacki, M.; Choudhury, S.; Chowdhury, T.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Concas, M.; Conesa Balbastre, G.; Conesa Del Valle, Z.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Costanza, S.; Crkovská, J.; Crochet, P.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; de, S.; de Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; de Falco, A.; de Gruttola, D.; De Marco, N.; de Pasquale, S.; de Souza, R. D.; Degenhardt, H. F.; Deisting, A.; Deloff, A.; Deplano, C.; Dhankher, P.; di Bari, D.; di Mauro, A.; di Nezza, P.; di Ruzza, B.; Dietel, T.; Dillenseger, P.; Ding, Y.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Doremalen, L. V. R.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Dudi, S.; Duggal, A. K.; Dukhishyam, M.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erhardt, F.; Espagnon, B.; Eulisse, G.; Eum, J.; Evans, D.; Evdokimov, S.; Fabbietti, L.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Fernández Téllez, A.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Francisco, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gajdosova, K.; Gallio, M.; Galvan, C. D.; Ganoti, P.; Garabatos, C.; Garcia-Solis, E.; Garg, K.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Gay Ducati, M. B.; Germain, M.; Ghosh, J.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Graczykowski, L. K.; Graham, K. L.; Greiner, L.; Grelli, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Gronefeld, J. M.; Grosa, F.; Grosse-Oetringhaus, J. F.; Grosso, R.; Guber, F.; Guernane, R.; Guerzoni, B.; Guittiere, M.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Guzman, I. B.; Haake, R.; Hadjidakis, C.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Haque, M. R.; Harris, J. W.; Harton, A.; Hassan, H.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Hernandez, E. G.; Herrera Corral, G.; Herrmann, F.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hills, C.; Hippolyte, B.; Hohlweger, B.; Horak, D.; Hornung, S.; Hosokawa, R.; Hristov, P.; Hughes, C.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Iddon, J. P.; Iga Buitron, S. A.; Ilkaev, R.; Inaba, M.; Ippolitov, M.; Islam, M. S.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacak, B.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jaelani, S.; Jahnke, C.; Jakubowska, M. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jercic, M.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karczmarczyk, P.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Ketzer, B.; Khabanova, Z.; Khan, P.; Khan, S.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Khatun, A.; Khuntia, A.; Kielbowicz, M. M.; Kileng, B.; Kim, B.; Kim, D.; Kim, D. J.; Kim, E. J.; Kim, H.; Kim, J. S.; Kim, J.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Köhler, M. K.; Kollegger, T.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Konyushikhin, M.; Kopcik, M.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Králik, I.; Kravčáková, A.; Kreis, L.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kundu, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kushpil, S.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Lagana Fernandes, C.; Lai, Y. S.; Lakomov, I.; Langoy, R.; Lapidus, K.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lavicka, R.; Lea, R.; Leardini, L.; Lee, S.; Lehas, F.; Lehner, S.; Lehrbach, J.; Lemmon, R. C.; Leogrande, E.; León Monzón, I.; Lévai, P.; Li, X.; Li, X. L.; Lien, J.; Lietava, R.; Lim, B.; Lindal, S.; Lindenstruth, V.; Lindsay, S. W.; Lippmann, C.; Lisa, M. A.; Litichevskyi, V.; Liu, A.; Llope, W. J.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Loncar, P.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Luhder, J. R.; Lunardon, M.; Luparello, G.; Lupi, M.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Mao, Y.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martinengo, P.; Martinez, J. A. L.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Masciocchi, S.; Masera, M.; Masoni, A.; Massacrier, L.; Masson, E.; Mastroserio, A.; Mathis, A. M.; Matuoka, P. F. T.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzilli, M.; Mazzoni, M. A.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Mhlanga, S.; Miake, Y.; Mieskolainen, M. M.; Mihaylov, D. L.; Mikhaylov, K.; Mischke, A.; Mishra, A. N.; Miśkowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, A. P.; Mohanty, B.; Mohisin Khan, M.; Moreira de Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Münning, K.; Munoz, M. I. A.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Myers, C. J.; Myrcha, J. W.; Nag, D.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Narayan, A.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Negrao de Oliveira, R. A.; Nellen, L.; Nesbo, S. V.; Neskovic, G.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Nobuhiro, A.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, H.; Ohlson, A.; Olah, L.; Oleniacz, J.; Oliveira da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Pachmayer, Y.; Pacik, V.; Pagano, D.; Paić, G.; Palni, P.; Pan, J.; Pandey, A. K.; Panebianco, S.; Papikyan, V.; Pareek, P.; Park, J.; Parmar, S.; Passfeld, A.; Pathak, S. P.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Peng, X.; Pereira, L. G.; Pereira da Costa, H.; Peresunko, D.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrovici, M.; Petta, C.; Pezzi, R. P.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Płoskoń, M.; Planinic, M.; Pliquett, F.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Poppenborg, H.; Porteboeuf-Houssais, S.; Pozdniakov, V.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Punin, V.; Putschke, J.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Rana, D. B.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Ratza, V.; Ravasenga, I.; Read, K. F.; Redlich, K.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reshetin, A.; Reygers, K.; Riabov, V.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rodríguez Cahuantzi, M.; Røed, K.; Rogalev, R.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Rokita, P. S.; Ronchetti, F.; Rosas, E. D.; Roslon, K.; Rosnet, P.; Rossi, A.; Rotondi, A.; Roukoutakis, F.; Roy, C.; Roy, P.; Rueda, O. V.; Rui, R.; Rumyantsev, B.; Rustamov, A.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Saha, S. K.; Sahoo, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Sandoval, A.; Sarkar, A.; Sarkar, D.; Sarkar, N.; Sarma, P.; Sas, M. H. P.; Scapparone, E.; Scarlassara, F.; Schaefer, B.; Scheid, H. S.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schmidt, M. O.; Schmidt, M.; Schmidt, N. V.; Schukraft, J.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sett, P.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shahoyan, R.; Shaikh, W.; Shangaraev, A.; Sharma, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shimomura, M.; Shirinkin, S.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silaeva, S.; Silvermyr, D.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singhal, V.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Soramel, F.; Sorensen, S.; Sozzi, F.; Sputowska, I.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Stocco, D.; Storetvedt, M. M.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Suzuki, K.; Swain, S.; Szabo, A.; Szarka, I.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thakur, D.; Thakur, S.; Thomas, D.; Thoresen, F.; Tieulent, R.; Tikhonov, A.; Timmins, A. R.; Toia, A.; Toppi, M.; Torres, S. R.; Tripathy, S.; Trogolo, S.; Trombetta, G.; Tropp, L.; Trubnikov, V.; Trzaska, W. H.; Trzeciak, B. A.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Umaka, E. N.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; van der Maarel, J.; van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vázquez Doce, O.; Vechernin, V.; Veen, A. M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vermunt, L.; Vernet, R.; Vértesi, R.; Vickovic, L.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Virgili, T.; Vislavicius, V.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Voscek, D.; Vranic, D.; Vrláková, J.; Wagner, B.; Wang, H.; Wang, M.; Watanabe, Y.; Weber, M.; Weber, S. G.; Wegrzynek, A.; Weiser, D. F.; Wenzel, S. C.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Willems, G. A.; Williams, M. C. S.; Willsher, E.; Windelband, B.; Witt, W. E.; Xu, R.; Yalcin, S.; Yamakawa, K.; Yang, P.; Yano, S.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yun, E.; Yurchenko, V.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zhu, Y.; Zichichi, A.; Zimmermann, M. B.; Zinovjev, G.; Zmeskal, J.; Zou, S.; Alice Collaboration

2018-05-01

The production of Z0 bosons at large rapidities in Pb-Pb collisions at √{sNN } = 5.02TeV is reported. Z0 candidates are reconstructed in the dimuon decay channel (Z0 →μ+μ-), based on muons selected with pseudo-rapidity - 4.0 < η < - 2.5 and pT > 20GeV/ c. The invariant yield and the nuclear modification factor, RAA, are presented as a function of rapidity and collision centrality. The value of RAA for the 0-20% central Pb-Pb collisions is 0.67 ± 0.11(stat.) ± 0.03(syst.) ± 0.06(corr. syst.), exhibiting a deviation of 2.6σ from unity. The results are well-described by calculations that include nuclear modifications of the parton distribution functions, while the predictions using vacuum PDFs deviate from data by 2.3σ in the 0-90% centrality class and by 3σ in the 0-20% central collisions.

Probing the Topology of Density Matrices

NASA Astrophysics Data System (ADS)

Bardyn, Charles-Edouard; Wawer, Lukas; Altland, Alexander; Fleischhauer, Michael; Diehl, Sebastian

2018-01-01

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the "ensemble geometric phase" (EGP)—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

Wide baseline stereo matching based on double topological relationship consistency

NASA Astrophysics Data System (ADS)

Zou, Xiaohong; Liu, Bin; Song, Xiaoxue; Liu, Yang

2009-07-01

Stereo matching is one of the most important branches in computer vision. In this paper, an algorithm is proposed for wide-baseline stereo vision matching. Here, a novel scheme is presented called double topological relationship consistency (DCTR). The combination of double topological configuration includes the consistency of first topological relationship (CFTR) and the consistency of second topological relationship (CSTR). It not only sets up a more advanced model on matching, but discards mismatches by iteratively computing the fitness of the feature matches and overcomes many problems of traditional methods depending on the powerful invariance to changes in the scale, rotation or illumination across large view changes and even occlusions. Experimental examples are shown where the two cameras have been located in very different orientations. Also, epipolar geometry can be recovered using RANSAC by far the most widely method adopted possibly. By the method, we can obtain correspondences with high precision on wide baseline matching problems. Finally, the effectiveness and reliability of this method are demonstrated in wide-baseline experiments on the image pairs.

Towards topological quantum computer

NASA Astrophysics Data System (ADS)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Topology, structures, and energy landscapes of human chromosomes

PubMed Central

Zhang, Bin; Wolynes, Peter G.

2015-01-01

Chromosome conformation capture experiments provide a rich set of data concerning the spatial organization of the genome. We use these data along with a maximum entropy approach to derive a least-biased effective energy landscape for the chromosome. Simulations of the ensemble of chromosome conformations based on the resulting information theoretic landscape not only accurately reproduce experimental contact probabilities, but also provide a picture of chromosome dynamics and topology. The topology of the simulated chromosomes is probed by computing the distribution of their knot invariants. The simulated chromosome structures are largely free of knots. Topologically associating domains are shown to be crucial for establishing these knotless structures. The simulated chromosome conformations exhibit a tendency to form fibril-like structures like those observed via light microscopy. The topologically associating domains of the interphase chromosome exhibit multistability with varying liquid crystalline ordering that may allow discrete unfolding events and the landscape is locally funneled toward “ideal” chromosome structures that represent hierarchical fibrils of fibrils. PMID:25918364

Computational models of location-invariant orthographic processing

NASA Astrophysics Data System (ADS)

Dandurand, Frédéric; Hannagan, Thomas; Grainger, Jonathan

2013-03-01

We trained three topologies of backpropagation neural networks to discriminate 2000 words (lexical representations) presented at different positions of a horizontal letter array. The first topology (zero-deck) contains no hidden layer, the second (one-deck) has a single hidden layer, and for the last topology (two-deck), the task is divided in two subtasks implemented as two stacked neural networks, with explicit word-centred letters as intermediate representations. All topologies successfully simulated two key benchmark phenomena observed in skilled human reading: transposed-letter priming and relative-position priming. However, the two-deck topology most accurately simulated the ability to discriminate words from nonwords, while containing the fewest connection weights. We analysed the internal representations after training. Zero-deck networks implement a letter-based scheme with a position bias to differentiate anagrams. One-deck networks implement a holographic overlap coding in which representations are essentially letter-based and words are linear combinations of letters. Two-deck networks also implement holographic-coding.

Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of self-interference incoherent holographic systems.

PubMed

Rosen, Joseph; Kelner, Roy

2014-11-17

The Lagrange invariant is a well-known law for optical imaging systems formulated in the frame of ray optics. In this study, we reformulate this law in terms of wave optics and relate it to the resolution limits of various imaging systems. Furthermore, this modified Lagrange invariant is generalized for imaging along the z axis, resulting with the axial Lagrange invariant which can be used to analyze the axial resolution of various imaging systems. To demonstrate the effectiveness of the theory, analysis of the lateral and the axial imaging resolutions is provided for Fresnel incoherent correlation holography (FINCH) systems.

Orbital selective spin-texture in a topological insulator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Bahadur, E-mail: bahadursingh24@gmail.com; Prasad, R.

Three-dimensional topological insulators support a metallic non-trivial surface state with unique spin texture, where spin and momentum are locked perpendicular to each other. In this work, we investigate the orbital selective spin-texture associated with the topological surface states in Sb2Te{sub 3}, using the first principles calculations. Sb2Te{sub 3} is a strong topological insulator with a p-p type bulk band inversion at the Γ-point and supports a single topological metallic surface state with upper (lower) Dirac-cone has left (right) handed spin-texture. Here, we show that the topological surface state has an additional locking between the spin and orbitals, leading to anmore » orbital selective spin-texture. The out-of-plane orbitals (p{sub z} orbitals) have an isotropic orbital texture for both the Dirac cones with an associated left and right handed spin-texture for the upper and lower Dirac cones, respectively. In contrast, the in-planar orbital texture (p{sub x} and p{sub y} projections) is tangential for the upper Dirac-cone and is radial for the lower Dirac-cone surface state. The dominant in-planar orbital texture in both the Dirac cones lead to a right handed orbital-selective spin-texture.« less

Measurement of the cross-section for electroweak production of dijets in association with a Z boson in pp collisions at s = 13   TeV with the ATLAS detector

DOE PAGES

Aaboud, M.; Aad, G.; Abbott, B.; ...

2017-10-27

The cross-section for the production of two jets in association with a leptonically decaying Z boson (Zjj ) is measured in proton–proton collisions at a centre-of-mass energy of 13 TeV, using data recorded with the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 3.2 fb -1. The electroweak Zjj cross-section is extracted in a fiducial region chosen to enhance the electroweak contribution relative to the dominant Drell–Yan Zjj process, which is constrained using a data-driven approach. The measured fiducial electroweak cross-section is σmore » $$Zjj\\atop{EW}$$ 119 ± 16 (stat.) ± 20 (syst.) ± 2 (lumi.) fb for dijet invariant mass greater than 250 GeV, and 34.2 ± 5.8 (stat.) ± 5.5 (syst.) ± 0.7 (lumi.) fb for dijet invariant mass greater than 1 TeV. Standard Model predictions are in agreement with the measurements. Lastly, the inclusive Zjj cross-section is also measured in six different fiducial regions with varying contributions from electroweak and Drell–Yan Zjj production.« less

Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles.

PubMed

Bhatnagar, Akshay; Gustavsson, K; Mitra, Dhrubaditya

2018-02-01

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component V_{R} for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D_{2}. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011)PLEEE81539-375510.1103/PhysRevE.84.045304; J. Turbul. 15, 34 (2014)1468-524810.1080/14685248.2013.875188] that the scale invariant part of the distribution has two asymptotic regimes: (1) |V_{R}|≪R, where the distribution depends solely on R, and (2) |V_{R}|≫R, where the distribution is a function of |V_{R}| alone. The probability distributions in these two regimes are matched along a straight line: |V_{R}|=z^{*}R. Our simulations confirm that this is indeed correct. We further obtain D_{2} and z^{*} as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St.

Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles

NASA Astrophysics Data System (ADS)

Bhatnagar, Akshay; Gustavsson, K.; Mitra, Dhrubaditya

2018-02-01

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component VR for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D2. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011), 10.1103/PhysRevE.84.045304; J. Turbul. 15, 34 (2014), 10.1080/14685248.2013.875188] that the scale invariant part of the distribution has two asymptotic regimes: (1) | VR|≪R , where the distribution depends solely on R , and (2) | VR|≫R , where the distribution is a function of | VR| alone. The probability distributions in these two regimes are matched along a straight line: | VR|= z*R . Our simulations confirm that this is indeed correct. We further obtain D2 and z* as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St.

Measurement of the cross-section for electroweak production of dijets in association with a Z boson in pp collisions at √{ s } = 13 TeV with the ATLAS detector

NASA Astrophysics Data System (ADS)

Aaboud, M.; Aad, G.; Abbott, B.; Abdinov, O.; Abeloos, B.; Abidi, S. H.; Abouzeid, O. S.; Abraham, N. L.; Abramowicz, H.; Abreu, H.; Abreu, R.; Abulaiti, Y.; Acharya, B. S.; Adachi, S.; Adamczyk, L.; Adelman, J.; Adersberger, M.; Adye, T.; Affolder, A. A.; Afik, Y.; Agatonovic-Jovin, T.; Agheorghiesei, C.; Aguilar-Saavedra, J. A.; Ahlen, S. P.; Ahmadov, F.; Aielli, G.; Akatsuka, S.; Akerstedt, H.; Åkesson, T. P. A.; Akilli, E.; Akimov, A. V.; Alberghi, G. L.; Albert, J.; Albicocco, P.; Alconada Verzini, M. J.; Alderweireldt, S. C.; Aleksa, M.; Aleksandrov, I. N.; Alexa, C.; Alexander, G.; Alexopoulos, T.; Alhroob, M.; Ali, B.; Aliev, M.; Alimonti, G.; Alison, J.; Alkire, S. P.; Allbrooke, B. M. M.; Allen, B. W.; Allport, P. P.; Aloisio, A.; Alonso, A.; Alonso, F.; Alpigiani, C.; Alshehri, A. A.; Alstaty, M. I.; Alvarez Gonzalez, B.; Álvarez Piqueras, D.; Alviggi, M. G.; Amadio, B. T.; Amaral Coutinho, Y.; Amelung, C.; Amidei, D.; Amor Dos Santos, S. P.; Amoroso, S.; Amundsen, G.; Anastopoulos, C.; Ancu, L. S.; Andari, N.; Andeen, T.; Anders, C. F.; Anders, J. K.; Anderson, K. J.; Andreazza, A.; Andrei, V.; Angelidakis, S.; Angelozzi, I.; Angerami, A.; Anisenkov, A. V.; Anjos, N.; Annovi, A.; Antel, C.; Antonelli, M.; Antonov, A.; Antrim, D. J.; Anulli, F.; Aoki, M.; Aperio Bella, L.; Arabidze, G.; Arai, Y.; Araque, J. P.; Araujo Ferraz, V.; Arce, A. T. H.; Ardell, R. E.; Arduh, F. A.; Arguin, J.-F.; Argyropoulos, S.; Arik, M.; Armbruster, A. J.; Armitage, L. J.; Arnaez, O.; Arnold, H.; Arratia, M.; Arslan, O.; Artamonov, A.; Artoni, G.; Artz, S.; Asai, S.; Asbah, N.; Ashkenazi, A.; Asquith, L.; Assamagan, K.; Astalos, R.; Atkinson, M.; Atlay, N. B.; Augsten, K.; Avolio, G.; Axen, B.; Ayoub, M. K.; Azuelos, G.; Baas, A. E.; Baca, M. J.; Bachacou, H.; Bachas, K.; Backes, M.; Bagnaia, P.; Bahmani, M.; Bahrasemani, H.; Baines, J. T.; Bajic, M.; Baker, O. K.; Baldin, E. M.; Balek, P.; Balli, F.; Balunas, W. K.; Banas, E.; Bandyopadhyay, A.; Banerjee, Sw.; Bannoura, A. A. E.; Barak, L.; Barberio, E. L.; Barberis, D.; Barbero, M.; Barillari, T.; Barisits, M.-S.; Barkeloo, J. T.; Barklow, T.; Barlow, N.; Barnes, S. L.; Barnett, B. M.; Barnett, R. M.; Barnovska-Blenessy, Z.; Baroncelli, A.; Barone, G.; Barr, A. J.; Barranco Navarro, L.; Barreiro, F.; Barreiro Guimarães da Costa, J.; Bartoldus, R.; Barton, A. E.; Bartos, P.; Basalaev, A.; Bassalat, A.; Bates, R. L.; Batista, S. J.; Batley, J. R.; Battaglia, M.; Bauce, M.; Bauer, F.; Bawa, H. S.; Beacham, J. B.; Beattie, M. D.; Beau, T.; Beauchemin, P. H.; Bechtle, P.; Beck, H. P.; Beck, H. C.; Becker, K.; Becker, M.; Becot, C.; Beddall, A. J.; Beddall, A.; Bednyakov, V. A.; Bedognetti, M.; Bee, C. P.; Beermann, T. A.; Begalli, M.; Begel, M.; Behr, J. K.; Bell, A. S.; Bella, G.; Bellagamba, L.; Bellerive, A.; Bellomo, M.; Belotskiy, K.; Beltramello, O.; Belyaev, N. L.; Benary, O.; Benchekroun, D.; Bender, M.; Bendtz, K.; Benekos, N.; Benhammou, Y.; Benhar Noccioli, E.; Benitez, J.; Benjamin, D. P.; Benoit, M.; Bensinger, J. R.; Bentvelsen, S.; Beresford, L.; Beretta, M.; Berge, D.; Bergeaas Kuutmann, E.; Berger, N.; Beringer, J.; Berlendis, S.; Bernard, N. R.; Bernardi, G.; Bernius, C.; Bernlochner, F. U.; Berry, T.; Berta, P.; Bertella, C.; Bertoli, G.; Bertolucci, F.; Bertram, I. A.; Bertsche, C.; Bertsche, D.; Besjes, G. J.; Bessidskaia Bylund, O.; Bessner, M.; Besson, N.; Bethani, A.; Bethke, S.; Bevan, A. J.; Beyer, J.; Bianchi, R. M.; Biebel, O.; Biedermann, D.; Bielski, R.; Bierwagen, K.; Biesuz, N. V.; Biglietti, M.; Billoud, T. R. V.; Bilokon, H.; Bindi, M.; Bingul, A.; Bini, C.; Biondi, S.; Bisanz, T.; Bittrich, C.; Bjergaard, D. M.; Black, J. E.; Black, K. M.; Blair, R. E.; Blazek, T.; Bloch, I.; Blocker, C.; Blue, A.; Blum, W.; Blumenschein, U.; Blunier, S.; Bobbink, G. J.; Bobrovnikov, V. S.; Bocchetta, S. S.; Bocci, A.; Bock, C.; Boehler, M.; Boerner, D.; Bogavac, D.; Bogdanchikov, A. G.; Bohm, C.; Boisvert, V.; Bokan, P.; Bold, T.; Boldyrev, A. S.; Bolz, A. E.; Bomben, M.; Bona, M.; Boonekamp, M.; Borisov, A.; Borissov, G.; Bortfeldt, J.; Bortoletto, D.; Bortolotto, V.; Boscherini, D.; Bosman, M.; Bossio Sola, J. D.; Boudreau, J.; Bouffard, J.; Bouhova-Thacker, E. V.; Boumediene, D.; Bourdarios, C.; Boutle, S. K.; Boveia, A.; Boyd, J.; Boyko, I. R.; Bracinik, J.; Brandt, A.; Brandt, G.; Brandt, O.; Bratzler, U.; Brau, B.; Brau, J. E.; Breaden Madden, W. D.; Brendlinger, K.; Brennan, A. J.; Brenner, L.; Brenner, R.; Bressler, S.; Briglin, D. L.; Bristow, T. M.; Britton, D.; Britzger, D.; Brochu, F. M.; Brock, I.; Brock, R.; Brooijmans, G.; Brooks, T.; Brooks, W. K.; Brosamer, J.; Brost, E.; Broughton, J. H.; Bruckman de Renstrom, P. A.; Bruncko, D.; Bruni, A.; Bruni, G.; Bruni, L. S.; Brunt, Bh; Bruschi, M.; Bruscino, N.; Bryant, P.; Bryngemark, L.; Buanes, T.; Buat, Q.; Buchholz, P.; Buckley, A. G.; Budagov, I. A.; Buehrer, F.; Bugge, M. K.; Bulekov, O.; Bullock, D.; Burch, T. J.; Burdin, S.; Burgard, C. D.; Burger, A. M.; Burghgrave, B.; Burka, K.; Burke, S.; Burmeister, I.; Burr, J. T. P.; Busato, E.; Büscher, D.; Büscher, V.; Bussey, P.; Butler, J. M.; Buttar, C. M.; Butterworth, J. M.; Butti, P.; Buttinger, W.; Buzatu, A.; Buzykaev, A. R.; Cabrera Urbán, S.; Caforio, D.; Cairo, V. M.; Cakir, O.; Calace, N.; Calafiura, P.; Calandri, A.; Calderini, G.; Calfayan, P.; Callea, G.; Caloba, L. P.; Calvente Lopez, S.; Calvet, D.; Calvet, S.; Calvet, T. P.; Camacho Toro, R.; Camarda, S.; Camarri, P.; Cameron, D.; Caminal Armadans, R.; Camincher, C.; Campana, S.; Campanelli, M.; Camplani, A.; Campoverde, A.; Canale, V.; Cano Bret, M.; Cantero, J.; Cao, T.; Capeans Garrido, M. D. M.; Caprini, I.; Caprini, M.; Capua, M.; Carbone, R. M.; Cardarelli, R.; Cardillo, F.; Carli, I.; Carli, T.; Carlino, G.; Carlson, B. T.; Carminati, L.; Carney, R. M. D.; Caron, S.; Carquin, E.; Carrá, S.; Carrillo-Montoya, G. D.; Casadei, D.; Casado, M. P.; Casolino, M.; Casper, D. W.; Castelijn, R.; Castillo Gimenez, V.; Castro, N. F.; Catinaccio, A.; Catmore, J. R.; Cattai, A.; Caudron, J.; Cavaliere, V.; Cavallaro, E.; Cavalli, D.; Cavalli-Sforza, M.; Cavasinni, V.; Celebi, E.; Ceradini, F.; Cerda Alberich, L.; Cerqueira, A. S.; Cerri, A.; Cerrito, L.; Cerutti, F.; Cervelli, A.; Cetin, S. A.; Chafaq, A.; Chakraborty, D.; Chan, S. K.; Chan, W. S.; Chan, Y. L.; Chang, P.; Chapman, J. D.; Charlton, D. G.; Chau, C. C.; Chavez Barajas, C. A.; Che, S.; Cheatham, S.; Chegwidden, A.; Chekanov, S.; Chekulaev, S. V.; Chelkov, G. A.; Chelstowska, M. A.; Chen, C.; Chen, H.; Chen, J.; Chen, S.; Chen, S.; Chen, X.; Chen, Y.; Cheng, H. C.; Cheng, H. J.; Cheplakov, A.; Cheremushkina, E.; Cherkaoui El Moursli, R.; Cheu, E.; Cheung, K.; Chevalier, L.; Chiarella, V.; Chiarelli, G.; Chiodini, G.; Chisholm, A. S.; Chitan, A.; Chiu, Y. H.; Chizhov, M. V.; Choi, K.; Chomont, A. R.; Chouridou, S.; Chow, Y. S.; Christodoulou, V.; Chu, M. C.; Chudoba, J.; Chuinard, A. J.; Chwastowski, J. J.; Chytka, L.; Ciftci, A. K.; Cinca, D.; Cindro, V.; Cioara, I. A.; Ciocca, C.; Ciocio, A.; Cirotto, F.; Citron, Z. H.; Citterio, M.; Ciubancan, M.; Clark, A.; Clark, B. L.; Clark, M. R.; Clark, P. J.; Clarke, R. N.; Clement, C.; Coadou, Y.; Cobal, M.; Coccaro, A.; Cochran, J.; Colasurdo, L.; Cole, B.; Colijn, A. P.; Collot, J.; Colombo, T.; Conde Muiño, P.; Coniavitis, E.; Connell, S. H.; Connelly, I. A.; Constantinescu, S.; Conti, G.; Conventi, F.; Cooke, M.; Cooper-Sarkar, A. M.; Cormier, F.; Cormier, K. J. R.; Corradi, M.; Corriveau, F.; Cortes-Gonzalez, A.; Cortiana, G.; Costa, G.; Costa, M. J.; Costanzo, D.; Cottin, G.; Cowan, G.; Cox, B. E.; Cranmer, K.; Crawley, S. J.; Creager, R. A.; Cree, G.; Crépé-Renaudin, S.; Crescioli, F.; Cribbs, W. A.; Cristinziani, M.; Croft, V.; Crosetti, G.; Cueto, A.; Cuhadar Donszelmann, T.; Cukierman, A. R.; Cummings, J.; Curatolo, M.; Cúth, J.; Czekierda, S.; Czodrowski, P.; D'Amen, G.; D'Auria, S.; D'Eramo, L.; D'Onofrio, M.; da Cunha Sargedas de Sousa, M. J.; da Via, C.; Dabrowski, W.; Dado, T.; Dai, T.; Dale, O.; Dallaire, F.; Dallapiccola, C.; Dam, M.; Dandoy, J. R.; Daneri, M. F.; Dang, N. P.; Daniells, A. C.; Dann, N. S.; Danninger, M.; Dano Hoffmann, M.; Dao, V.; Darbo, G.; Darmora, S.; Dassoulas, J.; Dattagupta, A.; Daubney, T.; Davey, W.; David, C.; Davidek, T.; Davis, D. R.; Davison, P.; Dawe, E.; Dawson, I.; de, K.; de Asmundis, R.; de Benedetti, A.; de Castro, S.; de Cecco, S.; de Groot, N.; de Jong, P.; de la Torre, H.; de Lorenzi, F.; de Maria, A.; de Pedis, D.; de Salvo, A.; de Sanctis, U.; de Santo, A.; de Vasconcelos Corga, K.; de Vivie de Regie, J. B.; Debbe, R.; Debenedetti, C.; Dedovich, D. V.; Dehghanian, N.; Deigaard, I.; Del Gaudio, M.; Del Peso, J.; Delgove, D.; Deliot, F.; Delitzsch, C. M.; Dell'Acqua, A.; Dell'Asta, L.; Dell'Orso, M.; Della Pietra, M.; Della Volpe, D.; Delmastro, M.; Delporte, C.; Delsart, P. A.; Demarco, D. A.; Demers, S.; Demichev, M.; Demilly, A.; Denisov, S. P.; Denysiuk, D.; Derendarz, D.; Derkaoui, J. E.; Derue, F.; Dervan, P.; Desch, K.; Deterre, C.; Dette, K.; Devesa, M. R.; Deviveiros, P. O.; Dewhurst, A.; Dhaliwal, S.; di Bello, F. A.; di Ciaccio, A.; di Ciaccio, L.; di Clemente, W. K.; di Donato, C.; di Girolamo, A.; di Girolamo, B.; di Micco, B.; di Nardo, R.; di Petrillo, K. F.; di Simone, A.; di Sipio, R.; di Valentino, D.; Diaconu, C.; Diamond, M.; Dias, F. A.; Diaz, M. A.; Diehl, E. B.; Dietrich, J.; Díez Cornell, S.; Dimitrievska, A.; Dingfelder, J.; Dita, P.; Dita, S.; Dittus, F.; Djama, F.; Djobava, T.; Djuvsland, J. I.; Do Vale, M. A. B.; Dobos, D.; Dobre, M.; Doglioni, C.; Dolejsi, J.; Dolezal, Z.; Donadelli, M.; Donati, S.; Dondero, P.; Donini, J.; Dopke, J.; Doria, A.; Dova, M. T.; Doyle, A. T.; Drechsler, E.; Dris, M.; Du, Y.; Duarte-Campderros, J.; Dubreuil, A.; Duchovni, E.; Duckeck, G.; Ducourthial, A.; Ducu, O. A.; Duda, D.; Dudarev, A.; Dudder, A. Chr.; Duffield, E. M.; Duflot, L.; Dührssen, M.; Dumancic, M.; Dumitriu, A. E.; Duncan, A. K.; Dunford, M.; Duran Yildiz, H.; Düren, M.; Durglishvili, A.; Duschinger, D.; Dutta, B.; Duvnjak, D.; Dyndal, M.; Dziedzic, B. S.; Eckardt, C.; Ecker, K. M.; Edgar, R. C.; Eifert, T.; Eigen, G.; Einsweiler, K.; Ekelof, T.; El Kacimi, M.; El Kosseifi, R.; Ellajosyula, V.; Ellert, M.; Elles, S.; Ellinghaus, F.; Elliot, A. A.; Ellis, N.; Elmsheuser, J.; Elsing, M.; Emeliyanov, D.; Enari, Y.; Endner, O. C.; Ennis, J. S.; Erdmann, J.; Ereditato, A.; Ernst, M.; Errede, S.; Escalier, M.; Escobar, C.; Esposito, B.; Estrada Pastor, O.; Etienvre, A. I.; Etzion, E.; Evans, H.; Ezhilov, A.; Ezzi, M.; Fabbri, F.; Fabbri, L.; Fabiani, V.; Facini, G.; Fakhrutdinov, R. M.; Falciano, S.; Falla, R. J.; Faltova, J.; Fang, Y.; Fanti, M.; Farbin, A.; Farilla, A.; Farina, C.; Farina, E. M.; Farooque, T.; Farrell, S.; Farrington, S. M.; Farthouat, P.; Fassi, F.; Fassnacht, P.; Fassouliotis, D.; Faucci Giannelli, M.; Favareto, A.; Fawcett, W. J.; Fayard, L.; Fedin, O. L.; Fedorko, W.; Feigl, S.; Feligioni, L.; Feng, C.; Feng, E. J.; Feng, H.; Fenton, M. J.; Fenyuk, A. B.; Feremenga, L.; Fernandez Martinez, P.; Fernandez Perez, S.; Ferrando, J.; Ferrari, A.; Ferrari, P.; Ferrari, R.; Ferreira de Lima, D. E.; Ferrer, A.; Ferrere, D.; Ferretti, C.; Fiedler, F.; Filipčič, A.; Filipuzzi, M.; Filthaut, F.; Fincke-Keeler, M.; Finelli, K. D.; Fiolhais, M. C. N.; Fiorini, L.; Fischer, A.; Fischer, C.; Fischer, J.; Fisher, W. C.; Flaschel, N.; Fleck, I.; Fleischmann, P.; Fletcher, R. R. M.; Flick, T.; Flierl, B. M.; Flores Castillo, L. R.; Flowerdew, M. J.; Forcolin, G. T.; Formica, A.; Förster, F. A.; Forti, A.; Foster, A. G.; Fournier, D.; Fox, H.; Fracchia, S.; Francavilla, P.; Franchini, M.; Franchino, S.; Francis, D.; Franconi, L.; Franklin, M.; Frate, M.; Fraternali, M.; Freeborn, D.; Fressard-Batraneanu, S. M.; Freund, B.; Froidevaux, D.; Frost, J. A.; Fukunaga, C.; Fusayasu, T.; Fuster, J.; Gabaldon, C.; Gabizon, O.; Gabrielli, A.; Gabrielli, A.; Gach, G. P.; Gadatsch, S.; Gadomski, S.; Gagliardi, G.; Gagnon, L. G.; Galea, C.; Galhardo, B.; Gallas, E. J.; Gallop, B. J.; Gallus, P.; Galster, G.; Gan, K. K.; Ganguly, S.; Gao, Y.; Gao, Y. S.; Garay Walls, F. M.; García, C.; García Navarro, J. E.; García Pascual, J. A.; Garcia-Sciveres, M.; Gardner, R. W.; Garelli, N.; Garonne, V.; Gascon Bravo, A.; Gasnikova, K.; Gatti, C.; Gaudiello, A.; Gaudio, G.; Gavrilenko, I. L.; Gay, C.; Gaycken, G.; Gazis, E. N.; Gee, C. N. P.; Geisen, J.; Geisen, M.; Geisler, M. P.; Gellerstedt, K.; Gemme, C.; Genest, M. H.; Geng, C.; Gentile, S.; Gentsos, C.; George, S.; Gerbaudo, D.; Gershon, A.; Geßner, G.; Ghasemi, S.; Ghneimat, M.; Giacobbe, B.; Giagu, S.; Giangiacomi, N.; Giannetti, P.; Gibson, S. M.; Gignac, M.; Gilchriese, M.; Gillberg, D.; Gilles, G.; Gingrich, D. M.; Giordani, M. P.; Giorgi, F. M.; Giraud, P. F.; Giromini, P.; Giugliarelli, G.; Giugni, D.; Giuli, F.; Giuliani, C.; Giulini, M.; Gjelsten, B. K.; Gkaitatzis, S.; Gkialas, I.; Gkougkousis, E. L.; Gkountoumis, P.; Gladilin, L. K.; Glasman, C.; Glatzer, J.; Glaysher, P. C. F.; Glazov, A.; Goblirsch-Kolb, M.; Godlewski, J.; Goldfarb, S.; Golling, T.; Golubkov, D.; Gomes, A.; Gonçalo, R.; Goncalves Gama, R.; Goncalves Pinto Firmino da Costa, J.; Gonella, G.; Gonella, L.; Gongadze, A.; González de La Hoz, S.; Gonzalez-Sevilla, S.; Goossens, L.; Gorbounov, P. A.; Gordon, H. A.; Gorelov, I.; Gorini, B.; Gorini, E.; Gorišek, A.; Goshaw, A. T.; Gössling, C.; Gostkin, M. I.; Gottardo, C. A.; Goudet, C. R.; Goujdami, D.; Goussiou, A. G.; Govender, N.; Gozani, E.; Graber, L.; Grabowska-Bold, I.; Gradin, P. O. J.; Gramling, J.; Gramstad, E.; Grancagnolo, S.; Gratchev, V.; Gravila, P. M.; Gray, C.; Gray, H. M.; Greenwood, Z. D.; Grefe, C.; Gregersen, K.; Gregor, I. M.; Grenier, P.; Grevtsov, K.; Griffiths, J.; Grillo, A. A.; Grimm, K.; Grinstein, S.; Gris, Ph.; Grivaz, J.-F.; Groh, S.; Gross, E.; Grosse-Knetter, J.; Grossi, G. C.; Grout, Z. J.; Grummer, A.; Guan, L.; Guan, W.; Guenther, J.; Guescini, F.; Guest, D.; Gueta, O.; Gui, B.; Guido, E.; Guillemin, T.; Guindon, S.; Gul, U.; Gumpert, C.; Guo, J.; Guo, W.; Guo, Y.; Gupta, R.; Gupta, S.; Gustavino, G.; Gutelman, B. J.; Gutierrez, P.; Gutierrez Ortiz, N. G.; Gutschow, C.; Guyot, C.; Guzik, M. P.; Gwenlan, C.; Gwilliam, C. B.; Haas, A.; Haber, C.; Hadavand, H. K.; Haddad, N.; Hadef, A.; Hageböck, S.; Hagihara, M.; Hakobyan, H.; Haleem, M.; Haley, J.; Halladjian, G.; Hallewell, G. D.; Hamacher, K.; Hamal, P.; Hamano, K.; Hamilton, A.; Hamity, G. N.; Hamnett, P. G.; Han, L.; Han, S.; Hanagaki, K.; Hanawa, K.; Hance, M.; Haney, B.; Hanke, P.; Hansen, J. B.; Hansen, J. D.; Hansen, M. C.; Hansen, P. H.; Hara, K.; Hard, A. S.; Harenberg, T.; Hariri, F.; Harkusha, S.; Harrington, R. D.; Harrison, P. F.; Hartmann, N. M.; Hasegawa, Y.; Hasib, A.; Hassani, S.; Haug, S.; Hauser, R.; Hauswald, L.; Havener, L. B.; Havranek, M.; Hawkes, C. M.; Hawkings, R. J.; Hayakawa, D.; Hayden, D.; Hays, C. P.; Hays, J. M.; Hayward, H. S.; Haywood, S. J.; Head, S. J.; Heck, T.; Hedberg, V.; Heelan, L.; Heer, S.; Heidegger, K. K.; Heim, S.; Heim, T.; Heinemann, B.; Heinrich, J. J.; Heinrich, L.; Heinz, C.; Hejbal, J.; Helary, L.; Held, A.; Hellman, S.; Helsens, C.; Henderson, R. C. W.; Heng, Y.; Henkelmann, S.; Henriques Correia, A. M.; Henrot-Versille, S.; Herbert, G. H.; Herde, H.; Herget, V.; Hernández Jiménez, Y.; Herr, H.; Herten, G.; Hertenberger, R.; Hervas, L.; Herwig, T. C.; Hesketh, G. G.; Hessey, N. P.; Hetherly, J. 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J.; Rieger, J.; Rifki, O.; Rijssenbeek, M.; Rimoldi, A.; Rimoldi, M.; Rinaldi, L.; Ripellino, G.; Ristić, B.; Ritsch, E.; Riu, I.; Rizatdinova, F.; Rizvi, E.; Rizzi, C.; Roberts, R. T.; Robertson, S. H.; Robichaud-Veronneau, A.; Robinson, D.; Robinson, J. E. M.; Robson, A.; Rocco, E.; Roda, C.; Rodina, Y.; Rodriguez Bosca, S.; Rodriguez Perez, A.; Rodriguez Rodriguez, D.; Roe, S.; Rogan, C. S.; Røhne, O.; Roloff, J.; Romaniouk, A.; Romano, M.; Romano Saez, S. M.; Romero Adam, E.; Rompotis, N.; Ronzani, M.; Roos, L.; Rosati, S.; Rosbach, K.; Rose, P.; Rosien, N.-A.; Rossi, E.; Rossi, L. P.; Rosten, J. H. N.; Rosten, R.; Rotaru, M.; Rothberg, J.; Rousseau, D.; Rozanov, A.; Rozen, Y.; Ruan, X.; Rubbo, F.; Rühr, F.; Ruiz-Martinez, A.; Rurikova, Z.; Rusakovich, N. A.; Russell, H. L.; Rutherfoord, J. P.; Ruthmann, N.; Ryabov, Y. F.; Rybar, M.; Rybkin, G.; Ryu, S.; Ryzhov, A.; Rzehorz, G. F.; Saavedra, A. F.; Sabato, G.; Sacerdoti, S.; Sadrozinski, H. F.-W.; Sadykov, R.; Safai Tehrani, F.; Saha, P.; Sahinsoy, M.; Saimpert, M.; Saito, M.; Saito, T.; Sakamoto, H.; Sakurai, Y.; Salamanna, G.; Salazar Loyola, J. E.; Salek, D.; Sales de Bruin, P. H.; Salihagic, D.; Salnikov, A.; Salt, J.; Salvatore, D.; Salvatore, F.; Salvucci, A.; Salzburger, A.; Sammel, D.; Sampsonidis, D.; Sampsonidou, D.; Sánchez, J.; Sanchez Martinez, V.; Sanchez Pineda, A.; Sandaker, H.; Sandbach, R. L.; Sander, C. O.; Sandhoff, M.; Sandoval, C.; Sankey, D. P. C.; Sannino, M.; Sano, Y.; Sansoni, A.; Santoni, C.; Santos, H.; Santoyo Castillo, I.; Sapronov, A.; Saraiva, J. G.; Sarrazin, B.; Sasaki, O.; Sato, K.; Sauvan, E.; Savage, G.; Savard, P.; Savic, N.; Sawyer, C.; Sawyer, L.; Saxon, J.; Sbarra, C.; Sbrizzi, A.; Scanlon, T.; Scannicchio, D. A.; Schaarschmidt, J.; Schacht, P.; Schachtner, B. M.; Schaefer, D.; Schaefer, L.; Schaefer, R.; Schaeffer, J.; Schaepe, S.; Schaetzel, S.; Schäfer, U.; Schaffer, A. C.; Schaile, D.; Schamberger, R. D.; Schegelsky, V. A.; Scheirich, D.; Schernau, M.; Schiavi, C.; Schier, S.; Schildgen, L. K.; Schillo, C.; Schioppa, M.; Schlenker, S.; Schmidt-Sommerfeld, K. R.; Schmieden, K.; Schmitt, C.; Schmitt, S.; Schmitz, S.; Schnoor, U.; Schoeffel, L.; Schoening, A.; Schoenrock, B. D.; Schopf, E.; Schott, M.; Schouwenberg, J. F. P.; Schovancova, J.; Schramm, S.; Schuh, N.; Schulte, A.; Schultens, M. J.; Schultz-Coulon, H.-C.; Schulz, H.; Schumacher, M.; Schumm, B. A.; Schune, Ph.; Schwartzman, A.; Schwarz, T. A.; Schweiger, H.; Schwemling, Ph.; Schwienhorst, R.; Schwindling, J.; Sciandra, A.; Sciolla, G.; Scornajenghi, M.; Scuri, F.; Scutti, F.; Searcy, J.; Seema, P.; Seidel, S. C.; Seiden, A.; Seixas, J. M.; Sekhniaidze, G.; Sekhon, K.; Sekula, S. J.; Semprini-Cesari, N.; Senkin, S.; Serfon, C.; Serin, L.; Serkin, L.; Sessa, M.; Seuster, R.; Severini, H.; Sfiligoj, T.; Sforza, F.; Sfyrla, A.; Shabalina, E.; Shaikh, N. W.; Shan, L. Y.; Shang, R.; Shank, J. T.; Shapiro, M.; Shatalov, P. B.; Shaw, K.; Shaw, S. M.; Shcherbakova, A.; Shehu, C. Y.; Shen, Y.; Sherafati, N.; Sherwood, P.; Shi, L.; Shimizu, S.; Shimmin, C. O.; Shimojima, M.; Shipsey, I. P. J.; Shirabe, S.; Shiyakova, M.; Shlomi, J.; Shmeleva, A.; Shoaleh Saadi, D.; Shochet, M. J.; Shojaii, S.; Shope, D. R.; Shrestha, S.; Shulga, E.; Shupe, M. A.; Sicho, P.; Sickles, A. M.; Sidebo, P. E.; Sideras Haddad, E.; Sidiropoulou, O.; Sidoti, A.; Siegert, F.; Sijacki, Dj.; Silva, J.; Silverstein, S. B.; Simak, V.; Simic, Lj.; Simion, S.; Simioni, E.; Simmons, B.; Simon, M.; Sinervo, P.; Sinev, N. B.; Sioli, M.; Siragusa, G.; Siral, I.; Sivoklokov, S. Yu.; Sjölin, J.; Skinner, M. B.; Skubic, P.; Slater, M.; Slavicek, T.; Slawinska, M.; Sliwa, K.; Slovak, R.; Smakhtin, V.; Smart, B. H.; Smiesko, J.; Smirnov, N.; Smirnov, S. Yu.; Smirnov, Y.; Smirnova, L. N.; Smirnova, O.; Smith, J. W.; Smith, M. N. K.; Smith, R. W.; Smizanska, M.; Smolek, K.; Snesarev, A. A.; Snyder, I. M.; Snyder, S.; Sobie, R.; Socher, F.; Soffer, A.; Søgaard, A.; Soh, D. A.; Sokhrannyi, G.; Solans Sanchez, C. A.; Solar, M.; Soldatov, E. Yu.; Soldevila, U.; Solodkov, A. A.; Soloshenko, A.; Solovyanov, O. V.; Solovyev, V.; Sommer, P.; Son, H.; Sopczak, A.; Sosa, D.; Sotiropoulou, C. L.; Soualah, R.; Soukharev, A. M.; South, D.; Sowden, B. C.; Spagnolo, S.; Spalla, M.; Spangenberg, M.; Spanò, F.; Sperlich, D.; Spettel, F.; Spieker, T. M.; Spighi, R.; Spigo, G.; Spiller, L. A.; Spousta, M.; St. Denis, R. D.; Stabile, A.; Stamen, R.; Stamm, S.; Stanecka, E.; Stanek, R. W.; Stanescu, C.; Stanitzki, M. M.; Stapf, B. S.; Stapnes, S.; Starchenko, E. A.; Stark, G. H.; Stark, J.; Stark, S. H.; Staroba, P.; Starovoitov, P.; Stärz, S.; Staszewski, R.; Steinberg, P.; Stelzer, B.; Stelzer, H. J.; Stelzer-Chilton, O.; Stenzel, H.; Stewart, G. A.; Stockton, M. C.; Stoebe, M.; Stoicea, G.; Stolte, P.; Stonjek, S.; Stradling, A. R.; Straessner, A.; Stramaglia, M. E.; Strandberg, J.; Strandberg, S.; Strauss, M.; Strizenec, P.; Ströhmer, R.; Strom, D. M.; Stroynowski, R.; Strubig, A.; Stucci, S. A.; Stugu, B.; Styles, N. A.; Su, D.; Su, J.; Suchek, S.; Sugaya, Y.; Suk, M.; Sulin, V. V.; Sultan, Dms; Sultansoy, S.; Sumida, T.; Sun, S.; Sun, X.; Suruliz, K.; Suster, C. J. E.; Sutton, M. R.; Suzuki, S.; Svatos, M.; Swiatlowski, M.; Swift, S. P.; Sykora, I.; Sykora, T.; Ta, D.; Tackmann, K.; Taenzer, J.; Taffard, A.; Tafirout, R.; Tahirovic, E.; Taiblum, N.; Takai, H.; Takashima, R.; Takasugi, E. H.; Takeshita, T.; Takubo, Y.; Talby, M.; Talyshev, A. A.; Tanaka, J.; Tanaka, M.; Tanaka, R.; Tanaka, S.; Tanioka, R.; Tannenwald, B. B.; Tapia Araya, S.; Tapprogge, S.; Tarem, S.; Tartarelli, G. F.; Tas, P.; Tasevsky, M.; Tashiro, T.; Tassi, E.; Tavares Delgado, A.; Tayalati, Y.; Taylor, A. C.; Taylor, A. J.; Taylor, G. N.; Taylor, P. T. E.; Taylor, W.; Teixeira-Dias, P.; Temple, D.; Ten Kate, H.; Teng, P. K.; Teoh, J. J.; Tepel, F.; Terada, S.; Terashi, K.; Terron, J.; Terzo, S.; Testa, M.; Teuscher, R. J.; Theveneaux-Pelzer, T.; Thiele, F.; Thomas, J. P.; Thomas-Wilsker, J.; Thompson, P. D.; Thompson, A. S.; Thomsen, L. A.; Thomson, E.; Tibbetts, M. J.; Ticse Torres, R. E.; Tikhomirov, V. O.; Tikhonov, Yu. A.; Timoshenko, S.; Tipton, P.; Tisserant, S.; Todome, K.; Todorova-Nova, S.; Todt, S.; Tojo, J.; Tokár, S.; Tokushuku, K.; Tolley, E.; Tomlinson, L.; Tomoto, M.; Tompkins, L.; Toms, K.; Tong, B.; Tornambe, P.; Torrence, E.; Torres, H.; Torró Pastor, E.; Toth, J.; Touchard, F.; Tovey, D. R.; Treado, C. J.; Trefzger, T.; Tresoldi, F.; Tricoli, A.; Trigger, I. M.; Trincaz-Duvoid, S.; Tripiana, M. F.; Trischuk, W.; Trocmé, B.; Trofymov, A.; Troncon, C.; Trottier-McDonald, M.; Trovatelli, M.; Truong, L.; Trzebinski, M.; Trzupek, A.; Tsang, K. W.; Tseng, J. C.-L.; Tsiareshka, P. V.; Tsipolitis, G.; Tsirintanis, N.; Tsiskaridze, S.; Tsiskaridze, V.; Tskhadadze, E. G.; Tsui, K. M.; Tsukerman, I. I.; Tsulaia, V.; Tsuno, S.; Tsybychev, D.; Tu, Y.; Tudorache, A.; Tudorache, V.; Tulbure, T. T.; Tuna, A. N.; Tupputi, S. A.; Turchikhin, S.; Turgeman, D.; Turk Cakir, I.; Turra, R.; Tuts, P. M.; Ucchielli, G.; Ueda, I.; Ughetto, M.; Ukegawa, F.; Unal, G.; Undrus, A.; Unel, G.; Ungaro, F. C.; Unno, Y.; Unverdorben, C.; Urban, J.; Urquijo, P.; Urrejola, P.; Usai, G.; Usui, J.; Vacavant, L.; Vacek, V.; Vachon, B.; Vadla, K. O. H.; Vaidya, A.; Valderanis, C.; Valdes Santurio, E.; Valente, M.; Valentinetti, S.; Valero, A.; Valéry, L.; Valkar, S.; Vallier, A.; Valls Ferrer, J. A.; van den Wollenberg, W.; van der Graaf, H.; van Gemmeren, P.; van Nieuwkoop, J.; van Vulpen, I.; van Woerden, M. C.; Vanadia, M.; Vandelli, W.; Vaniachine, A.; Vankov, P.; Vardanyan, G.; Vari, R.; Varnes, E. W.; Varni, C.; Varol, T.; Varouchas, D.; Vartapetian, A.; Varvell, K. E.; Vasquez, J. G.; Vasquez, G. A.; Vazeille, F.; Vazquez Schroeder, T.; Veatch, J.; Veeraraghavan, V.; Veloce, L. M.; Veloso, F.; Veneziano, S.; Ventura, A.; Venturi, M.; Venturi, N.; Venturini, A.; Vercesi, V.; Verducci, M.; Verkerke, W.; Vermeulen, A. T.; Vermeulen, J. C.; Vetterli, M. C.; Viaux Maira, N.; Viazlo, O.; Vichou, I.; Vickey, T.; Vickey Boeriu, O. E.; Viehhauser, G. H. A.; Viel, S.; Vigani, L.; Villa, M.; Villaplana Perez, M.; Vilucchi, E.; Vincter, M. G.; Vinogradov, V. B.; Vishwakarma, A.; Vittori, C.; Vivarelli, I.; Vlachos, S.; Vogel, M.; Vokac, P.; Volpi, G.; von der Schmitt, H.; von Toerne, E.; Vorobel, V.; Vorobev, K.; Vos, M.; Voss, R.; Vossebeld, J. H.; Vranjes, N.; Vranjes Milosavljevic, M.; Vrba, V.; Vreeswijk, M.; Vuillermet, R.; Vukotic, I.; Wagner, P.; Wagner, W.; Wagner-Kuhr, J.; Wahlberg, H.; Wahrmund, S.; Walder, J.; Walker, R.; Walkowiak, W.; Wallangen, V.; Wang, C.; Wang, C.; Wang, F.; Wang, H.; Wang, H.; Wang, J.; Wang, J.; Wang, Q.; Wang, R.; Wang, S. M.; Wang, T.; Wang, W.; Wang, W.; Wang, Z.; Wanotayaroj, C.; Warburton, A.; Ward, C. P.; Wardrope, D. R.; Washbrook, A.; Watkins, P. M.; Watson, A. T.; Watson, M. F.; Watts, G.; Watts, S.; Waugh, B. M.; Webb, A. F.; Webb, S.; Weber, M. S.; Weber, S. W.; Weber, S. A.; Webster, J. S.; Weidberg, A. R.; Weinert, B.; Weingarten, J.; Weirich, M.; Weiser, C.; Weits, H.; Wells, P. S.; Wenaus, T.; Wengler, T.; Wenig, S.; Wermes, N.; Werner, M. D.; Werner, P.; Wessels, M.; Weston, T. D.; Whalen, K.; Whallon, N. L.; Wharton, A. M.; White, A. S.; White, A.; White, M. J.; White, R.; Whiteson, D.; Whitmore, B. W.; Wickens, F. J.; Wiedenmann, W.; Wielers, M.; Wiglesworth, C.; Wiik-Fuchs, L. A. M.; Wildauer, A.; Wilk, F.; Wilkens, H. G.; Williams, H. H.; Williams, S.; Willis, C.; Willocq, S.; Wilson, J. A.; Wingerter-Seez, I.; Winkels, E.; Winklmeier, F.; Winston, O. J.; Winter, B. T.; Wittgen, M.; Wobisch, M.; Wolf, T. M. H.; Wolff, R.; Wolter, M. W.; Wolters, H.; Wong, V. W. S.; Worm, S. D.; Wosiek, B. K.; Wotschack, J.; Wozniak, K. W.; Wu, M.; Wu, S. L.; Wu, X.; Wu, Y.; Wyatt, T. R.; Wynne, B. M.; Xella, S.; Xi, Z.; Xia, L.; Xu, D.; Xu, L.; Xu, T.; Yabsley, B.; Yacoob, S.; Yamaguchi, D.; Yamaguchi, Y.; Yamamoto, A.; Yamamoto, S.; Yamanaka, T.; Yamane, F.; Yamatani, M.; Yamazaki, Y.; Yan, Z.; Yang, H.; Yang, H.; Yang, Y.; Yang, Z.; Yao, W.-M.; Yap, Y. C.; Yasu, Y.; Yatsenko, E.; Yau Wong, K. H.; Ye, J.; Ye, S.; Yeletskikh, I.; Yigitbasi, E.; Yildirim, E.; Yorita, K.; Yoshihara, K.; Young, C.; Young, C. J. S.; Yu, J.; Yu, J.; Yuen, S. P. Y.; Yusuff, I.; Zabinski, B.; Zacharis, G.; Zaidan, R.; Zaitsev, A. M.; Zakharchuk, N.; Zalieckas, J.; Zaman, A.; Zambito, S.; Zanzi, D.; Zeitnitz, C.; Zemaityte, G.; Zemla, A.; Zeng, J. C.; Zeng, Q.; Zenin, O.; Ženiš, T.; Zerwas, D.; Zhang, D.; Zhang, F.; Zhang, G.; Zhang, H.; Zhang, J.; Zhang, L.; Zhang, L.; Zhang, M.; Zhang, P.; Zhang, R.; Zhang, R.; Zhang, X.; Zhang, Y.; Zhang, Z.; Zhao, X.; Zhao, Y.; Zhao, Z.; Zhemchugov, A.; Zhou, B.; Zhou, C.; Zhou, L.; Zhou, M.; Zhou, M.; Zhou, N.; Zhu, C. G.; Zhu, H.; Zhu, J.; Zhu, Y.; Zhuang, X.; Zhukov, K.; Zibell, A.; Zieminska, D.; Zimine, N. I.; Zimmermann, C.; Zimmermann, S.; Zinonos, Z.; Zinser, M.; Ziolkowski, M.; Živković, L.; Zobernig, G.; Zoccoli, A.; Zou, R.; Zur Nedden, M.; Zwalinski, L.; Atlas Collaboration

2017-12-01

The cross-section for the production of two jets in association with a leptonically decaying Z boson (Zjj) is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV, using data recorded with the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 3.2 fb-1. The electroweak Zjj cross-section is extracted in a fiducial region chosen to enhance the electroweak contribution relative to the dominant Drell-Yan Zjj process, which is constrained using a data-driven approach. The measured fiducial electroweak cross-section is σEWZjj = 119 ± 16 (stat .) ± 20 (syst .) ± 2 (lumi .) fb for dijet invariant mass greater than 250 GeV, and 34.2 ± 5.8 (stat .) ± 5.5 (syst .) ± 0.7 (lumi .) fb for dijet invariant mass greater than 1 TeV. Standard Model predictions are in agreement with the measurements. The inclusive Zjj cross-section is also measured in six different fiducial regions with varying contributions from electroweak and Drell-Yan Zjj production.

Power spectrum scale invariance identifies prefrontal dysregulation in paranoid schizophrenia.

PubMed

Radulescu, Anca R; Rubin, Denis; Strey, Helmut H; Mujica-Parodi, Lilianne R

2012-07-01

Theory and experimental evidence suggest that complex living systems function close to the boundary of chaos, with erroneous organization to an improper dynamical range (too stiff or chaotic) underlying system-wide dysregulation and disease. We hypothesized that erroneous organization might therefore also characterize paranoid schizophrenia, via optimization abnormalities in the prefrontal-limbic circuit regulating emotion. To test this, we acquired fMRI scans from 35 subjects (N = 9 patients with paranoid schizophrenia and N = 26 healthy controls), while they viewed affect-valent stimuli. To quantify dynamic regulation, we analyzed the power spectrum scale invariance (PSSI) of fMRI time-courses and computed the geometry of time-delay (Poincaré) maps, a measure of variability. Patients and controls showed distinct PSSI in two clusters (k(1) : Z = 4.3215, P = 0.00002 and k(2) : Z = 3.9441, P = 0.00008), localized to the orbitofrontal/medial prefrontal cortex (Brodmann Area 10), represented by β close to white noise in patients (β ≈ 0) and in the pink noise range in controls (β ≈ -1). Interpreting the meaning of PSSI differences, the Poincaré maps indicated less variability in patients than controls (Z = -1.9437, P = 0.05 for k(1) ; Z = -2.5099, P = 0.01 for k(2) ). That the dynamics identified Brodmann Area 10 is consistent with previous schizophrenia research, which implicates this area in deficits of working memory, executive functioning, emotional regulation and underlying biological abnormalities in synaptic (glutamatergic) transmission. Our results additionally cohere with a large body of work finding pink noise to be the normal range of central function at the synaptic, cellular, and small network levels, and suggest that patients show less supple responsivity of this region. Copyright © 2011 Wiley-Liss, Inc.

Interactive Spacecraft Trajectory Design Strategies Featuring Poincare Map Topology

NASA Astrophysics Data System (ADS)

Schlei, Wayne R.

Space exploration efforts are shifting towards inexpensive and more agile vehicles. Versatility regarding spacecraft trajectories refers to the agility to correct deviations from an intended path or even the ability to adapt the future path to a new destination--all with limited spaceflight resources (i.e., small DeltaV budgets). Trajectory design methods for such nimble vehicles incorporate equally versatile procedures that allow for rapid and interactive decision making while attempting to reduce Delta V budgets, leading to a versatile trajectory design platform. A versatile design paradigm requires the exploitation of Poincare map topology , or the interconnected web of dynamical structures, existing within the chaotic dynamics of multi-body gravitational models to outline low-Delta V transfer options residing nearby to a current path. This investigation details an autonomous procedure to extract the periodic orbits (topology nodes) and correlated asymptotic flow structures (or the invariant manifolds representing topology links). The autonomous process summarized in this investigation (termed PMATE) overcomes discontinuities on the Poincare section that arise in the applied multi-body model (the planar circular restricted three-body problem) and detects a wide variety of novel periodic orbits. New interactive capabilities deliver a visual analytics foundation for versatile spaceflight design, especially for initial guess generation and manipulation. Such interactive strategies include the selection of states and arcs from Poincare section visualizations and the capabilities to draw and drag trajectories to remove dependency on initial state input. Furthermore, immersive selection is expanded to cull invariant manifold structures, yielding low-DeltaV or even DeltaV-free transfers between periodic orbits. The application of interactive design strategies featuring a dense extraction of Poincare map topology is demonstrated for agile spaceflight with a simple spacecraft rerouting scenario incorporating a very limited Delta V budget. In the Earth-Moon system, a low-DeltaV transfer from low Earth orbit (LEO) to the distant retrograde orbit (DRO) vicinity is derived with interactive topology-based design tactics. Finally, Poincare map topology is exploited in the Saturn-Enceladus system to explore a possible ballistic capture scenario around Enceladus.

Topology, edge states, and zero-energy states of ultracold atoms in one-dimensional optical superlattices with alternating on-site potentials or hopping coefficients

NASA Astrophysics Data System (ADS)

He, Yan; Wright, Kevin; Kouachi, Said; Chien, Chih-Chun

2018-02-01

One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices allow a systematic study of those properties in superlattices with or without boundaries. While superlattices with additional modulating parameters are shown to have quantized topological invariants in the augmented parameter space, we also found localized or zero-energy states associated with symmetries of the Hamiltonians. Probing those states in ultracold atoms is possible by utilizing recently proposed methods analyzing particle depletion or the local density of states. Moreover, we summarize feasible realizations of configurable optical superlattices using currently available techniques.

Topological Structures of Gravitational Vacuum as a Factor of Unclustered DM

NASA Astrophysics Data System (ADS)

Burdyuzha, V.; Pacheco, J.; Vereshkov, G.

2003-03-01

Topological structures of gravitational vacuum which could be produced in the result of the first relativistic phase transition or in the result of defect creation of the Universe from "nothing" are discussed. The concrete physical meaning is imparted to the parametrizational noninvariant members of Wheeler -DeWitt equation which may be considered as vacuum topological defects of different dimensions (worm-holes, micromembranes, microstrings and monopoles). After Universe inflation defects smoothed, stretches and broken up. They must be isotropic distributed on background of the expanding Universe. The part of them has survived and now they are perceiving as the structures of Λ -term, quintessence and unclustered dark matter. Mathematical illustration of these processes may be spontaneous breaking of global Lorentz-invariance of quantum geometrodynamics equations.

Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2.

PubMed

Yan, Mingzhe; Huang, Huaqing; Zhang, Kenan; Wang, Eryin; Yao, Wei; Deng, Ke; Wan, Guoliang; Zhang, Hongyun; Arita, Masashi; Yang, Haitao; Sun, Zhe; Yao, Hong; Wu, Yang; Fan, Shoushan; Duan, Wenhui; Zhou, Shuyun

2017-08-15

Topological semimetals have recently attracted extensive research interests as host materials to condensed matter physics counterparts of Dirac and Weyl fermions originally proposed in high energy physics. Although Lorentz invariance is required in high energy physics, it is not necessarily obeyed in condensed matter physics, and thus Lorentz-violating type-II Weyl/Dirac fermions could be realized in topological semimetals. The recent realization of type-II Weyl fermions raises the question whether their spin-degenerate counterpart-type-II Dirac fermions-can be experimentally realized too. Here, we report the experimental evidence of type-II Dirac fermions in bulk stoichiometric PtTe 2 single crystal. Angle-resolved photoemission spectroscopy measurements and first-principles calculations reveal a pair of strongly tilted Dirac cones along the Γ-A direction, confirming PtTe 2 as a type-II Dirac semimetal. Our results provide opportunities for investigating novel quantum phenomena (e.g., anisotropic magneto-transport) and topological phase transition.Whether the spin-degenerate counterpart of Lorentz-violating Weyl fermions, the Dirac fermions, can be realized remains as an open question. Here, Yan et al. report experimental evidence of such type-II Dirac fermions in bulk PtTe 2 single crystal with a pair of strongly tilted Dirac cones.

Spin valley and giant quantum spin Hall gap of hydrofluorinated bismuth nanosheet.

PubMed

Gao, Heng; Wu, Wei; Hu, Tao; Stroppa, Alessandro; Wang, Xinran; Wang, Baigeng; Miao, Feng; Ren, Wei

2018-05-09

Spin-valley and electronic band topological properties have been extensively explored in quantum material science, yet their coexistence has rarely been realized in stoichiometric two-dimensional (2D) materials. We theoretically predict the quantum spin Hall effect (QSHE) in the hydrofluorinated bismuth (Bi 2 HF) nanosheet where the hydrogen (H) and fluorine (F) atoms are functionalized on opposite sides of bismuth (Bi) atomic monolayer. Such Bi 2 HF nanosheet is found to be a 2D topological insulator with a giant band gap of 0.97 eV which might host room temperature QSHE. The atomistic structure of Bi 2 HF nanosheet is noncentrosymmetric and the spontaneous polarization arises from the hydrofluorinated morphology. The phonon spectrum and ab initio molecular dynamic (AIMD) calculations reveal that the proposed Bi 2 HF nanosheet is dynamically and thermally stable. The inversion symmetry breaking together with spin-orbit coupling (SOC) leads to the coupling between spin and valley in Bi 2 HF nanosheet. The emerging valley-dependent properties and the interplay between intrinsic dipole and SOC are investigated using first-principles calculations combined with an effective Hamiltonian model. The topological invariant of the Bi 2 HF nanosheet is confirmed by using Wilson loop method and the calculated helical metallic edge states are shown to host QSHE. The Bi 2 HF nanosheet is therefore a promising platform to realize room temperature QSHE and valley spintronics.

On Topological Indices of Certain Families of Nanostar Dendrimers.

PubMed

Husin, Mohamad Nazri; Hasni, Roslan; Arif, Nabeel Ezzulddin; Imran, Muhammad

2016-06-24

A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

Discovery of Weyl Fermion Semimetals and Topological Fermi Arc States

NASA Astrophysics Data System (ADS)

Hasan, M. Zahid; Xu, Su-Yang; Belopolski, Ilya; Huang, Shin-Ming

2017-03-01

Weyl semimetals are conductors whose low-energy bulk excitations are Weyl fermions, whereas their surfaces possess metallic Fermi arc surface states. These Fermi arc surface states are protected by a topological invariant associated with the bulk electronic wave functions of the material. Recently, it has been shown that the TaAs and NbAs classes of materials harbor such a state of topological matter. We review the basic phenomena and experimental history of the discovery of the first Weyl semimetals, starting with the observation of topological Fermi arcs and Weyl nodes in TaAs and NbAs by angle and spin-resolved surface and bulk sensitive photoemission spectroscopy and continuing through magnetotransport measurements reporting the Adler-Bell-Jackiw chiral anomaly. We hope that this article provides a useful introduction to the theory of Weyl semimetals, a summary of recent experimental discoveries, and a guideline to future directions.

Topological Anisotropy of Stone-Wales Waves in Graphenic Fragments

PubMed Central

Ori, Ottorino; Cataldo, Franco; Putz, Mihai V.

2011-01-01

Stone-Wales operators interchange four adjacent hexagons with two pentagon-heptagon 5|7 pairs that, graphically, may be iteratively propagated in the graphene layer, originating a new interesting structural defect called here Stone-Wales wave. By minimization, the Wiener index topological invariant evidences a marked anisotropy of the Stone-Wales defects that, topologically, are in fact preferably generated and propagated along the diagonal of the graphenic fragments, including carbon nanotubes and graphene nanoribbons. This peculiar edge-effect is shown in this paper having a predominant topological origin, leaving to future experimental investigations the task of verifying the occurrence in nature of wave-like defects similar to the ones proposed here. Graph-theoretical tools used in this paper for the generation and the propagation of the Stone-Wales defects waves are applicable to investigate isomeric modifications of chemical structures with various dimensionality like fullerenes, nanotubes, graphenic layers, schwarzites, zeolites. PMID:22174641

Topological mechanical metamaterials have perfectly directional bulk response

NASA Astrophysics Data System (ADS)

Rocklin, D. Zeb

The elastic response of typical materials to a local load is stress and strain in all directions. Here, we show contrariwise that mechanical frames with balanced numbers of constraints and degrees of freedom (the ''Maxwell'' condition) can experience stress and/or strain on only one side of a load. Kane and Lubensky showed, in a recent, seminal work, that such systems possess a topologically nontrivial phonon band structure corresponding to the electronic modes of topological insulators. Applying bulk-boundary correspondence, they demonstrated a signature physical consequence: the shifting of zero modes resultant from missing bonds from one edge to another. We now show that the same topological invariant governs such a system's bulk response: when bonds are swollen at one point the lattice does not distort evenly around it but instead only on one side dictated by the topological polarization. Similarly, when general forces are applied to a polarized lattice tension is induced in bonds only on one side of the applied force. Hence, topological polarization represents a sharp and robust way to direct force and motion and the response (Green's) function is a fundamental bulk signature of topological polarization. Bethe/KIC Fellowship, and the National Science Foundation Grant No. NSF DMR- 1308089.

Composite particle theory of three-dimensional gapped fermionic phases: Fractional topological insulators and charge-loop excitation symmetry

NASA Astrophysics Data System (ADS)

Ye, Peng; Hughes, Taylor L.; Maciejko, Joseph; Fradkin, Eduardo

2016-09-01

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of Z2 gauge theory) is a U(1 )×U(1 ) Chern-Simons theory in which gauge charges (i.e., e and m particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact U(1 )×U(1 ) gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and U(1 )×U(1 ) magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-Hückel-type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and Θ ≠π , the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry (Charles ) of 3D Abelian topological phases. We show that line twist defects, which realize Charles transformations, exhibit non-Abelian fusion properties.

Optical Selection Rule of Excitons in Gapped Chiral Fermion Systems

NASA Astrophysics Data System (ADS)

Zhang, Xiaoou; Shan, Wen-Yu; Xiao, Di

2018-02-01

We show that the exciton optical selection rule in gapped chiral fermion systems is governed by their winding number w , a topological quantity of the Bloch bands. Specifically, in a CN-invariant chiral fermion system, the angular momentum of bright exciton states is given by w ±1 +n N with n being an integer. We demonstrate our theory by proposing two chiral fermion systems capable of hosting dark s -like excitons: gapped surface states of a topological crystalline insulator with C4 rotational symmetry and biased 3 R -stacked MoS2 bilayers. In the latter case, we show that gating can be used to tune the s -like excitons from bright to dark by changing the winding number. Our theory thus provides a pathway to electrical control of optical transitions in two-dimensional material.

Integration of element specific persistent homology and machine learning for protein-ligand binding affinity prediction.

PubMed

Cang, Zixuan; Wei, Guo-Wei

2018-02-01

Protein-ligand binding is a fundamental biological process that is paramount to many other biological processes, such as signal transduction, metabolic pathways, enzyme construction, cell secretion, and gene expression. Accurate prediction of protein-ligand binding affinities is vital to rational drug design and the understanding of protein-ligand binding and binding induced function. Existing binding affinity prediction methods are inundated with geometric detail and involve excessively high dimensions, which undermines their predictive power for massive binding data. Topology provides the ultimate level of abstraction and thus incurs too much reduction in geometric information. Persistent homology embeds geometric information into topological invariants and bridges the gap between complex geometry and abstract topology. However, it oversimplifies biological information. This work introduces element specific persistent homology (ESPH) or multicomponent persistent homology to retain crucial biological information during topological simplification. The combination of ESPH and machine learning gives rise to a powerful paradigm for macromolecular analysis. Tests on 2 large data sets indicate that the proposed topology-based machine-learning paradigm outperforms other existing methods in protein-ligand binding affinity predictions. ESPH reveals protein-ligand binding mechanism that can not be attained from other conventional techniques. The present approach reveals that protein-ligand hydrophobic interactions are extended to 40Å  away from the binding site, which has a significant ramification to drug and protein design. Copyright © 2017 John Wiley & Sons, Ltd.

Perovskite ThTaN3: A large-thermopower topological crystalline insulator

NASA Astrophysics Data System (ADS)

Jung, Myung-Chul; Lee, Kwan-Woo; Pickett, Warren E.

2018-03-01

ThTaN3, a rare cubic perovskite nitride semiconductor, has been studied using ab initio methods. Spin-orbit coupling (SOC) results in band inversion and a band gap of 150 meV at the zone center. Despite trivial Z2 indices, two pairs of spin-polarized surface bands cross the gap near the zone center, indicating that this system is a topological crystalline insulator with the mirror Chern number of | Cm|=2 protected by the mirror and C4 rotational symmetries. Additionally, SOC doubles the Seebeck coefficient, leading to a maximum of ˜400 μ V /K at 150 K for carrier-doping levels of several 1017/cm3.ThTaN3 combines excellent bulk thermopower with parallel conduction through topological surface states that may point toward new possibilities for platforms for engineering devices with larger figures of merit.

Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry.

PubMed

Robles-Llana, Daniel; Rocek, Martin; Saueressig, Frank; Theis, Ulrich; Vandoren, Stefan

2007-05-25

We find the D(-1)- and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi-Yau threefolds. These combine with known perturbative and world sheet instanton corrections into a single modular invariant function that determines the hypermultiplet low-energy effective action.

Architectures for Parafermionic Topological Matter in Two Dimensions

NASA Astrophysics Data System (ADS)

Burrello, Michele; van Heck, Bernard; Cobanera, Emilio

2013-03-01

Recent proposals exploit edge modes of fractional topological insulators (FTIs), induced superconducting pairing, and back-scattering to realize one-dimensional systems of parafermions. We extend these proposals to two dimensions and analyze the effect of the superconducting islands' charging energy on the parafermions they host. We focus on two two-dimensional architectures, the tile and stripe configurations, characterized by different distributions of FTIs and derive the associated parafermionic effective Hamiltonians. The tile model realizes the Z2 m toric code in low-order perturbation theory and hence possesses full topological quantum order. By exploiting dualities, we obtain the phase diagram and generalized order parameters for both the tile and stripe models of parafermions. This work was supported by the Dutch Science Foundation NWO/FOM and an ERC Advanced Investigator grant.

Evidence for topologically protected surface states and a superconducting phase in [Tl4](Tl(1-x)Sn(x))Te3 using photoemission, specific heat, and magnetization measurements, and density functional theory.

PubMed

Arpino, K E; Wallace, D C; Nie, Y F; Birol, T; King, P D C; Chatterjee, S; Uchida, M; Koohpayeh, S M; Wen, J-J; Page, K; Fennie, C J; Shen, K M; McQueen, T M

2014-01-10

We report the discovery of surface states in the perovskite superconductor [Tl4]TlTe3 (Tl5Te3) and its nonsuperconducting tin-doped derivative [Tl4](Tl0.4Sn0.6)Te3 as observed by angle-resolved photoemission spectroscopy. Density functional theory calculations predict that the surface states are protected by a Z2 topology of the bulk band structure. Specific heat and magnetization measurements show that Tl5Te3 has a superconducting volume fraction in excess of 95%. Thus Tl5Te3 is an ideal material in which to study the interplay of bulk band topology and superconductivity.

Topological Constraints on Transvection between White Genes within the Transposing Element Te35b in Drosophila Melanogaster

PubMed Central

Gubb, D.; Roote, J.; Trenear, J.; Coulson, D.; Ashburner, M.

1997-01-01

The transposable element TE35B carries two copies of the white (w) gene at 35B1.2 on the second chromosome. These w genes are suppressed in a zeste-1 (z(1)) mutant background in a synapsis-dependent manner. Single-copy derivatives of the original TE35B stock give red eyes when heterozygous, but zeste eyes when homozygous. TE35B derivatives carrying single, double or triple copies of w were crossed to generate flies carrying from two to five ectopic w genes. Within this range, z(1)-mediated suppression is insensitive to copynumber and does not distinguish between w genes that are in cis or in trans. Suppression does not require the juxtaposition of even numbers of w genes, but is extremely sensitive to chromosomal topology. When arranged in a tight cluster, in triple-copy TE derivatives, w genes are nonsuppressible. Breakpoints falling within TE35B and separating two functional w genes act as partial suppressors of z(1). Similarly, breakpoints immediately proximal or distal to both w genes give partial suppression. This transvection-dependent downregulation of w genes may result from mis-activation of the X-chromosome dosage compensation mechanism. PMID:9215897

Excitation of trapped modes from a metasurface composed of only Z-shaped meta-atoms

NASA Astrophysics Data System (ADS)

Dhouibi, Abdallah; Nawaz Burokur, Shah; Lupu, Anatole; de Lustrac, André; Priou, Alain

2013-10-01

A printed planar Z-shaped meta-atom has recently been proposed as an alternative design to the conventional electric-LC resonator for achieving negative permittivity. Transforming the LC topology of the resonator helps to facilitate transposition of geometrical parameters for the optical regime and also to improve the metamaterial homogeneity. In this work, we discuss about the excitation of a dark or trapped mode in such Z-shaped meta-atom. The electromagnetic behavior of the meta-atom has been investigated through both simulations and experiments in the microwave regime. Our results show that the Z meta-atom exhibits a trapped mode resonance. Depending on the orientation of the polarized electromagnetic field with respect to the Z atom topology and the incident plane, the excitation of the dark mode can lead either to a narrowband resonance in reflection or to a very asymmetric Fano-like resonance in transmission, analog of electromagnetically induced transparency. Compared to other structures, the Z meta-atom presents the advantage of having the dark mode resonance spectrally spaced with respect to the bright mode resonances, which could simplify the observation of the dark mode at much shorter wavelengths.

T-duality and α'-corrections

NASA Astrophysics Data System (ADS)

Marqués, Diego; Nuñez, Carmen A.

2015-10-01

We construct an O( d, d) invariant universal formulation of the first-order α'-corrections of the string effective actions involving the dilaton, metric and two-form fields. Two free parameters interpolate between four-derivative terms that are even and odd with respect to a Z 2-parity transformation that changes the sign of the two-form field. The Z 2-symmetric model reproduces the closed bosonic string, and the heterotic string effective action is obtained through a Z 2-parity-breaking choice of parameters. The theory is an extension of the generalized frame formulation of Double Field Theory, in which the gauge transformations are deformed by a first-order generalized Green-Schwarz transformation. This deformation defines a duality covariant gauge principle that requires and fixes the four-derivative terms. We discuss the O( d, d) structure of the theory and the (non-)covariance of the required field redefinitions.

Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor

NASA Astrophysics Data System (ADS)

Kim, Youngseok; Philip, Timothy M.; Park, Moon Jip; Gilbert, Matthew J.; University of Illinois at Urbana; Champaign Team

As a promising candidate system to realize topological superconductivity (SC), 3D time-reversal invariant topological insulators (TI) proximity-coupled to s-wave superconductors have been intensively studied. Recent experiments on proximity-coupled TI have shown that superconductivity may be induced in ultrathin TI. One proposal to observe the topological SC in proximity-coupled ultrathin TI system is to add magnetic dopants to the TI. However, detailed study on the impact of the experimental parameters on possible topological phase is sparse. In this work, we investigate ultrathin, magnetically-doped, proximity-coupled TI in order to determine the experimentally relevant parameters needed to observe topological SC. We find that, due to the spin-momentum locked nature of the surface states in TI, the induced s-wave order parameter within the surface states persists even at large magnitudes of the Zeeman energy, allowing us to explore the system in parameter space. We elucidate the phase diagram as a function of: the hybridization gap, Zeeman energy, and chemical potential of the TI system. Our findings provide a useful guide in choosing relevant parameters to facilitate the observation of topological SC in thin film TI-superconductor hybrid systems. National Science Foundation (NSF) under Grant CAREER ECCS-1351871.

Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

PubMed Central

Mu, Lin

2018-01-01

This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multi-component persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for protein-ligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 protein-ligand complexes from the PDBBind database and 128,374 ligand-target and decoy-target pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in protein-ligand binding affinity prediction and ligand-decoy discrimination. PMID:29309403

Linear systems with structure group and their feedback invariants

NASA Technical Reports Server (NTRS)

Martin, C.; Hermann, R.

1977-01-01

A general method described by Hermann and Martin (1976) for the study of the feedback invariants of linear systems is considered. It is shown that this method, which makes use of ideas of topology and algebraic geometry, is very useful in the investigation of feedback problems for which the classical methods are not suitable. The transfer function as a curve in the Grassmanian is examined. The general concepts studied in the context of specific systems and applications are organized in terms of the theory of Lie groups and algebraic geometry. Attention is given to linear systems which have a structure group, linear mechanical systems, and feedback invariants. The investigation shows that Lie group techniques are powerful and useful tools for analysis of the feedback structure of linear systems.

Baryonic Z{sup '} Explanation for the CDF Wjj Excess

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheung, Kingman; Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwan; Song, Jeonghyeon

2011-05-27

The latest CDF anomaly, the excess of dijet events in the invariant-mass window 120-160 GeV in associated production with a W boson, can be explained by a baryonic Z{sup '} model in which the Z{sup '} boson has negligible couplings to leptons. Although this Z{sup '} model is hardly subject to the Drell-Yan constraint from Tevatron, it is constrained by the dijet data from UA2 ({radical}(s)=630 GeV), and the precision measurements at LEP through the mixing with the SM Z boson. We show that under these constraints this model can still explain the excess in the M{sub jj{approx}}120-160 GeV window,more » as well as the claimed cross section {sigma}(WZ{sup '}){approx}4 pb. Implications at the Tevatron would be the associated production of {gamma}Z{sup '}, ZZ{sup '}, and Z{sup '}Z{sup '} with the Z{sup '}{yields}jj. We show that with tightened jet cuts and improved systematic uncertainties both {gamma}Z{sup '}{yields}{gamma}jj and ZZ{sup '}{yields}l{sup +}l{sup -}jj channels could be useful to probe this model at the Tevatron.« less

Theory of the disordered ν =5/2 quantum thermal Hall state: Emergent symmetry and phase diagram

NASA Astrophysics Data System (ADS)

Lian, Biao; Wang, Juven

2018-04-01

Fractional quantum Hall (FQH) system at Landau level filling fraction ν =5 /2 has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance σx y=5 e2/2 h . Thermal Hall conductances of the Pf and APf states are quantized at κx y=7 /2 and κx y=3 /2 , respectively, in a proper unit. However, a recent experiment shows the thermal Hall conductance of ν =5 /2 FQH state is κx y=5 /2 . It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a κx y=5 /2 phase. In this paper, we do perturbative and nonperturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold Λ1, which is lowered to an emergent U (1 )×U (1) symmetry at energy scales between Λ1 and a higher value Λ2, and is finally lowered to the composite fermion parity symmetry Z2F above Λ2. Based on the emergent symmetries, we propose a phase diagram of the disordered ν =5 /2 FQH system and show that a κx y=5 /2 phase arises at disorder energy scales Λ >Λ1 . Furthermore, we show the gapped double-semion sector of ND compact domain walls contributes nonlocal topological degeneracy 2ND-1, causing a low-temperature peak in the heat capacity. We implement a nonperturbative method to bootstrap generic topological 1 +1 D domain walls (two-surface defects) applicable to any 2 +1 D non-Abelian topological order. We also identify potentially relevant spin topological quantum field theories (TQFTs) for various ν =5 /2 FQH states in terms of fermionic version of U (1) ±8 Chern-Simons theory ×Z8 -class TQFTs.

Optimal Topology Control and Power Allocation for Minimum Energy Consumption in Consensus Networks

DTIC Science & Technology

2011-12-16

network topologies, such as small world graphs, can greatly increase the convergence rate. In [9], the authors show that nonbipartite Ramanujan graphs...unclassified c . THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 23384 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 60...of iterations necessary to achieve consensus. From this perspec- tive, enforcing a small world, scale-free, or Ramanujan graph topology may not be the

Equivariant branes and equivariant homological mirror symmetry

NASA Astrophysics Data System (ADS)

Ashwinkumar, Meer; Tan, Meng-Chwan

2018-03-01

We describe supersymmetric A-branes and B-branes in open N =(2 ,2 ) dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror description as branes in gauged Landau-Ginzburg models with neutral matter. We then study correlation functions in the topological A-twisted version of the GNLSM and identify their values with open Hamiltonian Gromov-Witten invariants. Supersymmetry breaking can occur in the A-twisted GNLSM due to nonperturbative open symplectic vortices, and we canonically Becchi-Rouet-Stora-Tyutin quantize the mirror theory to analyze this phenomenon.

The Kitaev honeycomb model on surfaces of genus g ≥ 2

NASA Astrophysics Data System (ADS)

Brennan, John; Vala, Jiří

2018-05-01

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan–Wigner fermionization to a surface with genus g = 2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled {Z}}}2 phase and the non-Abelian Ising topological phase on lattices with the genus up to g = 6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.

Small dark energy and stable vacuum from Dilaton-Gauss-Bonnet coupling in TMT

NASA Astrophysics Data System (ADS)

Guendelman, Eduardo I.; Nishino, Hitoshi; Rajpoot, Subhash

2017-04-01

In two measures theories (TMT), in addition to the Riemannian measure of integration, being the square root of the determinant of the metric, we introduce a metric-independent density Φ in four dimensions defined in terms of scalars \\varphi _a by Φ =\\varepsilon ^{μ ν ρ σ } \\varepsilon _{abcd} (partial _{μ }\\varphi _a)(partial _{ν }\\varphi _b) (partial _{ρ }\\varphi _c) (partial _{σ }\\varphi _d). With the help of a dilaton field φ we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton φ to the Gauss-Bonnet (GB) topological density {√{-g}} φ ( R_{μ ν ρ σ }^2 - 4 R_{μ ν }^2 + R^2 ) we obtain a theory that is scale invariant up to a total divergence. Integration of the \\varphi _a field equation leads to an integration constant that breaks the global scale symmetry. We discuss the stabilizing effects of the coupling of the dilaton to the GB-topological density on the vacua with a very small cosmological constant and the resolution of the `TMT Vacuum-Manifold Problem' which exists in the zero cosmological-constant vacuum limit. This problem generically arises from an effective potential that is a perfect square, and it gives rise to a vacuum manifold instead of a unique vacuum solution in the presence of many different scalars, like the dilaton, the Higgs, etc. In the non-zero cosmological-constant case this problem disappears. Furthermore, the GB coupling to the dilaton eliminates flat directions in the effective potential, and it totally lifts the vacuum-manifold degeneracy.

Possible realization of interacting symmetry-protected topological phases in topological crystalline insulators

NASA Astrophysics Data System (ADS)

Isobe, Hiroki; Fu, Liang

2015-03-01

The effects of electron-electron interaction in edge states of mirror-symmetry protected topological crystalline insulators (TCI's) are discussed. The analysis is performed by using bosonized Hamiltonian following the Tomonaga-Luttinger liquid theory. When two pairs of helical edge states exist, electron-electron interaction could gap out one edge mode, which is a possible realization of interacting symmetry-protected topological (SPT) phases. This type of SPT phase is closely related to a Luther-Emery liquid in spinful 1D system. We also propose a method of detecting the SPT phases by STM. The other focus of the study is the classification of SPT phases in mirror-symmetry protected TCI's. By adopting the Chern-Simons theory, we find that electron-electron interaction reduces the classification from Z to Z4. It means that the edge states can be gapped out when four pairs of edge states exist. In other cases, the edge modes cannot be fully gapped. Each of these states corresponds to a different SPT phase depending on the relevant interaction process.

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry

NASA Astrophysics Data System (ADS)

Yan, Mu-Lin

2012-06-01

The de Sitter invariant Special Relativity (dS-SR) is SR with constant curvature, and a natural extension of usual Einstein SR (E-SR). In this paper, we solve the dS-SR Dirac equation of Hydrogen by means of the adiabatic approach and the quasi-stationary perturbation calculations of QM. Hydrogen atom is located in the light cone of the Universe. FRW metric and ΛCDM cosmological model are used to discuss this issue. To the atom, effects of de Sitter space-time geometry described by Beltrami metric are taken into account. The dS-SR Dirac equation turns out to be a time dependent quantum Hamiltonian system. We reveal that: (i) The fundamental physics constants me, ℏ, e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α ≡ e2/(ℏc) keeps to be invariant; (ii) (2s1/2-2p1/2)-splitting due to dS-SR QM effects: By means of perturbation theory, that splitting ΔE(z) are calculated analytically, which belongs to Script O(1/R2)-physics of dS-SR QM. Numerically, we find that when |R| ≃ {103 Gly, 104 Gly, 105 Gly}, and z ≃ {1, or 2}, the ΔE(z) ≫ 1 (Lamb shift). This indicates that for these cases the hyperfine structure effects due to QED could be ignored, and the dS-SR fine structure effects are dominant. This effect could be used to determine the universal constant R in dS-SR, and be thought as a new physics beyond E-SR.

Bifurcations of edge states—topologically protected and non-protected—in continuous 2D honeycomb structures

NASA Astrophysics Data System (ADS)

Fefferman, C. L.; Lee-Thorp, J. P.; Weinstein, M. I.

2016-03-01

Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or ‘edge’ and are localized transverse to it. This paper summarizes and extends the authors’ work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D honeycomb structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrödinger operator. Numerical simulations for honeycomb structures of varying contrasts and ‘rational edges’ (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.

Knoto-ID: a tool to study the entanglement of open protein chains using the concept of knotoids.

PubMed

Dorier, Julien; Goundaroulis, Dimos; Benedetti, Fabrizio; Stasiak, Andrzej

2018-05-02

The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the curve into a loop, which alters the geometry of curve. Knoto-ID allows evaluating the entanglement of open curves without the need to close them, using the recent concept of knotoids which is a generalization of the classical knot theory to open curves. Knoto-ID can analyse the global topology of the full chain as well as the local topology by exhaustively studying all subchains or only determining the knotted core. Knoto-ID permits to localize topologically non-trivial protein folds that are not detected by informatics tools detecting knotted protein folds. Knoto-ID is written in C ++ and includes R (www.R-project.org) scripts to generate plots of projections maps, fingerprint matrices and disk matrices. Knoto-ID is distributed under the GNU General Public License (GPL), version 2 or any later version and is available at https://github.com/sib-swiss/Knoto-ID. A binary distribution for Mac OS X, Linux and Windows with detailed user guide and examples can be obtained from https://www.vital-it.ch/software/Knoto-ID. julien.dorier@sib.swiss.

A configuration space of homologous proteins conserving mutual information and allowing a phylogeny inference based on pair-wise Z-score probabilities.

PubMed

Bastien, Olivier; Ortet, Philippe; Roy, Sylvaine; Maréchal, Eric

2005-03-10

Popular methods to reconstruct molecular phylogenies are based on multiple sequence alignments, in which addition or removal of data may change the resulting tree topology. We have sought a representation of homologous proteins that would conserve the information of pair-wise sequence alignments, respect probabilistic properties of Z-scores (Monte Carlo methods applied to pair-wise comparisons) and be the basis for a novel method of consistent and stable phylogenetic reconstruction. We have built up a spatial representation of protein sequences using concepts from particle physics (configuration space) and respecting a frame of constraints deduced from pair-wise alignment score properties in information theory. The obtained configuration space of homologous proteins (CSHP) allows the representation of real and shuffled sequences, and thereupon an expression of the TULIP theorem for Z-score probabilities. Based on the CSHP, we propose a phylogeny reconstruction using Z-scores. Deduced trees, called TULIP trees, are consistent with multiple-alignment based trees. Furthermore, the TULIP tree reconstruction method provides a solution for some previously reported incongruent results, such as the apicomplexan enolase phylogeny. The CSHP is a unified model that conserves mutual information between proteins in the way physical models conserve energy. Applications include the reconstruction of evolutionary consistent and robust trees, the topology of which is based on a spatial representation that is not reordered after addition or removal of sequences. The CSHP and its assigned phylogenetic topology, provide a powerful and easily updated representation for massive pair-wise genome comparisons based on Z-score computations.

8-Spinors and structure of solitons in generalized Mie electrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rybakov, Yu. P., E-mail: soliton4@mail.ru

2013-02-15

A generalization of Mie electrodynamics is considered. It includes a 8-spinor field and higher powers of the Mie invariant A{sub {mu}}A{sup {mu}}. Particular topological properties of 8-spinors are indicated and are associated with the existence of the remarkable Brioschi identity of eight squares, which permits deriving a natural 8-spinor unification of the Skyrme model of baryons and the Faddeev model of leptons, these particles being treated as topological solitons. Two types of soliton configurations admitted by the model are constructed. These are charged static and neutral lightlike (luxons) ones.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Estimating Topology of Discrete Dynamical Networks

NASA Astrophysics Data System (ADS)

Guo, Shu-Juan; Fu, Xin-Chu

2010-07-01

In this paper, by applying Lasalle's invariance principle and some results about the trace of a matrix, we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamical evolution of the network. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known. Finally, two examples, including a Hénon map and a central network, are illustrated to verify the theoretical results.

LDRD Report: Topological Design Optimization of Convolutes in Next Generation Pulsed Power Devices.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cyr, Eric C.; von Winckel, Gregory John; Kouri, Drew Philip

This LDRD project was developed around the ambitious goal of applying PDE-constrained opti- mization approaches to design Z-machine components whose performance is governed by elec- tromagnetic and plasma models. This report documents the results of this LDRD project. Our differentiating approach was to use topology optimization methods developed for structural design and extend them for application to electromagnetic systems pertinent to the Z-machine. To achieve this objective a suite of optimization algorithms were implemented in the ROL library part of the Trilinos framework. These methods were applied to standalone demonstration problems and the Drekar multi-physics research application. Out of thismore » exploration a new augmented Lagrangian approach to structural design problems was developed. We demonstrate that this approach has favorable mesh-independent performance. Both the final design and the algorithmic performance were independent of the size of the mesh. In addition, topology optimization formulations for the design of conducting networks were developed and demonstrated. Of note, this formulation was used to develop a design for the inner magnetically insulated transmission line on the Z-machine. The resulting electromagnetic device is compared with theoretically postulated designs.« less

Topological networks for quantum communication between distant qubits

NASA Astrophysics Data System (ADS)

Lang, Nicolai; Büchler, Hans Peter

2017-11-01

Efficient communication between qubits relies on robust networks, which allow for fast and coherent transfer of quantum information. It seems natural to harvest the remarkable properties of systems characterized by topological invariants to perform this task. Here, we show that a linear network of coupled bosonic degrees of freedom, characterized by topological bands, can be employed for the efficient exchange of quantum information over large distances. Important features of our setup are that it is robust against quenched disorder, all relevant operations can be performed by global variations of parameters, and the time required for communication between distant qubits approaches linear scaling with their distance. We demonstrate that our concept can be extended to an ensemble of qubits embedded in a two-dimensional network to allow for communication between all of them.

Syntheses and crystal structures of two topologically related modifications of Cs(2)[(UO(2))(2)(MoO(4))(3)].

PubMed

Krivovichev, S V; Cahill, C L; Burns, P C

2002-01-14

Two polymorphs of Cs(2)(UO(2))(2)(MoO(4))(3) have been synthesized by hydrothermal (alpha-phase) and high-temperature (beta-phase) routes. Both were characterized by single-crystal X-ray diffraction: alpha-Cs(2)(UO(2))(2)(MoO(4))(3), orthorhombic, Pna2(1), a = 20.4302(15) A, b = 8.5552(7) A, c = 9.8549(7) A, Z = 4; beta-Cs(2)(UO(2))(2)(MoO(4))(3), tetragonal, P4(2)/n, a = 10.1367(8) A, c = 16.2831(17) A, Z = 4. The structures of both phases consist of linked UO(7) pentagonal bipyramids and MoO(4) tetrahedra: alpha-Cs(2)(UO(2))(2)(MoO(4))(3) is a framework compound with large channels parallel to the c axis. Two cesium sites are located in these channels and are coordinated by 8 and 10 oxygen atoms. The structure of beta-Cs(2)(UO(2))(2)(MoO(4))(3) contains corrugated [(UO(2))(2)(MoO(4))(3)] sheets that are parallel to (001). The cesium cations are located between the sheets and are coordinated by eight oxygen atoms. The structures are topologically related; both can be described in terms of chains of 5-connected UO(7) pentagonal bipyramids and 3- and 4-connected MoO(4) tetrahedra.

Burning invariant manifolds for reaction fronts in three-dimensional fluid flows

NASA Astrophysics Data System (ADS)

Mitchell, Kevin; Solomon, Tom

2017-11-01

The geometry of reaction fronts that propagate in fully three-dimensional (3D) fluid flows is studied using the tools of dynamical systems theory. The evolution of an infinitesimal front element is modeled as a six-dimensional ODE-three dimensions for the position of the front element and three for the orientation of its unit normal. This generalizes an earlier approach to understanding front propagation in two-dimensional (2D) fluid flows. As in 2D, the 3D system exhibits prominent burning invariant manifolds (BIMs). In 3D, BIMs are two-dimensional dynamically defined surfaces that form one-way barriers to the propagation of reaction fronts within the fluid. Due to the third dimension, BIMs in 3D exhibit a richer topology than their cousins in 2D. In particular, whereas BIMs in both 2D and 3D can originate from fixed points of the dynamics, BIMs in 3D can also originate from limit cycles. Such BIMs form robust tube-like channels that guide and constrain the evolution of the front within the bulk of the fluid. Supported by NSF Grant CMMI-1201236.

Fractal universe and quantum gravity.

PubMed

Calcagni, Gianluca

2010-06-25

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.

Majorana fermions and orthogonal complex structures

NASA Astrophysics Data System (ADS)

Calderón-García, J. S.; Reyes-Lega, A. F.

2018-05-01

Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain “doubling” of the Hilbert space. In this work, we show that this redundancy in the Hilbert space can be completely lifted if the relevant orthogonal structure is taken into account. Such an approach allows for a treatment of Majorana fermions which is both physically and mathematically transparent. Furthermore, an explicit connection between orthogonal complex structures and the topological ℤ2-invariant is given.

Black hole entropy and Lorentz-diffeomorphism Noether charge

NASA Astrophysics Data System (ADS)

Jacobson, Ted; Mohd, Arif

2015-12-01

We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.

Irreversible Markov chains in spin models: Topological excitations

NASA Astrophysics Data System (ADS)

Lei, Ze; Krauth, Werner

2018-01-01

We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations while spin waves decorrelate very quickly. Using a Fréchet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent z∼ 2 at the critical temperature to z∼ 0 in the limit of zero temperature. We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model. Mixing times (describing the approach towards equilibrium from the least favorable initial state) however remain much larger than equilibrium correlation times at low temperatures. We also describe the respective influence of topological monopole-antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.

Microdosimetry of DNA conformations: relation between direct effect of (60)Co gamma rays and topology of DNA geometrical models in the calculation of A-, B- and Z-DNA radiation-induced damage yields.

PubMed

Semsarha, Farid; Raisali, Gholamreza; Goliaei, Bahram; Khalafi, Hossein

2016-05-01

In order to obtain the energy deposition pattern of ionizing radiation in the nanometric scale of genetic material and to investigate the different sensitivities of the DNA conformations, direct effects of (60)Co gamma rays on the three A, B and Z conformations of DNA have been studied. For this purpose, single-strand breaks (SSB), double-strand breaks (DSB), base damage (BD), hit probabilities and three microdosimetry quantities (imparted energy, mean chord length and lineal energy) in the mentioned DNA conformations have been calculated and compared by using GEometry ANd Tracking 4 (Geant4) toolkit. The results show that A-, B- and Z-DNA conformations have the highest yields of DSB (1.2 Gy(-1) Gbp(-1)), SSB (25.2 Gy(-1) Gbp(-1)) and BD (4.81 Gy(-1) Gbp(-1)), respectively. Based on the investigation of direct effects of radiation, it can be concluded that the DSB yield is largely correlated to the topological characteristics of DNA models, although the SSB yield is not. Moreover, according to the comparative results of the present study, a reliable candidate parameter for describing the relationship between DNA damage yields and geometry of DNA models in the theoretical radiation biology research studies would be the mean chord length (4 V/S) of the models.

Numeric invariants from multidimensional persistence

DOE PAGES

Skryzalin, Jacek; Carlsson, Gunnar

2017-05-19

Topological data analysis is the study of data using techniques from algebraic topology. Often, one begins with a finite set of points representing data and a “filter” function which assigns a real number to each datum. Using both the data and the filter function, one can construct a filtered complex for further analysis. For example, applying the homology functor to the filtered complex produces an algebraic object known as a “one-dimensional persistence module”, which can often be interpreted as a finite set of intervals representing various geometric features in the data. If one runs the above process incorporating multiple filtermore » functions simultaneously, one instead obtains a multidimensional persistence module. Unfortunately, these are much more difficult to interpret. In this article, we analyze the space of multidimensional persistence modules from the perspective of algebraic geometry. First we build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence instead of one-dimensional persistence. Fruthermore, we argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Finally, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data. This paper extends the results of Adcock et al. (Homol Homotopy Appl 18(1), 381–402, 2016) by constructing numeric invariants from the computation of a multidimensional persistence module as given by Carlsson et al. (J Comput Geom 1(1), 72–100, 2010).« less

ℓ1-norm and entanglement in screening out braiding from Yang-Baxter equation associated with Z3 parafermion

NASA Astrophysics Data System (ADS)

Yu, Li-Wei; Ge, Mo-Lin

2017-03-01

The relationships between quantum entangled states and braid matrices have been well studied in recent years. However, most of the results are based on qubits. In this paper, we investigate the applications of 2-qutrit entanglement in the braiding associated with Z3 parafermion. The 2-qutrit entangled state | Ψ (θ) >, generated by the action of the localized unitary solution R ˘ (θ) of YBE on 2-qutrit natural basis, achieves its maximal ℓ1-norm and maximal von Neumann entropy simultaneously at θ = π / 3. Meanwhile, at θ = π / 3, the solutions of YBE reduces braid matrices, which implies the role of ℓ1-norm and entropy plays in determining real physical quantities. On the other hand, we give a new realization of 4-anyon topological basis by qutrit entangled states, then the 9 × 9 localized braid representation in 4-qutrit tensor product space (C3) ⊗ 4 is reduced to Jones representation of braiding in the 4-anyon topological basis. Hence, we conclude that the entangled states are powerful tools in analysing the characteristics of braiding and R ˘ -matrix.

Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids

NASA Astrophysics Data System (ADS)

Ackerman, Paul J.; Smalyukh, Ivan I.

2017-04-01

Three-dimensional (3D) topological solitons are continuous but topologically nontrivial field configurations localized in 3D space and embedded in a uniform far-field background, that behave like particles and cannot be transformed to a uniform state through smooth deformations. Many topologically nontrivial 3D solitonic fields have been proposed. Yet, according to the Hobart-Derrick theorem, physical systems cannot host them, except for nonlinear theories with higher-order derivatives such as the Skyrme-Faddeev model. Experimental discovery of such solitons is hindered by the need for spatial imaging of the 3D fields, which is difficult in high-energy physics and cosmology. Here we experimentally realize and numerically model stationary topological solitons in a fluid chiral ferromagnet formed by colloidal dispersions of magnetic nanoplates. Such solitons have closed-loop preimages--3D regions with a single orientation of the magnetization field. We discuss localized structures with different linking of preimages quantified by topological Hopf invariants. The chirality is found to help in overcoming the constraints of the Hobart-Derrick theorem, like in two-dimensional ferromagnetic solitons, dubbed `baby skyrmions'. Our experimental platform may lead to solitonic condensed matter phases and technological applications.

Robust spatial memory maps in flickering neuronal networks: a topological model

NASA Astrophysics Data System (ADS)

Dabaghian, Yuri; Babichev, Andrey; Memoli, Facundo; Chowdhury, Samir; Rice University Collaboration; Ohio State University Collaboration

It is widely accepted that the hippocampal place cells provide a substrate of the neuronal representation of the environment--the ``cognitive map''. However, hippocampal network, as any other network in the brain is transient: thousands of hippocampal neurons die every day and the connections formed by these cells constantly change due to various forms of synaptic plasticity. What then explains the remarkable reliability of our spatial memories? We propose a computational approach to answering this question based on a couple of insights. First, we propose that the hippocampal cognitive map is fundamentally topological, and hence it is amenable to analysis by topological methods. We then apply several novel methods from homology theory, to understand how dynamic connections between cells influences the speed and reliability of spatial learning. We simulate the rat's exploratory movements through different environments and study how topological invariants of these environments arise in a network of simulated neurons with ``flickering'' connectivity. We find that despite transient connectivity the network of place cells produces a stable representation of the topology of the environment.

Self-organization in multilayer network with adaptation mechanisms based on competition

NASA Astrophysics Data System (ADS)

Pitsik, Elena N.; Makarov, Vladimir V.; Nedaivozov, Vladimir O.; Kirsanov, Daniil V.; Goremyko, Mikhail V.

2018-04-01

The paper considers the phenomena of competition in multiplex network whose structure evolves corresponding to dynamics of it's elements, forming closed loop of self-learning with the aim to reach the optimal topology. Numerical analysis of proposed model shows that it is possible to obtain scale-invariant structures for corresponding parameters as well as the structures with homogeneous distribution of connections in the layers. Revealed phenomena emerges as the consequence of the self-organization processes related to structure-dynamical selflearning based on homeostasis and homophily, as well as the result of the competition between the network's layers for optimal topology. It was shown that in the mode of partial and cluster synchronization the network reaches scale-free topology of complex nature that is different from layer to layer. However, in the mode of global synchronization the homogeneous topologies on all layer of the network are observed. This phenomenon is tightly connected with the competitive processes that represent themselves as the natural mechanism of reaching the optimal topology of the links in variety of real-world systems.

Directly detecting isospin-violating dark matter

NASA Astrophysics Data System (ADS)

Kelso, Chris; Kumar, Jason; Marfatia, Danny; Sandick, Pearl

2018-03-01

We consider the prospects for multiple dark matter direct detection experiments to determine if the interactions of a dark matter candidate are isospin-violating. We focus on theoretically well-motivated examples of isospin-violating dark matter (IVDM), including models in which dark matter interactions with nuclei are mediated by a dark photon, a Z , or a squark. We determine that the best prospects for distinguishing IVDM from the isospin-invariant scenario arise in the cases of dark photon-or Z -mediated interactions, and that the ideal experimental scenario would consist of large exposure xenon- and neon-based detectors. If such models just evade current direct detection limits, then one could distinguish such models from the standard isospin-invariant case with two detectors with of order 100 ton-year exposure.

Motions, efforts and actuations in constrained dynamic systems: a multi-link open-chain example

NASA Astrophysics Data System (ADS)

Duke Perreira, N.

1999-08-01

The effort-motion method, which describes the dynamics of open- and closed-chain topologies of rigid bodies interconnected with revolute and prismatic pairs, is interpreted geometrically. Systems are identified for which the simultaneous control of forces and velocities is desirable, and a representative open-chain system is selected for use in the ensuing analysis. Gauge invariant transformations are used to recast the commonly used kinetic and kinematic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions then recast the invariant equations into orthogonal and reciprocal sets of motion and effort equations written in state variable form. The ideal actuation is found that simultaneously achieves the obtainable portions of the desired constraining efforts and motions. The performance is then evaluated of using the actuation closest to the ideal actuation.

Measurement of the Effective Weak Mixing Angle in p p ¯ → Z / γ * → e + e - Events

DOE PAGES

Abazov, V.  M.; Abbott, B.; Acharya, B.  S.; ...

2015-07-22

We present a measurement of the fundamental parameter of the standard model, the weak mixing angle sin 2θ ℓ eff which determines the relative strength of weak and electromagnetic interactions, in pp¯→Z/γ*→e +e - events at a center of mass energy of 1.96 TeV, using data corresponding to 9.7 fb -1 of integrated luminosity collected by the D0 detector at the Fermilab Tevatron. The effective weak mixing angle is extracted from the forward-backward charge asymmetry as a function of the invariant mass around the Z boson pole. The measured value of sin 2θ ℓ eff=0.23147±0.00047 is the most precise measurementmore » from light quark interactions to date, with a precision close to the best LEP and SLD results.« less

Measurement of the Effective Weak Mixing Angle in p p ¯ → Z / γ * → e + e - Events

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abazov, V. M.; Abbott, B.; Acharya, B. S.

2015-07-22

We present a measurement of the fundamental parameter of the standard model, the weak mixing angle sin 2θ ℓ eff which determines the relative strength of weak and electromagnetic interactions, in pp¯→Z/γ*→e +e - events at a center of mass energy of 1.96 TeV, using data corresponding to 9.7 fb -1 of integrated luminosity collected by the D0 detector at the Fermilab Tevatron. The effective weak mixing angle is extracted from the forward-backward charge asymmetry as a function of the invariant mass around the Z boson pole. The measured value of sin 2θ ℓ eff=0.23147±0.00047 is the most precise measurementmore » from light quark interactions to date, with a precision close to the best LEP and SLD results.« less

Hadronic production of W and Z bosons at large transverse momentum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berger, Edmond L.; Gao, Jun; Kang, Zhong-Bo

2015-06-01

We introduce a modified factorization formalism in quantum chromodynamics for hadronic production of W and Z bosons at large transverse momentum p(T). When p(T) is much larger than the invariant mass Q of the vector boson, this new factorization formalism systematically resums the large fragmentation logarithms, alpha(m)(s)ln(m) (p(T)(2)/Q(2)), to all orders in the strong coupling alpha(s). Using our modified factorization formalism, we present the next-to-leading-order (NLO) predictions for W and Z boson production at high p(T) at the CERN Large Hadron Collider and at a future 100 TeV proton-proton collider. Our NLO results are about 5% larger in normalization, andmore » they show improved convergence and moderate reduction of the scale variation compared to the NLO predictions derived in a conventional fixed-order perturbative expansion.« less

A new member of ferrous sulfates, FeSO{sub 4}·2H{sub 2}O with PtS topology showing spin-canted long-range antiferromagnetic ordering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Long; Liu, Wei, E-mail: weiliu@ouc.edu.cn; Cao, Lixin

2015-11-15

A sanderite ferrous sulfate FeSO{sub 4}·2H{sub 2}O has been synthesized by the hydro/solvothermal method. Its crystal structure (Pccn, a=6.3160 Å, b=7.7550 Å, c=8.9880 Å, V=440.2 Å{sup 3}, Z=4) can be regarded as the condensation of alternately corner-shared FeO{sub 4}(H{sub 2}O){sub 2} octahedra and SO{sub 4} tetrahedra with a similar topology of PtS. By structural comparison with the known hydrated ferrous sulfates, the structural relation among them has been noted and discussed in detail. A variable temperature magnetic study shows a spin-canted long-range antiferromagnetic ordering in the low temperature regime, which might result from a possible phase transition during the coolingmore » from the high temperature. - Graphical abstract: As a new number of ferrous sulfates, sanderite FeSO{sub 4}·2H{sub 2}O has been synthesized under hydro/solvothermal conditions, which exhibits a similar topology of PtS. - Highlights: • Sanderite ferrous sulfate has been synthesized. • The topology of its structure is similar to that of PtS. • A structural relation between these hydrated ferrous sulfates is discovered.« less

Semiclassical theory of Landau levels and magnetic breakdown in topological metals

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Glazman, Leonid

2018-04-01

The Bohr-Sommerfeld quantization rule lies at the heart of the semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and de Haas-van Alphen oscillations for conventional metals, as well as for a host of topological metals which have emerged in the recent intercourse between band theory, crystalline symmetries, and topology. The essential ingredients in any quantization rule are connection formulas that match the semiclassical (WKB) wave function across regions of strong quantum fluctuations. Here, we propose (a) a multicomponent WKB wave function that describes transport within degenerate-band subspaces, and (b) the requisite connection formulas for saddle points and type-II Dirac points, where tunneling respectively occurs within the same band, and between distinct bands. (a) and (b) extend previous works by incorporating phase corrections that are subleading in powers of the field; these corrections include the geometric Berry phase, and account for the orbital magnetic moment and the Zeeman coupling. A comprehensive symmetry analysis is performed for such phase corrections occurring in closed orbits, which is applicable to solids in any (magnetic) space group. We have further formulated a graph-theoretic description of semiclassical orbits. This allows us to systematize the construction of quantization rules for a large class of closed orbits (with or without tunneling), as well as to formulate the notion of a topological invariant in semiclassical magnetotransport—as a quantity that is invariant under continuous deformations of the graph. Landau levels in the presence of tunneling are generically quasirandom, i.e., disordered on the scale of nearest-neighbor level spacings but having longer-ranged correlations; we develop a perturbative theory to determine Landau levels in such quasirandom spectra.

Topological Quantum Phase Transitions in Two-Dimensional Hexagonal Lattice Bilayers

NASA Astrophysics Data System (ADS)

Zhai, Xuechao; Jin, Guojun

2013-09-01

Since the successful fabrication of graphene, two-dimensional hexagonal lattice structures have become a research hotspot in condensed matter physics. In this short review, we theoretically focus on discussing the possible realization of a topological insulator (TI) phase in systems of graphene bilayer (GBL) and boron nitride bilayer (BNBL), whose band structures can be experimentally modulated by an interlayer bias voltage. Under the bias, a band gap can be opened in AB-stacked GBL but is still closed in AA-stacked GBL and significantly reduced in AA- or AB-stacked BNBL. In the presence of spin-orbit couplings (SOCs), further demonstrations indicate whether the topological quantum phase transition can be realized strongly depends on the stacking orders and symmetries of structures. It is observed that a bulk band gap can be first closed and then reopened when the Rashba SOC increases for gated AB-stacked GBL or when the intrinsic SOC increases for gated AA-stacked BNBL. This gives a distinct signal for a topological quantum phase transition, which is further characterized by a jump of the ℤ2 topological invariant. At fixed SOCs, the TI phase can be well switched by the interlayer bias and the phase boundaries are precisely determined. For AA-stacked GBL and AB-stacked BNBL, no strong TI phase exists, regardless of the strength of the intrinsic or Rashba SOCs. At last, a brief overview is given on other two-dimensional hexagonal materials including silicene and molybdenum disulfide bilayers.

Strong topological metal material with multiple Dirac cones

DOE PAGES

Ji, Huiwen; Valla, T.; Pletikosic, I.; ...

2016-01-25

We report a new, cleavable, strong topological metal, Zr 2Te 2P, which has the same tetradymite-type crystal structure as the topological insulator Bi 2Te 2Se. Instead of being a semiconductor, however, Zr 2Te 2P is metallic with a pseudogap between 0.2 and 0.7 eV above the Fermi energy (E F). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone with a largely linear dispersion over a 2 eV energy range. A third surface TRS-protected Dirac cone is predicted, andmore » observed using angle-resolved photoemission spectroscopy, making Z r2Te 2P the first system, to our knowledge, to realize TRS-protected Dirac cones at M¯ points. The high anisotropy of this Dirac cone is similar to the one in the hypothetical Dirac semimetal BiO 2. As a result, we propose that if E F can be tuned into the pseudogap where the Dirac dispersions exist, it may be possible to observe ultrahigh carrier mobility and large magnetoresistance in this material.« less

Topological insulators double perovskites: A2TePoO6 (A = Ca, Sr, Ba)

NASA Astrophysics Data System (ADS)

Lee, Po-Han; Zhou, Jian; Pi, Shu-Ting; Wang, Yin-Kuo

2017-12-01

Based on first-principle calculations and direct density functional theory calculations of surface bands, we predict a new class of three-dimensional (3D) Z2 topological insulators (TIs) with larger bulk bandgaps up to 0.4 eV in double perovskite materials A2TePoO6 (A = Ca, Sr, and Ba). The larger nontrivial gaps are induced by the symmetry-protected band contact along with band inversion occurring in the absence of spin-orbit coupling (SOC) making the SOC more effective than conventional TIs. The proposed materials are chemically inert and more robust to surface perturbations due to its intrinsic protection layer. This study provides the double perovskite material as a rich platform to design new TI-based electronic devices.

A bilayer Double Semion Model with Symmetry-Enriched Topological Order

NASA Astrophysics Data System (ADS)

Ortiz, Laura; Martin-Delgado, Miguel Angel

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry. We acknowledge financial support from the Spanish MINECO Grants FIS2012-33152, FIS2015-67411, and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. The research of M.A.M.-D. has been supported in part by the U.S. Army Research Office throu.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Doojin; Matchev, Konstantin T.; Moortgat, Filip

We consider SUSY-like events with two decay chains, each terminating in an invisible particle, whose true energy and momentum are not measured in the detector. Nevertheless, a useful educated guess about the invisible momenta can still be obtained by optimizing a suitable invariant mass function. We review and contrast several proposals in the literature for such ansatze: four versions of the M T 2-assisted on-shell reconstruction (MAOS), as well as several variants of the on-shell constrained M 2 variables. We compare the performance of these methods with regards to the mass determination of a new particle resonance along the decaymore » chain from the peak of the reconstructed invariant mass distribution. For concreteness, we consider the event topology of dilepton tt¯ events and study each of the three possible subsystems, in both a tt¯ and a SUSY example. We find that the M 2 variables generally provide sharper peaks and therefore better ansatze for the invisible momenta. We show that the performance can be further improved by preselecting events near the kinematic endpoint of the corresponding variable from which the momentum ansatz originates.« less

Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

NASA Astrophysics Data System (ADS)

Georgiev, Lachezar S.

2006-12-01

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma , in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the π/8 gate, are also explicitly implemented by quasihole braidings. Instead of the π/8 gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled- Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g3 .

Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice

NASA Astrophysics Data System (ADS)

Bouhon, Adrien; Schmidt, Johann; Black-Schaffer, Annica M.

2018-03-01

We establish the topology of the spin-singlet superconducting states in the bare hyperhoneycomb lattice, and we derive analytically the full phase diagram using only symmetry and topology in combination with simple energy arguments. The phase diagram is dominated by two states preserving time-reversal symmetry. We find a line-nodal state dominating at low doping levels that is topologically nontrivial and exhibits surface Majorana flatbands, which we show perfectly match the bulk-boundary correspondence using the Berry phase approach. At higher doping levels, we find a fully gapped state with trivial topology. By analytically calculating the topological invariant of the nodal lines, we derive the critical point between the line-nodal and fully gapped states as a function of both pairing parameters and doping. We find that the line-nodal state is favored not only at lower doping levels but also if symmetry-allowed deformations of the lattice are present. Adding simple energy arguments, we establish that a fully gapped state with broken time-reversal symmetry likely appears covering the actual phase transition. We find this fully gapped state to be topologically trivial, while we find an additional point-nodal state at very low doing levels that also break time-reversal symmetry and has nontrivial topology with associated Fermi surface arcs. We eventually address the robustness of the phase diagram to generalized models also including adiabatic spin-orbit coupling, and we show how all but the point-nodal state are reasonably stable.

Inferring topologies via driving-based generalized synchronization of two-layer networks

NASA Astrophysics Data System (ADS)

Wang, Yingfei; Wu, Xiaoqun; Feng, Hui; Lu, Jun-an; Xu, Yuhua

2016-05-01

The interaction topology among the constituents of a complex network plays a crucial role in the network’s evolutionary mechanisms and functional behaviors. However, some network topologies are usually unknown or uncertain. Meanwhile, coupling delays are ubiquitous in various man-made and natural networks. Hence, it is necessary to gain knowledge of the whole or partial topology of a complex dynamical network by taking into consideration communication delay. In this paper, topology identification of complex dynamical networks is investigated via generalized synchronization of a two-layer network. Particularly, based on the LaSalle-type invariance principle of stochastic differential delay equations, an adaptive control technique is proposed by constructing an auxiliary layer and designing proper control input and updating laws so that the unknown topology can be recovered upon successful generalized synchronization. Numerical simulations are provided to illustrate the effectiveness of the proposed method. The technique provides a certain theoretical basis for topology inference of complex networks. In particular, when the considered network is composed of systems with high-dimension or complicated dynamics, a simpler response layer can be constructed, which is conducive to circuit design. Moreover, it is practical to take into consideration perturbations caused by control input. Finally, the method is applicable to infer topology of a subnetwork embedded within a complex system and locate hidden sources. We hope the results can provide basic insight into further research endeavors on understanding practical and economical topology inference of networks.

A highly predictive A 4 flavor 3-3-1 model with radiative inverse seesaw mechanism

NASA Astrophysics Data System (ADS)

Cárcamo Hernández, A. E.; Long, H. N.

2018-04-01

We build a highly predictive 3-3-1 model, where the field content is extended by including several SU(3) L scalar singlets and six right handed Majorana neutrinos. In our model the {SU}{(3)}C× {SU}{(3)}L× U{(1)}X gauge symmetry is supplemented by the {A}4× {Z}4× {Z}6× {Z}16× {Z}16{\\prime } discrete group, which allows to get a very good description of the low energy fermion flavor data. In the model under consideration, the {A}4× {Z}4× {Z}6× {Z}16× {Z}16{\\prime } discrete group is broken at very high energy scale down to the preserved Z 2 discrete symmetry, thus generating the observed pattern of SM fermion masses and mixing angles and allowing the implementation of the loop level inverse seesaw mechanism for the generation of the light active neutrino masses, respectively. The obtained values for the physical observables in the quark sector agree with the experimental data, whereas those ones for the lepton sector also do, only for the case of inverted neutrino mass spectrum. The normal neutrino mass hierarchy scenario of the model is ruled out by the neutrino oscillation experimental data. We find an effective Majorana neutrino mass parameter of neutrinoless double beta decay of m ee = 46.9 meV, a leptonic Dirac CP violating phase of -81.37° and a Jarlskog invariant of about 10-2 for the inverted neutrino mass hierarchy. The preserved Z 2 symmetry allows for a stable scalar dark matter candidate.

Applications of invariants in general relativity

NASA Astrophysics Data System (ADS)

Pelavas, Nicos

This thesis explores various kinds of invariants and their use in general relativity. To start, the simplest invariants, those polynomial in the Riemann tensor, are examined and the currently accepted Carminati-Zakhary set is compared to the Carminati-McLenaghan set. A number of algebraic relations linking the two sets are given. The concept of gravitational entropy, as proposed by Penrose, has some physically appealing properties which have motivated attempts to quantify this notion using various invariants. We study this in the context of self-similar spacetimes. A general result is obtained which gives the Lie derivative of any invariant or ratio of invariants along a homothetic trajectory. A direct application of this result shows that the currently used gravitational epoch function fails to satisfy certain criteria. Based on this work, candidates for a gravitational epoch function are proposed that behave accordingly in these models. The instantaneous ergo surface in the Kerr solution is studied and shown to possess conical points at the poles when embedded in three dimensional Euclidean space. These intrinsic singularities had remained undiscovered for a generation. We generalize the Gauss-Bonnet theorem to accommodate these points and use it to compute a topological invariant, the Euler characteristic, for this surface. Interest in solutions admitting a cosmological constant has prompted us to study ergo surfaces in stationary non-asymptotically flat spacetimes. In these cases we show that there is in fact a family of ergo surfaces. By using a kinematic invariant constructed from timelike Killing vectors we try to find a preferred ergo surface. We illustrate to what extent this invariant fails to provide such a measure.

Geometrization of quantum physics

NASA Astrophysics Data System (ADS)

Ol'Khov, O. A.

2009-12-01

It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.

Topological defects in mixtures of superconducting condensates with different charges

NASA Astrophysics Data System (ADS)

Garaud, Julien; Babaev, Egor

2014-06-01

We investigate the topological defects in phenomenological models describing mixtures of charged condensates with commensurate electric charges. Such situations are expected to appear for example in liquid metallic deuterium. This is modeled by a multicomponent Ginzburg-Landau theory where the condensates are coupled to the same gauge field by different coupling constants whose ratio is a rational number. We also briefly discuss the case where electric charges are incommensurate. Flux quantization and finiteness of the energy per unit length dictate that the different condensates have different winding and thus different number of (fractional) vortices. Competing attractive and repulsive interactions lead to molecule-like bound states between fractional vortices. Such bound states have finite energy and carry integer flux quanta. These can be characterized by the CP1 topological invariant that motivates their denomination as skyrmions.

Interactions of 2.1 GeV/n He-4, C-12, N-14 and O-16 nuclei in emulsion

NASA Technical Reports Server (NTRS)

Heckman, H. H.; Greiner, D. E.; Lindstrom, P. J.; Shwe, H.

1975-01-01

The interaction mean-free-path lengths for He-4, C-12, N-14 and O-16 nuclei at 2.1 GeV/n have been measured in nuclear emulsion detectors. The angular distributions of Z equals 1 and 2 secondaries from the interactions of C, N and O beams are determined, and the topology of projectile fragmentation of these ions is examined.

Summer Conference on General Topology and Applications (10th) Held in Amsterdam on 15-18 August 1994

DTIC Science & Technology

1994-08-18

topology. Joint work by: I. Juhisz and Z. Szentmiid6ssy. Room: KC1.37 Time: TUE 16:40-1 7:00 ABSTRACTS 89 Forcing and Normality, II LUcia R. Junqueira...Gerard A. Venema (Calvin College, Grand Rapids, MI, USA) J. Vermeer (TU Delft, Delft, the Netherlands) Paolo Vitolo (Universita della Basilicata, Potenza

Morphological self-organizing feature map neural network with applications to automatic target recognition

NASA Astrophysics Data System (ADS)

Zhang, Shijun; Jing, Zhongliang; Li, Jianxun

2005-01-01

The rotation invariant feature of the target is obtained using the multi-direction feature extraction property of the steerable filter. Combining the morphological operation top-hat transform with the self-organizing feature map neural network, the adaptive topological region is selected. Using the erosion operation, the topological region shrinkage is achieved. The steerable filter based morphological self-organizing feature map neural network is applied to automatic target recognition of binary standard patterns and real-world infrared sequence images. Compared with Hamming network and morphological shared-weight networks respectively, the higher recognition correct rate, robust adaptability, quick training, and better generalization of the proposed method are achieved.