Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z 2 Topological Insulator

NASA Astrophysics Data System (ADS)

Deng, Hui-Xiong; Song, Zhi-Gang; Li, Shu-Shen; Wei, Su-Huai; Luo, Jun-Wei

2018-05-01

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, but the transition may also occur between different classes of topological Dirac phases. However, it is a fundamental challenge to realize quantum transition between Z2 nontrivial topological insulator (TI) and topological crystalline insulator (TCI) in one material because Z2 TI and TCI are hardly both co-exist in a single material due to their contradictory requirement on the number of band inversions. The Z2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas, the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Here, take PbSnTe2 alloy as an example, we show that at proper alloy composition the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z2 TI phase when the alloy is ordered from a random phase into a stable CuPt phase. Our results suggest that atomic-ordering provides a new platform to switch between different topological phases.

Photoinduced topological phase transition and spin polarization in a two-dimensional topological insulator

NASA Astrophysics Data System (ADS)

Chen, M. N.; Su, W.; Deng, M. X.; Ruan, Jiawei; Luo, W.; Shao, D. X.; Sheng, L.; Xing, D. Y.

2016-11-01

A great deal of attention has been paid to the topological phases engineered by photonics over the past few years. Here, we propose a topological quantum phase transition to a quantum anomalous Hall (QAH) phase induced by off-resonant circularly polarized light in a two-dimensional system that is initially in a quantum spin Hall phase or a trivial insulator phase. This provides an alternative method to realize the QAH effect, other than magnetic doping. The circularly polarized light effectively creates a Zeeman exchange field and a renormalized Dirac mass, which are tunable by varying the intensity of the light and drive the quantum phase transition. Both the transverse and longitudinal Hall conductivities are studied, and the former is consistent with the topological phase transition when the Fermi level lies in the band gap. A highly controllable spin-polarized longitudinal electrical current can be generated when the Fermi level is in the conduction band, which may be useful for designing topological spintronics.

Realization of a topological phase transition in a gyroscopic lattice

NASA Astrophysics Data System (ADS)

Mitchell, Noah P.; Nash, Lisa M.; Irvine, William T. M.

2018-03-01

Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structures. The ability to tune such a material through a topological phase transition in real time could enable the use of protected waves for information storage and readout. Here we dynamically tune through a topological phase transition by breaking inversion symmetry in a metamaterial composed of interacting gyroscopes. Through the transition, we track the divergence of the edge modes' localization length and the change in Chern number characterizing the topology of the material's band structure. This Rapid Communication provides a new axis with which to tune the response of mechanical topological metamaterials.

Disorder-induced transitions in resonantly driven Floquet topological insulators

NASA Astrophysics Data System (ADS)

Titum, Paraj; Lindner, Netanel H.; Refael, Gil

2017-08-01

We investigate the effects of disorder in Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by resonantly driving a transition between the valence and conduction bands. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a mobility gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse: we show that in the same quantum well, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet topological Anderson insulator (FTAI). We identify the conditions on the driving field necessary for observing such a transition.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

PubMed Central

Bucksch, Alexander; Atta-Boateng, Acheampong; Azihou, Akomian F.; Battogtokh, Dorjsuren; Baumgartner, Aly; Binder, Brad M.; Braybrook, Siobhan A.; Chang, Cynthia; Coneva, Viktoirya; DeWitt, Thomas J.; Fletcher, Alexander G.; Gehan, Malia A.; Diaz-Martinez, Diego Hernan; Hong, Lilan; Iyer-Pascuzzi, Anjali S.; Klein, Laura L.; Leiboff, Samuel; Li, Mao; Lynch, Jonathan P.; Maizel, Alexis; Maloof, Julin N.; Markelz, R. J. Cody; Martinez, Ciera C.; Miller, Laura A.; Mio, Washington; Palubicki, Wojtek; Poorter, Hendrik; Pradal, Christophe; Price, Charles A.; Puttonen, Eetu; Reese, John B.; Rellán-Álvarez, Rubén; Spalding, Edgar P.; Sparks, Erin E.; Topp, Christopher N.; Williams, Joseph H.; Chitwood, Daniel H.

2017-01-01

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics. PMID:28659934

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.

Quantization of geometric phase with integer and fractional topological characterization in a quantum Ising chain with long-range interaction.

PubMed

Sarkar, Sujit

2018-04-12

An attempt is made to study and understand the behavior of quantization of geometric phase of a quantum Ising chain with long range interaction. We show the existence of integer and fractional topological characterization for this model Hamiltonian with different quantization condition and also the different quantized value of geometric phase. The quantum critical lines behave differently from the perspective of topological characterization. The results of duality and its relation to the topological quantization is presented here. The symmetry study for this model Hamiltonian is also presented. Our results indicate that the Zak phase is not the proper physical parameter to describe the topological characterization of system with long range interaction. We also present quite a few exact solutions with physical explanation. Finally we present the relation between duality, symmetry and topological characterization. Our work provides a new perspective on topological quantization.

Unconventional transformation of spin Dirac phase across a topological quantum phase transition

PubMed Central

Xu, Su-Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J. Hugo; Shibayev, Pavel P.; Basak, Susmita; Chang, Tay-Rong; Jeng, Horng-Tay; Cava, Robert J.; Lin, Hsin; Bansil, Arun; Hasan, M. Zahid

2015-01-01

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality. PMID:25882717

A Non-Abelian Geometric Phase for Spin Systems

NASA Astrophysics Data System (ADS)

H M, Bharath; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

Berry's geometric phase has been used to characterize topological phase transitions. Recent works have addressed the question of whether generalizations of Berry's phase to mixed states can be used to characterize topological phase transitions. Berry's phase is essentially the geometric information stored in the overall phase of a quantum system. Here, we show that geometric information is also stored in the higher order spin moments of a quantum spin system. In particular, we show that when the spin vector of a quantum spin system with a spin 1 or higher is transported along a closed path inside the Bloch ball, the tensor of second moments picks up a geometric phase in the form of an SO(3) operator. Geometrically interpreting this phase is tantamount to defining a steradian angle for closed paths inside the Bloch ball. Typically the steradian angle is defined by projecting the path onto the surface of the Bloch ball. However, paths that pass through the center cannot be projected onto the surface. We show that the steradian angles of all paths, including those that pass through the center can be defined by projecting them onto a real projective plane, instead of a sphere. This steradian angle is equal to the geometric phase picked up by a spin system.

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.

Unconventional transformation of spin Dirac phase across a topological quantum phase transition

DOE PAGES

Xu, Su -Yang; Neupane, Madhab; Belopolski, Ilya; ...

2015-04-17

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from amore » surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results provide a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.« less

Topological transitions induced by antiferromagnetism in a thin-film topological insulator

NASA Astrophysics Data System (ADS)

Yin, Gen; He, Qinglin; Yu, Luyan; Pan, Lei; Wang, Kang

Ferromagnetism introduced in topological insulators (TIs) opens a non-trivial exchange band gap, providing an exciting platform to control the topological order through an external magnetic field. The magnetization induces a topological transition that breaks time-reversal symmetry, resulting in anomalous Hall effects. Recently, it was experimentally shown that the surface of an antiferromagnetic (AFM) thin film can magnetize the surface Dirac fermions in a TI thin film similar to the case induced by ferromagnetism. Here, we show that when a TI thin film is sandwiched between two antiferromagnetic layers, an unsynchronized magnetic reversal introduces two intermediate spin configurations during the scan of the external field, resulting in a new topological phase with second Chern numbers. This topological phase introduces two counter-propagating chiral edge modes inside the exchange gap, changing the total number of transport channels drastically when the fermi level is close to the Dirac point. Induced by this change, the magnetoresistance of the channel presents an antisymmetric feature during the field scan. With the the help of the high ordering temperature of AFM layers, this transport signature of the phase transition persists up to 90K experimentally. This work is supported by (i) SHINES, an EFRC by US-DOE, Office of Science, BES, #SC0012670. (ii) US-NSF (DMR-1411085), (iii) ARO program W911NF-15-1-10561, and (iv) FAME Center in STARnet, an SRC program by MARCO and DARPA.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions.

PubMed

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-04-22

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Geometrically unrestricted, topologically constrained control of liquid crystal defects using simultaneous holonomic magnetic and holographic optical manipulation.

PubMed

Varney, Michael C M; Jenness, Nathan J; Smalyukh, Ivan I

2014-02-01

Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions

PubMed Central

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-01-01

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems. PMID:27102945

Interaction phenomena at topological transitions in strongly anisotropic Dirac materials

NASA Astrophysics Data System (ADS)

Kotov, Valeri

2014-03-01

It is known that a topological (Lifshitz) transition can take place in graphene, strained uniaxially in the zig-zag direction. At such a transition the spectrum becomes semi-Dirac like, with linear, ultrarelativistic dispersion in one direction, and quadratic momentum dependence in the other. This type of transition also occurs in other materials as well as in artificial graphene lattices. We have found that long-range Coulomb interactions can lead to profound effects at such topological transitions. In particular, an unusually strong log squared renormalization behavior was found in the effective fermion mass, ultimately leading to very strong changes in the shape of the critical fermion spectrum. We also study the stability of such exotic spectrum towards spontaneous gap formation (excitonic transition). Ultimately we find that the interaction effects are much stronger at topological transitions in strongly anisotropic Dirac materials, compared to ``conventional'' isotropic graphene. Supported in part by DOE grant DE-FG02-08ER46512.

First Principles Study on Topological-Phase Transition in Ferroelectric Oxides

NASA Astrophysics Data System (ADS)

Yamauchi, Kunihiko; Barone, Paolo; Picozzi, Silvia

Graphene is known as a 2D topological insulator with zero energy gap and Dirac cone. In this study, we theoretically designed a honeycomb structure of Au ions embedded in a ferroelectric host oxide, in order to exploit structural distortions to control topological properties. We show that the polar structural distortion induces the emergence of spin-valley coupling, together with a topological transition from a quantum spin-Hall insulating phase to a trivial band insulator. The phase transition also affects the Berry curvature and spin-valley selection rules. Analogously to graphene, the microscopic origin of this topological phase is ascribed to a spin-valley-sublattice coupling, which arises from the interplay between trigonal crystal field and an ``effective'' spin-orbit interaction due to virtual excitations between eg and t2g states of transition-metal ions.

STM studies of topological phase transition in (Bi,In)2Se3

NASA Astrophysics Data System (ADS)

Zhang, Wenhan; Wang, Xueyun; Cheong, Sang-Wook; Wu, Weida; Weida Wu Team; Sang-Wook Cheong Collaboration

Topological insulators (TI) are a class of materials with insulating bulk and metallic surface state, which is the result of band inversion induced by strong spin-orbit coupling (SOC). The transition from topological phase to non-topological phase is of great significance. In theory, topological phase transition is realized by tuning SOC strength. It is characterized by the process of gap closing and reopening. Experimentally it was observed in two systems: TlBi(S1-xSex)2 and (Bi1-xInx)2 Se3 where the transition is realized by varying isovalent elements doping concentration. However, none of the previous studies addressed the impact of disorder, which is inevitable in doped systems. Here, we present a systematic scanning tunneling microscopy/spectroscopy study on (Bi1-xInx)2 Se3 single crystals with different In concentrations across the transition. Our results reveal an electronic inhomogeneity due to the random distribution of In defects which locally suppress the topological surface states. Our study provides a new angle of understanding the topological transition in the presence of strong disorders. This work is supported by NSF DMR-1506618.

Topological superconductivity in monolayer transition metal dichalcogenides.

PubMed

Hsu, Yi-Ting; Vaezi, Abolhassan; Fischer, Mark H; Kim, Eun-Ah

2017-04-11

Theoretically, it has been known that breaking spin degeneracy and effectively realizing spinless fermions is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here we propose to realize spinless fermions by splitting the spin degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological because of the near spin degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favours two topological superconducting states: interpocket paired state with Chern number 2 and intrapocket paired state with finite pair momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device-friendly platform of monolayer TMDs.

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.

Electronic topological transitions in the AgPd system

NASA Astrophysics Data System (ADS)

Skorodumova, N. V.; Simak, S. I.; Smirnova, E. A.; Vekilov, Yu. Kh.

1995-02-01

“First-principles” LMTO-CPA calculations of the Fermi surfaces and thermodynamic properties of AgPd random alloys are presented. We show that there are at least four electronic topological transitions (ETT) in the system. The changes of the Fermi surface topology lead to the appearance of peculiarities in the concentration dependence of the thermodynamic (ground state) properties.

Predicting a new phase (T'') of two-dimensional transition metal di-chalcogenides and strain-controlled topological phase transition

NASA Astrophysics Data System (ADS)

Ma, Fengxian; Gao, Guoping; Jiao, Yalong; Gu, Yuantong; Bilic, Ante; Zhang, Haijun; Chen, Zhongfang; Du, Aijun

2016-02-01

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological

Mitral Valve Chordae Tendineae: Topological and Geometrical Characterization.

PubMed

Khalighi, Amir H; Drach, Andrew; Bloodworth, Charles H; Pierce, Eric L; Yoganathan, Ajit P; Gorman, Robert C; Gorman, Joseph H; Sacks, Michael S

2017-02-01

Mitral valve (MV) closure depends upon the proper function of each component of the valve apparatus, which includes the annulus, leaflets, and chordae tendineae (CT). Geometry plays a major role in MV mechanics and thus highly impacts the accuracy of computational models simulating MV function and repair. While the physiological geometry of the leaflets and annulus have been previously investigated, little effort has been made to quantitatively and objectively describe CT geometry. The CT constitute a fibrous tendon-like structure projecting from the papillary muscles (PMs) to the leaflets, thereby evenly distributing the loads placed on the MV during closure. Because CT play a major role in determining the shape and stress state of the MV as a whole, their geometry must be well characterized. In the present work, a novel and comprehensive investigation of MV CT geometry was performed to more fully quantify CT anatomy. In vitro micro-tomography 3D images of ovine MVs were acquired, segmented, then analyzed using a curve-skeleton transform. The resulting data was used to construct B-spline geometric representations of the CT structures, enriched with a continuous field of cross-sectional area (CSA) data. Next, Reeb graph models were developed to analyze overall topological patterns, along with dimensional attributes such as segment lengths, 3D orientations, and CSA. Reeb graph results revealed that the topology of ovine MV CT followed a full binary tree structure. Moreover, individual chords are mostly planar geometries that together form a 3D load-bearing support for the MV leaflets. We further demonstrated that, unlike flow-based branching patterns, while individual CT branches became thinner as they propagated further away from the PM heads towards the leaflets, the total CSA almost doubled. Overall, our findings indicate a certain level of regularity in structure, and suggest that population-based MV CT geometric models can be generated to improve current MV

Thermally Driven Electronic Topological Transition in FeTi

NASA Astrophysics Data System (ADS)

Yang, F. C.; Muñoz, J. A.; Hellman, O.; Mauger, L.; Lucas, M. S.; Tracy, S. J.; Stone, M. B.; Abernathy, D. L.; Xiao, Yuming; Fultz, B.

2016-08-01

Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M5- phonon mode in B 2 -ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M5- phonon mode and an adiabatic electron-phonon interaction with an unusual temperature dependence.

Glass transition temperature and topological constraints of sodium borophosphate glass-forming liquids.

PubMed

Jiang, Qi; Zeng, Huidan; Liu, Zhao; Ren, Jing; Chen, Guorong; Wang, Zhaofeng; Sun, Luyi; Zhao, Donghui

2013-09-28

Sodium borophosphate glasses exhibit intriguing mixed network former effect, with the nonlinear compositional dependence of their glass transition temperature as one of the most typical examples. In this paper, we establish the widely applicable topological constraint model of sodium borophosphate mixed network former glasses to explain the relationship between the internal structure and nonlinear changes of glass transition temperature. The application of glass topology network was discussed in detail in terms of the unified methodology for the quantitative distribution of each coordinated boron and phosphorus units and glass transition temperature dependence of atomic constraints. An accurate prediction of composition scaling of the glass transition temperature was obtained based on topological constraint model.

Trivial topological phase of CaAgP and the topological nodal-line transition in CaAg (P1 -xA sx)

NASA Astrophysics Data System (ADS)

Xu, N.; Qian, Y. T.; Wu, Q. S.; Autès, G.; Matt, C. E.; Lv, B. Q.; Yao, M. Y.; Strocov, V. N.; Pomjakushina, E.; Conder, K.; Plumb, N. C.; Radovic, M.; Yazyev, O. V.; Qian, T.; Ding, H.; Mesot, J.; Shi, M.

2018-04-01

By performing angle-resolved photoemission spectroscopy and first-principles calculations, we address the topological phase of CaAgP and investigate the topological phase transition in CaAg (P1 -xA sx) . We reveal that in CaAgP, the bulk band gap and surface states with a large bandwidth are topologically trivial, in agreement with hybrid density functional theory calculations. The calculations also indicate that application of "negative" hydrostatic pressure can transform trivial semiconducting CaAgP into an ideal topological nodal-line semimetal phase. The topological transition can be realized by partial isovalent P/As substitution at x =0.38 .

Structural and topological phase transitions on the German Stock Exchange

NASA Astrophysics Data System (ADS)

Wiliński, M.; Sienkiewicz, A.; Gubiec, T.; Kutner, R.; Struzik, Z. R.

2013-12-01

We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing the FSE were found. The first transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees representing the market’s state for the period containing the crash. Subsequently, a transition is observed from this transient, (meta)stable state of the crash to a hierarchical scale-free MST decorated by several star-like trees after the worldwide financial crash. The phase transitions observed are analogous to the ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than those found by Onnela-Chakraborti-Kaski-Kertész for the S&P 500 index in the vicinity of Black Monday (October 19, 1987) and also in the vicinity of January 1, 1998. Our results provide an empirical foundation for the future theory of dynamical, structural and topological phase transitions on financial markets.

Thermally Driven Electronic Topological Transition in FeTi

DOE PAGES

Yang, F. C.; Muñoz, J. A.; Hellman, O.; ...

2016-08-08

In this paper, ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M 5 - phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. Finally, the thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M 5 - phonon mode andmore » an adiabatic electron-phonon interaction with an unusual temperature dependence.« less

Towards AN Integration of GIS and Bim Data: what are the Geometric and Topological Issues?

NASA Astrophysics Data System (ADS)

Arroyo Ohori, K.; Biljecki, F.; Diakité, A.; Krijnen, T.; Ledoux, H.; Stoter, J.

2017-10-01

Geographic information and building information modelling both model buildings and infrastructure, but the way in which they are modelled is usually complimentary and BIM-GIS integration is widely considered as a way forward for both domains. For one, more detailed BIM data can feed more general GIS data and GIS data can provide the context that is necessary to BIM data. While previous studies have focused on the theoretical aspects of such an integration at a schema level, in this paper we focus on explaining the geometric and topological issues we have found while trying to develop software to realise such an integration in practice and at a data level. In our preliminary results, which are presented here, we have found that many issues for such an integration remain: handling the geometric and topological problems in BIM models, dealing with bad georeferencing and figuring out the best way to convert data between IFC and CityGML are all open issues.

Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases.

PubMed

Zhou, Tao; Gao, Yi; Wang, Z D

2014-06-11

We study superconducting states in the presence of spin-orbital coupling and Zeeman field. It is found that a phase transition from a Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state occurs upon increasing the spin-orbital coupling. The nature of this topological phase transition and its critical property are investigated numerically. Physical properties of the topological superconducting phase are also explored. Moreover, the local density of states is calculated, through which the topological feature may be tested experimentally.

N-tuple topological/geometric cutoffs for 3D N-linear algebraic molecular codifications: variability, linear independence and QSAR analysis.

PubMed

García-Jacas, C R; Marrero-Ponce, Y; Barigye, S J; Hernández-Ortega, T; Cabrera-Leyva, L; Fernández-Castillo, A

2016-12-01

Novel N-tuple topological/geometric cutoffs to consider specific inter-atomic relations in the QuBiLS-MIDAS framework are introduced in this manuscript. These molecular cutoffs permit the taking into account of relations between more than two atoms by using (dis-)similarity multi-metrics and the concepts related with topological and Euclidean-geometric distances. To this end, the kth two-, three- and four-tuple topological and geometric neighbourhood quotient (NQ) total (or local-fragment) spatial-(dis)similarity matrices are defined, to represent 3D information corresponding to the relations between two, three and four atoms of the molecular structures that satisfy certain cutoff criteria. First, an analysis of a diverse chemical space for the most common values of topological/Euclidean-geometric distances, bond/dihedral angles, triangle/quadrilateral perimeters, triangle area and volume was performed in order to determine the intervals to take into account in the cutoff procedures. A variability analysis based on Shannon's entropy reveals that better distribution patterns are attained with the descriptors based on the cutoffs proposed (QuBiLS-MIDAS NQ-MDs) with regard to the results obtained when all inter-atomic relations are considered (QuBiLS-MIDAS KA-MDs - 'Keep All'). A principal component analysis shows that the novel molecular cutoffs codify chemical information captured by the respective QuBiLS-MIDAS KA-MDs, as well as information not captured by the latter. Lastly, a QSAR study to obtain deeper knowledge of the contribution of the proposed methods was carried out, using four molecular datasets (steroids (STER), angiotensin converting enzyme (ACE), thermolysin inhibitors (THER) and thrombin inhibitors (THR)) widely used as benchmarks in the evaluation of several methodologies. One to four variable QSAR models based on multiple linear regression were developed for each compound dataset following the original division into training and test sets. The

Topological Phase Transitions in Line-nodal Superconductors

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Han, Sangeun; Moon, Eun-Gook

Fathoming interplay between symmetry and topology of many-electron wave-functions deepens our understanding in quantum nature of many particle systems. Topology often protects zero-energy excitation, and in a certain class, symmetry is intrinsically tied to the topological protection. Namely, unless symmetry is broken, topological nature is intact. We study one specific case of such class, symmetry-protected line-nodal superconductors in three spatial dimensions (3d). Mismatch between phase spaces of order parameter fluctuation and line-nodal fermion excitation induces an exotic universality class in a drastic contrast to one of the conventional ϕ4 theory in 3d. Hyper-scaling violation and relativistic dynamic scaling with unusually large quantum critical region are main characteristics, and their implication in experiments is discussed. For example, continuous phase transition out of line-nodal superconductors has a linear phase boundary in a temperature-tuning parameter phase-diagram. This work was supported by the Brain Korea 21 PLUS Project of Korea Government and KAIST start-up funding.

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.

Geometric model of topological insulators from the Maxwell algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

2017-11-01

We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.

Magnification of signatures of a topological phase transition by quantum zero point motion

NASA Astrophysics Data System (ADS)

Lopes, Pedro L. e. S.; Ghaemi, Pouyan

2015-08-01

We show that the zero point motion of a vortex in superconducting doped topological insulators leads to significant changes in the electronic spectrum at the topological phase transition in this system. This topological phase transition is tuned by the doping level, and the corresponding effects are manifest in the density of states at energies which are on the order of the vortex fluctuation frequency. Although the electronic energy gap in the spectrum generated by a stationary vortex is but a small fraction of the bulk superconducting gap, the vortex fluctuation frequency may be much larger. As a result, this quantum zero point motion can induce a discontinuous change in the spectral features of the system at the topological vortex phase transition to energies which are well within the resolution of scanning tunneling microscopy. This discontinuous change is exclusive to superconducting systems in which we have a topological phase transition. Moreover, the phenomena studied in this paper present effects of Magnus forces on the vortex spectrum which are not present in the ordinary s -wave superconductors. Finally, we demonstrate explicitly that the vortex in this system is equivalent to a Kitaev chain. This allows for the mapping of the vortex fluctuating scenario in three dimensions into similar one-dimensional situations in which one may search for other novel signatures of topological phase transitions.

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.

Temperature-Induced Topological Phase Transition in HgTe Quantum Wells

NASA Astrophysics Data System (ADS)

Kadykov, A. M.; Krishtopenko, S. S.; Jouault, B.; Desrat, W.; Knap, W.; Ruffenach, S.; Consejo, C.; Torres, J.; Morozov, S. V.; Mikhailov, N. N.; Dvoretskii, S. A.; Teppe, F.

2018-02-01

We report a direct observation of temperature-induced topological phase transition between the trivial and topological insulator states in an HgTe quantum well. By using a gated Hall bar device, we measure and represent Landau levels in fan charts at different temperatures, and we follow the temperature evolution of a peculiar pair of "zero-mode" Landau levels, which split from the edge of electronlike and holelike subbands. Their crossing at a critical magnetic field Bc is a characteristic of inverted band structure in the quantum well. By measuring the temperature dependence of Bc, we directly extract the critical temperature Tc at which the bulk band gap vanishes and the topological phase transition occurs. Above this critical temperature, the opening of a trivial gap is clearly observed.

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.

Edge states and topological phase transitions in chains of dielectric nanoparticles

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

Kruk, Sergey; Slobozhanyuk, Alexey; Denkova, Denitza

Recently introduced field of topological photonics aims to explore the concepts of topological insulators for novel phenomena in optics. Here polymeric chains of subwavelength silicon nanodisks are studied and it is demonstrated that these chains can support two types of topological edge modes based on magnetic and electric Mie resonances, and their topological properties are fully dictated by the spatial arrangement of the nanoparticles in the chain. Here, it is observed experimentally and described how theoretically topological phase transitions at the nanoscale define a change from trivial to nontrivial topological states when the edge mode is excited.

Edge states and topological phase transitions in chains of dielectric nanoparticles

DOE PAGES

Kruk, Sergey; Slobozhanyuk, Alexey; Denkova, Denitza; ...

2017-01-12

Recently introduced field of topological photonics aims to explore the concepts of topological insulators for novel phenomena in optics. Here polymeric chains of subwavelength silicon nanodisks are studied and it is demonstrated that these chains can support two types of topological edge modes based on magnetic and electric Mie resonances, and their topological properties are fully dictated by the spatial arrangement of the nanoparticles in the chain. Here, it is observed experimentally and described how theoretically topological phase transitions at the nanoscale define a change from trivial to nontrivial topological states when the edge mode is excited.

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

Dynamical Detection of Topological Phase Transitions in Short-Lived Atomic Systems.

PubMed

Setiawan, F; Sengupta, K; Spielman, I B; Sau, Jay D

2015-11-06

We demonstrate that dynamical probes provide direct means of detecting the topological phase transition (TPT) between conventional and topological phases, which would otherwise be difficult to access because of loss or heating processes. We propose to avoid such heating by rapidly quenching in and out of the short-lived topological phase across the transition that supports gapless excitations. Following the quench, the distribution of excitations in the final conventional phase carries signatures of the TPT. We apply this strategy to study the TPT into a Majorana-carrying topological phase predicted in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. The resulting spin-resolved momentum distribution, computed by self-consistently solving the time-dependent Bogoliubov-de Gennes equations, exhibits Kibble-Zurek scaling and Stückelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.

Dynamical Detection of Topological Phase Transitions in Short-Lived Atomic Systems

NASA Astrophysics Data System (ADS)

Setiawan, F.; Sengupta, K.; Spielman, I. B.; Sau, Jay D.

2015-11-01

We demonstrate that dynamical probes provide direct means of detecting the topological phase transition (TPT) between conventional and topological phases, which would otherwise be difficult to access because of loss or heating processes. We propose to avoid such heating by rapidly quenching in and out of the short-lived topological phase across the transition that supports gapless excitations. Following the quench, the distribution of excitations in the final conventional phase carries signatures of the TPT. We apply this strategy to study the TPT into a Majorana-carrying topological phase predicted in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. The resulting spin-resolved momentum distribution, computed by self-consistently solving the time-dependent Bogoliubov-de Gennes equations, exhibits Kibble-Zurek scaling and Stückelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.

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.

Topological phase transitions and quantum Hall effect in the graphene family

NASA Astrophysics Data System (ADS)

Ledwith, P.; Kort-Kamp, W. J. M.; Dalvit, D. A. R.

2018-04-01

Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaks which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. This complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.

Plateau-Plateau Transitions in Disordered Topological Chern Insulators

NASA Astrophysics Data System (ADS)

Su, Ying; Avishai, Yshai; Wang, Xiangrong

Occurrence of the topological Anderson insulator (TAI) in the HgTe quantum well demonstrates that topological phase transition can be driven by disorder, where re-entrant 2e2 / h quantized conductance is contributed by helical edge states. Within a certain extension of the disordered Kane-Mele model for magnetic materials that violate time-reversal symmetry and inversion symmetry, it is shown that the physics of TAI becomes even richer due to lifted spin and valley degeneracies. Tuning either disorder or Fermi energy (in both topologically trivial and nontrivial phases) makes it possible to drive plateau-plateau transitions between distinct TAI phases characterized by different Chern numbers, marked by jumps of the quantized conductance from 0 to e2 / h and from e2 / h to 2e2 / h . An effective medium theory based on the Born approximation yields an accurate description of different TAI phases in parameter space. This work is supported by NSF of China Grant (No. 11374249) and Hong Kong RGC Grants (No. 163011151 and No. 605413). The research of Y.A. is partially supported by Israel Science Foundation Grant No. 400/2012.

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

Temperature-driven topological transition in 1T'-MoTe2

NASA Astrophysics Data System (ADS)

Berger, Ayelet Notis; Andrade, Erick; Kerelsky, Alexander; Edelberg, Drew; Li, Jian; Wang, Zhijun; Zhang, Lunyong; Kim, Jaewook; Zaki, Nader; Avila, Jose; Chen, Chaoyu; Asensio, Maria C.; Cheong, Sang-Wook; Bernevig, Bogdan A.; Pasupathy, Abhay N.

2018-01-01

The topology of Weyl semimetals requires the existence of unique surface states. Surface states have been visualized in spectroscopy measurements, but their connection to the topological character of the material remains largely unexplored. 1T'-MoTe2, presents a unique opportunity to study this connection. This material undergoes a phase transition at 240 K that changes the structure from orthorhombic (putative Weyl semimetal) to monoclinic (trivial metal), while largely maintaining its bulk electronic structure. Here, we show from temperature-dependent quasiparticle interference measurements that this structural transition also acts as a topological switch for surface states in 1T'-MoTe2. At low temperature, we observe strong quasiparticle scattering, consistent with theoretical predictions and photoemission measurements for the surface states in this material. In contrast, measurements performed at room temperature show the complete absence of the scattering wavevectors associated with the trivial surface states. These distinct quasiparticle scattering behaviors show that 1T'-MoTe2 is ideal for separating topological and trivial electronic phenomena via temperature-dependent measurements.

Uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials

NASA Astrophysics Data System (ADS)

Romera, E.; Calixto, M.

2015-05-01

Uncertainty relations are studied for a characterization of topological-band insulator transitions in 2D gapped Dirac materials isostructural with graphene. We show that the relative or Kullback-Leibler entropy in position and momentum spaces, and the standard variance-based uncertainty relation give sharp signatures of topological phase transitions in these systems.

Topological phase transitions from Harper to Fibonacci crystals

NASA Astrophysics Data System (ADS)

Amit, Guy; Dana, Itzhack

2018-02-01

Topological properties of Harper and generalized Fibonacci chains are studied in crystalline cases, i.e., for rational values of the modulation frequency. The Harper and Fibonacci crystals at fixed frequency are connected by an interpolating one-parameter Hamiltonian. As the parameter is varied, one observes topological phase transitions, i.e., changes in the Chern integers of two bands due to the degeneracy of these bands at some parameter value. For small frequency, corresponding to a semiclassical regime, the degeneracies are shown to occur when the average energy of the two bands is approximately equal to the energy of the classical separatrix. Spectral and topological features of the Fibonacci crystal for small frequency leave a clear imprint on the corresponding Hofstadter butterfly for arbitrary frequency.

Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

NASA Astrophysics Data System (ADS)

Pillay, Jason C.; McCulloch, Ian P.

2018-05-01

The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.

Phase-Field Simulations of Topological Structures and Topological Phase Transitions in Ferroelectric Oxide Heterostructures

NASA Astrophysics Data System (ADS)

Zijian Hong

vortex structure can be expected when the geometric length scale of the ferroelectrics is close to this value. The role of insulating STO is further revealed, which shows that a rich phase diagram can be formed by simply tuning the thickness of this layer. Wave-like polar spiral phase is simulated by substituting part of the PTO with BiFeO3 (BFO) in the PTO/STO superlattice (i.e., in a (PTO) 4/(BFO)4/(PTO)4/(STO)12 tricolor system) which has demonstrate ordered polar vortex lattice. This spiral phase is made up of semi-vortex cores that are floating up-down in the ferroelectric PTO layers, giving rise to a net in-plane polarization. An increase of Curie temperature and topological to regular domain transition temperature (over 200 K) is observed, due to the higher Curie temperature and larger spontaneous polarization in BFO layers. This unidirectional spiral state can be reversibly switched by experimentally feasible in-plane field, which evolves into a metastable vortex structure in-between two spiral phases with opposite in-plane directions. (Abstract shortened by ProQuest.).

Topological phase transitions and quantum Hall effect in the graphene family

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

Ledwith, Patrick John; Kort-Kamp, Wilton Junior de Melo; Dalvit, Diego Alejandro Roberto

Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaksmore » which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. As a result, this complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.« less

Topological phase transitions and quantum Hall effect in the graphene family

DOE PAGES

Ledwith, Patrick John; Kort-Kamp, Wilton Junior de Melo; Dalvit, Diego Alejandro Roberto

2018-04-15

Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaksmore » which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. As a result, this complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.« less

Geometrical protection of topological magnetic solitons in microprocessed chiral magnets

NASA Astrophysics Data System (ADS)

Mito, Masaki; Ohsumi, Hiroyuki; Tsuruta, Kazuki; Kotani, Yoshinori; Nakamura, Tetsuya; Togawa, Yoshihiko; Shinozaki, Misako; Kato, Yusuke; Kishine, Jun-ichiro; Ohe, Jun-ichiro; Kousaka, Yusuke; Akimitsu, Jun; Inoue, Katsuya

2018-01-01

A chiral soliton lattice stabilized in a monoaxial chiral magnet CrNb3S6 is a magnetic superlattice consisting of magnetic kinks with a ferromagnetic background. The magnetic kinks are considered to be topological magnetic solitons (TMSs). Changes in the TMS number yield discretized responses in magnetization and electrical conductivity, and this effect is more prominent in smaller crystals. We demonstrate that, in microprocessed CrNb3S6 crystals, TMSs are geometrically protected through element-selected micromagnetometry using soft x-ray magnetic circular dichroism (MCD). A series of x-ray MCD data is supported by mean-field and micromagnetic analyses. By designing the microcrystal geometry, TMS numbers can be successfully changed and fixed over a wide range of magnetic fields.

Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices.

PubMed

Cai, Xiaoming; Lang, Li-Jun; Chen, Shu; Wang, Yupeng

2013-04-26

We study the competition of disorder and superconductivity for a one-dimensional p-wave superconductor in incommensurate potentials. With the increase in the strength of the incommensurate potential, the system undergoes a transition from a topological superconducting phase to a topologically trivial localized phase. The phase boundary is determined both numerically and analytically from various aspects and the topological superconducting phase is characterized by the presence of Majorana edge fermions in the system with open boundary conditions. We also calculate the topological Z2 invariant of the bulk system and find it can be used to distinguish the different topological phases even for a disordered system.

Detection of topological phase transitions through entropy measurements: The case of germanene

NASA Astrophysics Data System (ADS)

Grassano, D.; Pulci, O.; Shubnyi, V. O.; Sharapov, S. G.; Gusynin, V. P.; Kavokin, A. V.; Varlamov, A. A.

2018-05-01

We propose a characterization tool for studies of the band structure of new materials promising for the observation of topological phase transitions. We show that a specific resonant feature in the entropy per electron dependence on the chemical potential may be considered as a fingerprint of the transition between topological and trivial insulator phases. The entropy per electron in a honeycomb two-dimensional crystal of germanene subjected to the external electric field is obtained from the first-principles calculation of the density of electronic states and the Maxwell relation. We demonstrate that, in agreement with the recent prediction of the analytical model, strong spikes in the entropy per particle dependence on the chemical potential appear at low temperatures. They are observed at the values of the applied bias both below and above the critical value that corresponds to the transition between the topological insulator and trivial insulator phases, whereas the giant resonant feature in the vicinity of the zero chemical potential is strongly suppressed at the topological transition point, in the low-temperature limit. In a wide energy range, the van Hove singularities in the electronic density of states manifest themselves as zeros in the entropy per particle dependence on the chemical potential.

Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions

NASA Astrophysics Data System (ADS)

Chatterjee, Shubhayu; Sachdev, Subir; Eberlein, Andreas

2017-08-01

We study thermal and electrical transport in metals and superconductors near a quantum phase transition where antiferromagnetic order disappears. The same theory can also be applied to quantum phase transitions involving the loss of certain classes of intrinsic topological order. For a clean superconductor, we recover and extend well-known universal results. The heat conductivity for commensurate and incommensurate antiferromagnetism coexisting with superconductivity shows a markedly different doping dependence near the quantum critical point, thus allowing us to distinguish between these states. In the dirty limit, the results for the conductivities are qualitatively similar for the metal and the superconductor. In this regime, the geometric properties of the Fermi surface allow for a very good phenomenological understanding of the numerical results on the conductivities. In the simplest model, we find that the conductivities do not track the doping evolution of the Hall coefficient, in contrast to recent experimental findings. We propose a doping dependent scattering rate, possibly due to quenched short-range charge fluctuations below optimal doping, to consistently describe both the Hall data and the longitudinal conductivities.

From bosonic topological transition to symmetric fermion mass generation

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; He, Yin-Chen; Vishwanath, Ashvin; Xu, Cenke

2018-03-01

A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal SO (4 ) symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors (Nf=4 ). Within a systematic renormalization group analysis, we identify the critical point with the desired O (4 ) emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous Nf=2 noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU (2 ) quantum chromodynamics-Higgs theory with Nf=4 flavors of SU (2 ) fundamental fermions and one SU (2 ) fundamental Higgs boson. This provides a consistency check on both theories.

Lassoing saddle splay and the geometrical control of topological defects

PubMed Central

Tran, Lisa; Lavrentovich, Maxim O.; Beller, Daniel A.; Li, Ningwei; Stebe, Kathleen J.; Kamien, Randall D.

2016-01-01

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4′-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system’s overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability. PMID:27222582

Lassoing saddle splay and the geometrical control of topological defects

NASA Astrophysics Data System (ADS)

Tran, Lisa; Lavrentovich, Maxim O.; Beller, Daniel A.; Li, Ningwei; Stebe, Kathleen J.; Kamien, Randall D.

2016-06-01

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.

Electronic topological transitions in Zn under compression

NASA Astrophysics Data System (ADS)

Kechin, Vladimir V.

2001-01-01

The electronic structure of hcp Zn under pressure up to 10 GPa has been calculated self-consistently by means of the scalar relativistic tight-binding linear muffin-tin orbital method. The calculations show that three electronic topological transitions (ETT's) occur in Zn when the c/a axial ratio diminishes under compression. One transition occurs at c/a~=1.82 when the ``needles'' appear around the symmetry point K of the Brillouin zone. The other two transitions occur at c/a~=3, when the ``butterfly'' and ``cigar'' appear simultaneously both around the L point. It has been shown that these ETT's are responsible for a number of anomalies observed in Zn at compression.

Disorder-driven topological phase transition in B i 2 S e 3 films

DOE PAGES

Brahlek, Matthew; Koirala, Nikesh; Salehi, Maryam; ...

2016-10-03

Topological insulators (TI) are a phase of matter that host unusual metallic states on their surfaces. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photo-emission spectroscopy and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI Bi 2Se 3 loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that theremore » is a change in material’s topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically-protected surface states, and will provoke new studies as to the fundamental nature of topological phase of matter in the presence of disorder.« less

Large magnetoresistance dips and perfect spin-valley filter induced by topological phase transitions in silicene

NASA Astrophysics Data System (ADS)

Prarokijjak, Worasak; Soodchomshom, Bumned

2018-04-01

Spin-valley transport and magnetoresistance are investigated in silicene-based N/TB/N/TB/N junction where N and TB are normal silicene and topological barriers. The topological phase transitions in TB's are controlled by electric, exchange fields and circularly polarized light. As a result, we find that by applying electric and exchange fields, four groups of spin-valley currents are perfectly filtered, directly induced by topological phase transitions. Control of currents, carried by single, double and triple channels of spin-valley electrons in silicene junction, may be achievable by adjusting magnitudes of electric, exchange fields and circularly polarized light. We may identify that the key factor behind the spin-valley current filtered at the transition points may be due to zero and non-zero Chern numbers. Electrons that are allowed to transport at the transition points must obey zero-Chern number which is equivalent to zero mass and zero-Berry's curvature, while electrons with non-zero Chern number are perfectly suppressed. Very large magnetoresistance dips are found directly induced by topological phase transition points. Our study also discusses the effect of spin-valley dependent Hall conductivity at the transition points on ballistic transport and reveals the potential of silicene as a topological material for spin-valleytronics.

Granular compaction and the topology of pore deformation

NASA Astrophysics Data System (ADS)

Saadatfar, Mohammad; Takeuchi, Hiroshi; Hanifpour, Maryam; Robins, Vanessa; Francois, Nicolas; Hiraoka, Yasuaki

2017-06-01

The mechanism of crystallisation in highly dissipative materials such as foams or granular materials is still widely unknown. In macroscopic granular materials high levels of energy need to be injected to overcome the natural propensity of these dissipative materials to form amorphous structures [1, 2]. The transition from disordered to ordered packings in such systems triggers a wide range of geometrical, topological and mechanical changes at multi length scales [3]. Formation of cavities and patterns by aggregates of grains and their evolution during this transition requires a complete topological description of the system. Here, crystallisation of three-dimensional packings of frictional spheres is studied at the grain scale with x-ray tomography. Using a novel and powerful topological tool, Persistent Homology, we describe the complete formation process of perfect tetrahedral and octahedral patterns: the two building blocks of FCC and HCP crystalline arrangements. Additionally we present possible and allowable deformations of these components that accurately reproduce the main topological features of the system. These results give new insights into the crystallisation of these highly dissipative materials.

Reentrant topological phase transition in a bridging model between Kitaev and Haldane chains

NASA Astrophysics Data System (ADS)

Sugimoto, Takanori; Ohtsu, Mitsuyoshi; Tohyama, Takami

2017-12-01

We present a reentrant phase transition in a bridging model between two different topological models: Kitaev and Haldane chains. This model is activated by introducing a bond alternation into the Kitaev chain [A. Y. Kitaev, Phys. Usp. 44, 131 (2001), 10.1070/1063-7869/44/10S/S29]. Without the bond alternation, the finite pairing potential induces a topological state defined by the zero-energy Majorana edge mode, while finite bond alternation without the pairing potential makes a different topological state similar to the Haldane state, which is defined by the local Berry phase in the bulk. The topologically ordered state corresponds to the Su-Schrieffer-Heeger state, which is classified as the same symmetry class. We thus find a phase transition between the two topological phases with a reentrant phenomenon, and extend the phase diagram in the plane of the pairing potential and the bond alternation by using three techniques: recursive equation, fidelity, and Pfaffian. In addition, we find that the phase transition is characterized by both the change of the position of Majorana zero-energy modes from one edge to the other edge and the emergence of a string order in the bulk, and that the reentrance is based on a sublattice U(1) rotation. Consequently, our paper and model not only open a direct way to discuss the bulk and edge topologies but demonstrate an example of the reentrant topologies.

Novel Quantum Criticality in Two Dimensional Topological Phase transitions

PubMed Central

Cho, Gil Young; Moon, Eun-Gook

2016-01-01

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality. PMID:26791803

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin-orbit coupling

NASA Astrophysics Data System (ADS)

Wang, Pei; Yi, Wei; Xianlong, Gao

2015-01-01

We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.

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.

Temperature-driven Topological Phase Transition in MoTe2

NASA Astrophysics Data System (ADS)

Notis Berger, Ayelet; Andrade, Erick; Kerelsky, Alex; Cheong, Sang-Wook; Li, Jian; Bernevig, B. Andrei; Pasupathy, Abhay

The discovery of several candidates predicted to be weyl semimetals has made it possible to experimentally study weyl fermions and their exotic properties. One example is MoTe2, a transition metal dichalcogenide. At temperatures below 240 K it is predicted to be a type II Weyl semimetal with four Weyl points close to the fermi level. As with most weyl semimetals, the complicated band structure causes difficulty in distinguishing features related to bulk states and those related to topological fermi arc surface states characteristic of weyl semimetals. MoTe2 is unique because of its temperature-driven phase change. At high temperatures, MoTe2 is monoclinic, with trivial surface states. When cooled below 240K, it undergoes a first order phase transition to become an orthorhombic weyl semimetal with topologically protected fermi arc surface states. We present STM and STS measurements on MoTe2 crystals in both states. In the orthorhombic phase, we observe scattering that is consistent with the presence of the Fermi-arc surface states. Upon warming into the monoclinic phase, these features disappear in the observed interference patterns, providing direct evidence of the topological nature of the fermi arcs in the Weyl phase

Revivals of electron currents and topological-band insulator transitions in 2D gapped Dirac materials

NASA Astrophysics Data System (ADS)

Romera, E.; Bolívar, J. C.; Roldán, J. B.; de los Santos, F.

2016-07-01

We have studied the time evolution of electron wave packets in silicene under perpendicular magnetic and electric fields to characterize topological-band insulator transitions. We have found that at the charge neutrality points, the periodicities exhibited by the wave packet dynamics (classical and revival times) reach maximum values, and that the electron currents reflect the transition from a topological insulator to a band insulator. This provides a signature of topological phase transition in silicene that can be extended to other 2D Dirac materials isostructural to graphene and with a buckled structure and a significant spin-orbit coupling.

Geometric Model of Topological Insulators from the Maxwell Algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. This work is part of the DITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).

Geometrical and topological issues in octree based automatic meshing

NASA Technical Reports Server (NTRS)

Saxena, Mukul; Perucchio, Renato

1987-01-01

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Acoustic Dirac degeneracy and topological phase transitions realized by rotating scatterers

NASA Astrophysics Data System (ADS)

Wen, Xinhua; Qiu, Chunyin; Lu, Jiuyang; He, Hailong; Ke, Manzhu; Liu, Zhengyou

2018-03-01

The artificial crystals for classical waves provide a good platform to explore the topological physics proposed originally in condensed matter systems. In this paper, acoustic Dirac degeneracy is realized by simply rotating the scatterers in sonic crystals, where the degeneracy is induced accidentally by modulating the scattering strength among the scatterers during the rotation process. This gives a flexible way to create a topological phase transition in acoustic systems. Edge states are further observed along the interface separating the two topologically distinct gapped sonic crystals.

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

Phase contrast imaging X-ray computed tomography: quantitative characterization of human patellar cartilage matrix with topological and geometrical features

NASA Astrophysics Data System (ADS)

Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel

2014-03-01

Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.

Optical transitions in two-dimensional topological insulators with point defects

NASA Astrophysics Data System (ADS)

Sablikov, Vladimir A.; Sukhanov, Aleksei A.

2016-12-01

Nontrivial properties of electronic states in topological insulators are inherent not only to the surface and boundary states, but to bound states localized at structure defects as well. We clarify how the unusual properties of the defect-induced bound states are manifested in optical absorption spectra in two-dimensional topological insulators. The calculations are carried out for defects with short-range potential. We find that the defects give rise to the appearance of specific features in the absorption spectrum, which are an inherent property of topological insulators. They have the form of two or three absorption peaks that are due to intracenter transitions between electron-like and hole-like bound states.

Phase transition solutions in geometrically constrained magnetic domain wall models

NASA Astrophysics Data System (ADS)

Chen, Shouxin; Yang, Yisong

2010-02-01

Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol'nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.

Phase Transitions on Random Lattices: How Random is Topological Disorder?

NASA Astrophysics Data System (ADS)

Barghathi, Hatem; Vojta, Thomas

2015-03-01

We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω = (d - 1) / (2 d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d + 1) ν > 2 rather than the usual Harris criterion dν > 2 , making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d > 1 . These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices. This work was supported by the NSF under Grant Nos. DMR-1205803 and PHYS-1066293. We acknowledge the hospitality of the Aspen Center for Physics.

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.

Multiple Dirac cones and topological magnetism in honeycomb-monolayer transition metal trichalcogenides

NASA Astrophysics Data System (ADS)

Sugita, Yusuke; Miyake, Takashi; Motome, Yukitoshi

2018-01-01

The discovery of monolayer graphene has initiated two fertile fields in condensed matter physics: Dirac semimetals and atomically thin layered materials. When these trends meet again in transition metal compounds, which possess spin and orbital degrees of freedom and strong electron correlations, more exotic phenomena are expected to emerge in the cross section of topological states of matter and Mott physics. Here, we show by using ab initio calculations that a monolayer form of transition metal trichalcogenides (TMTs), which has a honeycomb network of 4 d and 5 d transition metal cations, may exhibit multiple Dirac cones in the electronic structure of the half-filled eg orbitals. The Dirac cones are gapped by the spin-orbit coupling under the trigonal lattice distortion and, hence, can be tuned by tensile strain. Furthermore, we show that electron correlations and carrier doping turn the multiple Dirac semimetal into a topological ferromagnet with high Chern number. Our findings indicate that the honeycomb-monolayer TMTs provide a good playground for correlated Dirac electrons and topologically nontrivial magnetism.

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

Characterization of Lifshitz transitions in topological nodal line semimetals

NASA Astrophysics Data System (ADS)

Jiang, Hui; Li, Linhu; Gong, Jiangbin; Chen, Shu

2018-04-01

We introduce a two-band model of three-dimensional nodal line semimetals (NLSMs), the Fermi surface of which at half-filling may form various one-dimensional configurations of different topology. We study the symmetries and "drumhead" surface states of the model, and find that the transitions between different configurations, namely, the Lifshitz transitions, can be identified solely by the number of gap-closing points on some high-symmetry planes in the Brillouin zone. A global phase diagram of this model is also obtained accordingly. We then investigate the effect of some extra terms analogous to a two-dimensional Rashba-type spin-orbit coupling. The introduced extra terms open a gap for the NLSMs and can be useful in engineering different topological insulating phases. We demonstrate that the behavior of surface Dirac cones in the resulting insulating system has a clear correspondence with the different configurations of the original nodal lines in the absence of the gap terms.

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 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.

Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence

NASA Astrophysics Data System (ADS)

Xie, Yi-Chao; Ding, Guang-Yu; Xia, Ke-Qing

2018-05-01

We report an experimental observation of a flow topology transition via global bifurcation in a turbulent Rayleigh-Bénard convection. This transition corresponds to a spontaneous symmetry breaking with the flow becomes more turbulent. Simultaneous measurements of the large-scale flow (LSF) structure and the heat transport show that the LSF bifurcates from a high heat transport efficiency quadrupole state to a less symmetric dipole state with a lower heat transport efficiency. In the transition zone, the system switches spontaneously and stochastically between the two long-lived metastable states.

Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5

PubMed Central

Zhang, Yan; Wang, Chenlu; Yu, Li; Liu, Guodong; Liang, Aiji; Huang, Jianwei; Nie, Simin; Sun, Xuan; Zhang, Yuxiao; Shen, Bing; Liu, Jing; Weng, Hongming; Zhao, Lingxiao; Chen, Genfu; Jia, Xiaowen; Hu, Cheng; Ding, Ying; Zhao, Wenjuan; Gao, Qiang; Li, Cong; He, Shaolong; Zhao, Lin; Zhang, Fengfeng; Zhang, Shenjin; Yang, Feng; Wang, Zhimin; Peng, Qinjun; Dai, Xi; Fang, Zhong; Xu, Zuyan; Chen, Chuangtian; Zhou, X. J.

2017-01-01

The topological materials have attracted much attention for their unique electronic structure and peculiar physical properties. ZrTe5 has host a long-standing puzzle on its anomalous transport properties manifested by its unusual resistivity peak and the reversal of the charge carrier type. It is also predicted that single-layer ZrTe5 is a two-dimensional topological insulator and there is possibly a topological phase transition in bulk ZrTe5. Here we report high-resolution laser-based angle-resolved photoemission measurements on the electronic structure and its detailed temperature evolution of ZrTe5. Our results provide direct electronic evidence on the temperature-induced Lifshitz transition, which gives a natural understanding on underlying origin of the resistivity anomaly in ZrTe5. In addition, we observe one-dimensional-like electronic features from the edges of the cracked ZrTe5 samples. Our observations indicate that ZrTe5 is a weak topological insulator and it exhibits a tendency to become a strong topological insulator when the layer distance is reduced. PMID:28534501

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.

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).

Thermodynamic signature of Dirac electrons across a possible topological transition in ZrTe5

NASA Astrophysics Data System (ADS)

Nair, Nityan L.; Dumitrescu, Philipp T.; Channa, Sanyum; Griffin, Sinéad M.; Neaton, Jeffrey B.; Potter, Andrew C.; Analytis, James G.

2018-01-01

We combine transport, magnetization, and torque magnetometry measurements to investigate the electronic structure of ZrTe5, a system that is thought to be near a topological phase transition. At fields beyond the quantum limit, we observe a magnetization reversal from paramagnetic to diamagnetic response, which is characteristic of a Dirac semimetal. However, on increasing temperature across a corresponding transport anomaly, all signatures of this Dirac-like nature are completely suppressed, providing the first thermodynamic evidence of a possible topological phase transition in this compound. ZrTe5 may thus provide a rare, experimentally accessible example in which such phase transitions can be studied directly.

Topological Phase Transitions in Zinc-Blende Semimetals Driven Exclusively by Electronic Temperature

NASA Astrophysics Data System (ADS)

Trushin, Egor; Görling, Andreas

2018-04-01

We show that electronic phase transitions in zinc-blende semimetals with quadratic band touching (QBT) at the center of the Brillouin zone, like GaBi, InBi, or HgTe, can occur exclusively due to a change of the electronic temperature without the need to involve structural transformations or electron-phonon coupling. The commonly used Kohn-Sham density-functional methods based on local and semilocal density functionals employing the local density approximation (LDA) or generalized gradient approximations (GGAs), however, are not capable of describing such phenomena because they lack an intrinsic temperature dependence and account for temperature only via the occupation of bands, which essentially leads only to a shift of the Fermi level without changing the shape or topology of bands. Kohn-Sham methods using the exact temperature-dependent exchange potential, not to be confused with the Hartree-Fock exchange potential, on the other hand, describe such phase transitions. A simple modeling of correlation effects can be achieved by screening of the exchange. In the considered zinc-blende compounds the QBT is unstable at low temperatures and a transition to electronic states without QBT takes place. In the case of HgTe and GaBi Weyl points of type I and type II, respectively, emerge during the transitions. This demonstrates that Kohn-Sham methods can describe such topological phase transitions provided they are based on functionals more accurate than those within the LDA or GGA. Moreover, the electronic temperature is identified as a handle to tune topological materials.

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

NASA Astrophysics Data System (ADS)

Yin, Chuanhao; Jiang, Hui; Li, Linhu; Lü, Rong; Chen, Shu

2018-05-01

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems are integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number ν of a non-Hermitian system is equal to half of the summation of two winding numbers ν1 and ν2 associated with two exceptional points, respectively. The winding numbers ν1 and ν2 represent the times of the real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of ν1 and ν2 is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number ν1 and ν2.

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices

NASA Astrophysics Data System (ADS)

Hyart, T.; Ojajärvi, R.; Heikkilä, T. T.

2018-04-01

Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.

Minimum Interference Planar Geometric Topology in Wireless Sensor Networks

NASA Astrophysics Data System (ADS)

Nguyen, Trac N.; Huynh, Dung T.

The approach of using topology control to reduce interference in wireless sensor networks has attracted attention of several researchers. There are at least two definitions of interference in the literature. In a wireless sensor network the interference at a node may be caused by an edge that is transmitting data [15], or it occurs because the node itself is within the transmission range of another [3], [1], [6]. In this paper we show that the problem of assigning power to nodes in the plane to yield a planar geometric graph whose nodes have bounded interference is NP-complete under both interference definitions. Our results provide a rigorous proof for a theorem in [15] whose proof is unconvincing. They also address one of the open issues raised in [6] where Halldórsson and Tokuyama were concerned with the receiver model of node interference, and derived an O(sqrt {Δ}) upper bound for the maximum node interference of a wireless ad hoc network in the plane (Δ is the maximum interference of the so-called uniform radius network). The question as to whether this problem is NP-complete in the 2-dimensional case was left open.

Pressure-induced topological phase transitions and strongly anisotropic magnetoresistance in bulk black phosphorus

NASA Astrophysics Data System (ADS)

Li, Chun-Hong; Long, Yu-Jia; Zhao, Ling-Xiao; Shan, Lei; Ren, Zhi-An; Zhao, Jian-Zhou; Weng, Hong-Ming; Dai, Xi; Fang, Zhong; Ren, Cong; Chen, Gen-Fu

2017-03-01

We report the anisotropic magnetotransport measurement on a noncompound band semiconductor black phosphorus (BP) with magnetic field B up to 16 Tesla applied in both perpendicular and parallel to electric current I under hydrostatic pressures. The BP undergoes a topological Lifshitz transition from band semiconductor to a zero-gap Dirac semimetal state at a critical pressure Pc, characterized by a weak localization-weak antilocalization transition at low magnetic fields and the emergence of a nontrivial Berry phase of π detected by SdH magneto-oscillations in magnetoresistance curves. In the transition region, we observe a pressure-dependent negative MR only in the B ∥I configuration. This negative longitudinal MR is attributed to the Adler-Bell-Jackiw anomaly (topological E .B term) in the presence of weak antilocalization corrections.

Super Yang Mills, matrix models and geometric transitions

NASA Astrophysics Data System (ADS)

Ferrari, Frank

2005-03-01

I explain two applications of the relationship between four-dimensional N=1 supersymmetric gauge theories, zero-dimensional gauged matrix models, and geometric transitions in string theory. The first is related to the spectrum of BPS domain walls or BPS branes. It is shown that one can smoothly interpolate between a D-brane state, whose weak coupling tension scales as N˜1/g, and a closed string solitonic state, whose weak coupling tension scales as N˜1/gs2. This is part of a larger theory of N=1 quantum parameter spaces. The second is a new purely geometric approach to sum exactly over planar diagrams in zero dimension. It is an example of open/closed string duality. To cite this article: F. Ferrari, C. R. Physique 6 (2005).

Titan-Like Exoplanets: Variations in Geometric Albedo and Effective Transit Height with Haze Production Rate

NASA Technical Reports Server (NTRS)

Checlair, Jade; McKay, Christopher P.; Imanaka, Hiroshi

2016-01-01

Extensive studies characterizing Titan present an opportunity to study the atmospheric properties of Titan-like exoplanets. Using an existing model of Titan's atmospheric haze, we computed geometric albedo spectra and effective transit height spectra for six values of the haze production rate (zero haze to twice present) over a wide range of wavelengths (0.2-2 microns). In the geometric albedo spectra, the slope in the UV-visible changes from blue to red when varying the haze production rate values from zero to twice the current Titan value. This spectral feature is the most effective way to characterize the haze production rates. Methane absorption bands in the visible-NIR compete with the absorbing haze, being more prominent for smaller haze production rates. The effective transit heights probe a region of the atmosphere where the haze and gas are optically thin and that is thus not effectively probed by the geometric albedo. The effective transit height decreases smoothly with increasing wavelength, from 376 km to 123 km at 0.2 and 2 microns, respectively. When decreasing the haze production rate, the methane absorption bands become more prominent, and the effective transit height decreases with a steeper slope with increasing wavelength. The slope of the geometric albedo in the UV-visible increases smoothly with increasing haze production rate, while the slope of the effective transit height spectra is not sensitive to the haze production rate other than showing a sharp rise when the haze production rate increases from zero. We conclude that geometric albedo spectra provide the most sensitive indicator of the haze production rate and the background Rayleigh gas. Our results suggest that important and complementary information can be obtained from the geometric albedo and motivates improvements in the technology for direct imaging of nearby exoplanets.

Volumetric quantitative characterization of human patellar cartilage with topological and geometrical features on phase-contrast X-ray computed tomography.

PubMed

Nagarajan, Mahesh B; Coan, Paola; Huber, Markus B; Diemoz, Paul C; Wismüller, Axel

2015-11-01

Phase-contrast X-ray computed tomography (PCI-CT) has attracted significant interest in recent years for its ability to provide significantly improved image contrast in low absorbing materials such as soft biological tissue. In the research context of cartilage imaging, previous studies have demonstrated the ability of PCI-CT to visualize structural details of human patellar cartilage matrix and capture changes to chondrocyte organization induced by osteoarthritis. This study evaluates the use of geometrical and topological features for volumetric characterization of such chondrocyte patterns in the presence (or absence) of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and topological features derived from Minkowski Functionals were extracted from 1392 volumes of interest (VOI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify VOIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver operating characteristic curve (AUC). Our results show that the classification performance of SIM-derived geometrical features (AUC: 0.90 ± 0.09) is significantly better than Minkowski Functionals volume (AUC: 0.54 ± 0.02), surface (AUC: 0.72 ± 0.06), mean breadth (AUC: 0.74 ± 0.06) and Euler characteristic (AUC: 0.78 ± 0.04) (p < 10(-4)). These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as diagnostic imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies.

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

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.

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

Topology-driven phase transitions in the classical monomer-dimer-loop model.

PubMed

Li, Sazi; Li, Wei; Chen, Ziyu

2015-06-01

In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find a second-order phase transition between a trivial monomer-condensation and a loop-condensation (LC) phase, which cannot be distinguished by any local order parameter, while nevertheless the two phases have distinct topological properties. In the LC phase, we find two degenerate dominating eigenvalues in the transfer-matrix spectrum, as well as a nonvanishing (nonlocal) string order parameter, both of which identify the topological ergodicity breaking in the LC phase and can serve as the order parameter for detecting the phase transitions.

Geometric Assortative Growth Model for Small-World Networks

PubMed Central

2014-01-01

It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs. PMID:24578661

Topological Phase Transitions in the Photonic Spin Hall Effect

DOE PAGES

Kort-Kamp, Wilton Junior de Melo

2017-10-04

The recent synthesis of two-dimensional staggered materials opens up burgeoning opportunities to study optical spin-orbit interactions in semiconducting Dirac-like systems. In this work, we unveil topological phase transitions in the photonic spin Hall effect in the graphene family materials. It is shown that an external static electric field and a high frequency circularly polarized laser allow for active on-demand manipulation of electromagnetic beam shifts. The spin Hall effect of light presents a rich dependence with radiation degrees of freedom, and material properties, and features nontrivial topological properties. Finally, we discover that photonic Hall shifts are sensitive to spin and valleymore » properties of the charge carriers, providing an unprecedented pathway to investigate spintronics and valleytronics in staggered 2D semiconductors.« less

Strain-induced topological transition in SrRu 2O 6 and CaOs 2O 6

DOE PAGES

Ochi, Masayuki; Arita, Ryotaro; Trivedi, Nandini; ...

2016-05-24

The topological property of SrRumore » $$_2$$O$$_6$$ and isostructural CaOs$$_2$$O$$_6$$ under various strain conditions is investigated using density functional theory. Based on an analysis of parity eigenvalues, we anticipate that a three-dimensional strong topological insulating state should be realized when band inversion is induced at the A point in the hexagonal Brillouin zone. For SrRu$$_2$$O$$_6$$, such a transition requires rather unrealistic tuning, where only the $c$ axis is reduced while other structural parameters are unchanged. However, given the larger spin-orbit coupling and smaller lattice constants in CaOs$$_2$$O$$_6$$, the desired topological transition does occur under uniform compressive strain. Our study paves a way to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.« less

Topological phase transition and unexpected mass acquisition of Dirac fermion in TlBi(S1-xSex)2

NASA Astrophysics Data System (ADS)

Niu, Chengwang; Dai, Ying; Zhu, Yingtao; Lu, Jibao; Ma, Yandong; Huang, Baibiao

2012-10-01

Based on first-principles calculations and effective Hamiltonian analysis, we predict a topological phase transition from normal to topological insulators and the opening of a gap without breaking the time-reversal symmetry in TlBi(S1-xSex)2. The transition can be driven by modulating the Se concentration, and the rescaled spin-orbit coupling and lattice parameters are the key ingredients for the transition. For topological surface states, the Dirac cone evolves differently as the explicit breaking of inversion symmetry and the energy band can be opened under asymmetry surface. Our results present theoretical evidence for experimental observations [Xu et al., Science 332, 560 (2011); Sato et al., Nat. Phys. 7, 840 (2011)].

Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-12-01

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

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.

Importance of correlation effects in hcp iron revealed by a pressure-induced electronic topological transition.

PubMed

Glazyrin, K; Pourovskii, L V; Dubrovinsky, L; Narygina, O; McCammon, C; Hewener, B; Schünemann, V; Wolny, J; Muffler, K; Chumakov, A I; Crichton, W; Hanfland, M; Prakapenka, V B; Tasnádi, F; Ekholm, M; Aichhorn, M; Vildosola, V; Ruban, A V; Katsnelson, M I; Abrikosov, I A

2013-03-15

We discover that hcp phases of Fe and Fe(0.9)Ni(0.1) undergo an electronic topological transition at pressures of about 40 GPa. This topological change of the Fermi surface manifests itself through anomalous behavior of the Debye sound velocity, c/a lattice parameter ratio, and Mössbauer center shift observed in our experiments. First-principles simulations within the dynamic mean field approach demonstrate that the transition is induced by many-electron effects. It is absent in one-electron calculations and represents a clear signature of correlation effects in hcp Fe.

Nonlocal optical response in topological phase transitions in the graphene family

NASA Astrophysics Data System (ADS)

Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.; Woods, Lilia M.

2018-01-01

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. In particular, we find that the resonant behavior of the nonlocal Hall conductivity is strongly affected by the various topological phases present in these materials. We also consider the plasmon excitations in the graphene family and find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. We find a regime of wave vectors for which the plasmon relations for phases with trivial topology are essentially indistinguishable, while those for phases with nontrivial topology are distinct and are redshifted as the corresponding Chern number increases. The expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.

Nonlocal optical response in topological phase transitions in the graphene family

DOE PAGES

Rodriguez-Lopez, Pablo; de Melo Kort-Kamp, Wilton Junior; Dalvit, Diego Alejandro Roberto; ...

2018-01-22

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. In particular, we find that the resonant behavior of the nonlocal Hall conductivity is strongly affected by the various topological phases present in these materials. We also consider the plasmon excitations in the graphene family andmore » find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. Here, we find a regime of wave vectors for which the plasmon relations for phases with trivial topology are essentially indistinguishable, while those for phases with nontrivial topology are distinct and are redshifted as the corresponding Chern number increases. Finally, the expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.« less

Nonlocal optical response in topological phase transitions in the graphene family

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

Rodriguez-Lopez, Pablo; de Melo Kort-Kamp, Wilton Junior; Dalvit, Diego Alejandro Roberto

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. In particular, we find that the resonant behavior of the nonlocal Hall conductivity is strongly affected by the various topological phases present in these materials. We also consider the plasmon excitations in the graphene family andmore » find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. Here, we find a regime of wave vectors for which the plasmon relations for phases with trivial topology are essentially indistinguishable, while those for phases with nontrivial topology are distinct and are redshifted as the corresponding Chern number increases. Finally, the expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.« less

Long-range Coulomb interaction effects on the topological phase transitions between semimetals and insulators

NASA Astrophysics Data System (ADS)

Han, SangEun; Moon, Eun-Gook

2018-06-01

Topological states may be protected by a lattice symmetry in a class of topological semimetals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space concretely defines a chirality, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include a Dirac semimetal (DSM) in a distorted spinel, BiZnSiO4, protected by a mirror symmetry, and a DSM in Na3Bi , protected by a rotational symmetry. In these states, topology and chiral symmetry are intrinsically tied. In this Rapid Communication, the characteristic interplay between a chiral symmetry order parameter and an instantaneous long-range Coulomb interaction is investigated with the standard renormalization group method. We show that a topological transition associated with chiral symmetry is stable under the presence of a Coulomb interaction and the electron velocity always becomes faster than the one of a chiral symmetry order parameter. Thus, the transition must not be relativistic, which implies that supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. Asymptotically exact universal ratios of physical quantities such as the energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.

Triply degenerate nodal points and topological phase transitions in NaCu3Te2

NASA Astrophysics Data System (ADS)

Xia, Yunyouyou; Li, Gang

2017-12-01

Quasiparticle excitations of free electrons in condensed-matter physics, characterized by the dimensionality of the band crossing, can find their elementary-particle analogs in high-energy physics, such as Majorana, Weyl, and Dirac fermions, while crystalline symmetry allows more quasiparticle excitations and exotic fermions to emerge. Using symmetry analysis and ab initio calculations, we propose that the three-dimensional honeycomb crystal NaCu3Te2 hosts triply degenerate nodal points (TDNPs) residing at the Fermi level. Furthermore, in this system we find a tunable phase transition between a trivial insulator, a TDNP phase, and a weak topological insulator (TI), triggered by a symmetry-allowed perturbation and the spin-orbital coupling (SOC). Such a topological nontrivial ternary compound not only serves as a perfect candidate for studying three-component fermions, but also provides an excellent playground for understanding the topological phase transitions between TDNPs, TIs, and trivial insulators, which distinguishes this system from other TDNP candidates.

Topological phase transition of Dirac superconductors in the presence of pseudo-scalar pairings

NASA Astrophysics Data System (ADS)

Salehi, Morteza; Jafari, S. A.

2018-06-01

Motivated by recent developments in the field of topological superconductors, we show that there is a topological phase transition (TPT) for three dimensional Dirac superconductors (3DDS) in the presence of pseudo-scalar superconducting order parameter which leads to the appearance of a two dimensional Majorana sea (2DMS) on its surface. The perfect Andreev-Klein transmission, resonant peak with robust character in the differential conductance and 4π periodic Josephson current are experimental signatures of 2DMS.

Physarum polycephalum Percolation as a Paradigm for Topological Phase Transitions in Transportation Networks

NASA Astrophysics Data System (ADS)

Fessel, Adrian; Oettmeier, Christina; Bernitt, Erik; Gauthier, Nils C.; Döbereiner, Hans-Günther

2012-08-01

We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks.

Structural, vibrational, and electronic topological transitions of Bi1.5Sb0.5Te1.8Se1.2 under pressure

NASA Astrophysics Data System (ADS)

Kim, Joon-Seok; Juneja, Rinkle; Salke, Nilesh P.; Palosz, Witold; Swaminathan, Venkataraman; Trivedi, Sudhir; Singh, Abhishek K.; Akinwande, Deji; Lin, Jung-Fu

2018-03-01

Topological insulators have been the subject of intense research interest due to their unique surface states that are topologically protected against scattering or defects. However, the relationship between the crystal structure and topological insulator state remains to be clarified. Here, we show the effects of hydrostatic pressure on the structural, vibrational, and topological properties of the topological insulator Bi1.5Sb0.5Te1.8Se1.2 up to 45 GPa using X-ray diffraction and Raman spectroscopy in a diamond anvil cell, together with first-principles theoretical calculations. Two pressure-induced structural phase transitions were observed: from ambient rhombohedral R 3 ¯ m phase to a monoclinic C2/m phase at ˜13 GPa, and to a disordered I4/mmm phase at ˜22 GPa. In addition, the alloy undergoes several electronic transitions within the R 3 ¯ m phase: indirect to direct bulk band gap transition at ˜5.8 GPa, bulk gap closing with an appearance of Dirac semimetal (DSM) state at ˜8.2 GPa, and to a trivial semimetal state at ˜12.1 GPa. Anomalies in c/a ratio and Raman full width at half maximum that coincide with the DSM phase suggest the contribution of electron-phonon coupling to the transition. Compared to binary end members Bi2Te3, Bi2Se3, and Sb2Te3, the structural phase transition and anomaly were observed at higher pressures in Bi1.5Sb0.5Te1.8Se1.2. These results suggest that the topological transitions are precursors to the structural phase transitions.

Quantum algorithms for topological and geometric analysis of data

PubMed Central

Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo

2016-01-01

Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491

Topology Optimisation of Wideband Coaxial-to-Waveguide Transitions

NASA Astrophysics Data System (ADS)

Hassan, Emadeldeen; Noreland, Daniel; Wadbro, Eddie; Berggren, Martin

2017-03-01

To maximize the matching between a coaxial cable and rectangular waveguides, we present a computational topology optimisation approach that decides for each point in a given domain whether to hold a good conductor or a good dielectric. The conductivity is determined by a gradient-based optimisation method that relies on finite-difference time-domain solutions to the 3D Maxwell’s equations. Unlike previously reported results in the literature for this kind of problems, our design algorithm can efficiently handle tens of thousands of design variables that can allow novel conceptual waveguide designs. We demonstrate the effectiveness of the approach by presenting optimised transitions with reflection coefficients lower than -15 dB over more than a 60% bandwidth, both for right-angle and end-launcher configurations. The performance of the proposed transitions is cross-verified with a commercial software, and one design case is validated experimentally.

Topology Optimisation of Wideband Coaxial-to-Waveguide Transitions.

PubMed

Hassan, Emadeldeen; Noreland, Daniel; Wadbro, Eddie; Berggren, Martin

2017-03-23

To maximize the matching between a coaxial cable and rectangular waveguides, we present a computational topology optimisation approach that decides for each point in a given domain whether to hold a good conductor or a good dielectric. The conductivity is determined by a gradient-based optimisation method that relies on finite-difference time-domain solutions to the 3D Maxwell's equations. Unlike previously reported results in the literature for this kind of problems, our design algorithm can efficiently handle tens of thousands of design variables that can allow novel conceptual waveguide designs. We demonstrate the effectiveness of the approach by presenting optimised transitions with reflection coefficients lower than -15 dB over more than a 60% bandwidth, both for right-angle and end-launcher configurations. The performance of the proposed transitions is cross-verified with a commercial software, and one design case is validated experimentally.

Topology Optimisation of Wideband Coaxial-to-Waveguide Transitions

PubMed Central

Hassan, Emadeldeen; Noreland, Daniel; Wadbro, Eddie; Berggren, Martin

2017-01-01

To maximize the matching between a coaxial cable and rectangular waveguides, we present a computational topology optimisation approach that decides for each point in a given domain whether to hold a good conductor or a good dielectric. The conductivity is determined by a gradient-based optimisation method that relies on finite-difference time-domain solutions to the 3D Maxwell’s equations. Unlike previously reported results in the literature for this kind of problems, our design algorithm can efficiently handle tens of thousands of design variables that can allow novel conceptual waveguide designs. We demonstrate the effectiveness of the approach by presenting optimised transitions with reflection coefficients lower than −15 dB over more than a 60% bandwidth, both for right-angle and end-launcher configurations. The performance of the proposed transitions is cross-verified with a commercial software, and one design case is validated experimentally. PMID:28332585

Phase transition and field effect topological quantum transistor made of monolayer MoS2

NASA Astrophysics Data System (ADS)

Simchi, H.; Simchi, M.; Fardmanesh, M.; Peeters, F. M.

2018-06-01

We study topological phase transitions and topological quantum field effect transistor in monolayer molybdenum disulfide (MoS2) using a two-band Hamiltonian model. Without considering the quadratic (q 2) diagonal term in the Hamiltonian, we show that the phase diagram includes quantum anomalous Hall effect, quantum spin Hall effect, and spin quantum anomalous Hall effect regions such that the topological Kirchhoff law is satisfied in the plane. By considering the q 2 diagonal term and including one valley, it is shown that MoS2 has a non-trivial topology, and the valley Chern number is non-zero for each spin. We show that the wave function is (is not) localized at the edges when the q 2 diagonal term is added (deleted) to (from) the spin-valley Dirac mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons by using the nonequilibrium Green function method and show how this device works as a field effect topological quantum transistor.

Global regularizing flows with topology preservation for active contours and polygons.

PubMed

Sundaramoorthi, Ganesh; Yezzi, Anthony

2007-03-01

Active contour and active polygon models have been used widely for image segmentation. In some applications, the topology of the object(s) to be detected from an image is known a priori, despite a complex unknown geometry, and it is important that the active contour or polygon maintain the desired topology. In this work, we construct a novel geometric flow that can be added to image-based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon. We emphasize that, unlike other methods for topology preservation, the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change. The flow also serves as a global regularity term for the evolving contour, and has smoothness properties similar to curvature flow. These properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes. The proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles. The evolution of a single point on the contour depends on all other points of the contour, which is different from traditional curve evolutions in the computer vision literature.

Transition between strong and weak topological insulator in ZrTe5 and HfTe5

NASA Astrophysics Data System (ADS)

Fan, Zongjian; Liang, Qi-Feng; Chen, Y. B.; Yao, Shu-Hua; Zhou, Jian

2017-04-01

ZrTe5 and HfTe5 have attracted increasingly attention recently since the theoretical prediction of being topological insulators (TIs). However, subsequent works show many contradictions about their topolog-ical nature. Three possible phases, i.e. strong TI, weak TI, and Dirac semi-metal, have been observed in different experiments until now. Essentially whether ZrTe5 or HfTe5 has a band gap or not is still a question. Here, we present detailed first-principles calculations on the electronic and topological prop-erties of ZrTe5 and HfTe5 on variant volumes and clearly demonstrate the topological phase transition from a strong TI, going through an intermediate Dirac semi-metal state, then to a weak TI when the crystal expands. Our work might give a unified explain about the divergent experimental results and propose the crucial clue to further experiments to elucidate the topological nature of these materials.

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

2017-04-01

Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.

Studying topology and dynamical phase transitions with ultracold quantum gases in optical lattices

NASA Astrophysics Data System (ADS)

Sengstock, Klaus

Topological properties lie at the heart of many fascinating phenomena in solid-state systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentum-resolved state tomography from which we obtain the Berry curvature and Chern number. Furthermore, we study the time-evolution of the many-body wavefunction after a sudden quench of the lattce parameters and observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at critical times. Our measurements constitute the first observation of a so called dynamical topological phase transition`, which we show to be a fruitful concept for the understanding of quantum dynamics far from equilibrium

Topological transitions for lattice bosons in a magnetic field

PubMed Central

Huber, Sebastian D.; Lindner, Netanel H.

2011-01-01

The Hall response provides an important characterization of strongly correlated phases of matter. We study the Hall conductivity of interacting bosons on a lattice subjected to a magnetic field. We show that for any density or interaction strength, the Hall conductivity is characterized by an integer. We find that the phase diagram is intersected by topological transitions between different values of this integer. These transitions lead to surprising effects, including sign reversal of the Hall conductivity and extensive regions in the phase diagram where it acquires a negative sign, which implies that flux flow is reversed in these regions—vortices there flow upstream. Our findings have immediate applications to a wide range of phenomena in condensed matter physics, which are effectively described in terms of lattice bosons. PMID:22109548

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

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

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Emergent geometric frustration of artificial magnetic skyrmion crystals

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

Ma, Fusheng; Reichhardt, Charles; Gan, Weiliang

Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCsmore » highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. In conclusion, the spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.« less

Emergent geometric frustration of artificial magnetic skyrmion crystals

DOE PAGES

Ma, Fusheng; Reichhardt, Charles; Gan, Weiliang; ...

2016-10-05

Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCsmore » highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. In conclusion, the spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.« less

Efficient Geometric Probabilities of Multi-transiting Systems, Circumbinary Planets, and Exoplanet Mutual Events

NASA Astrophysics Data System (ADS)

Brakensiek, Joshua; Ragozzine, D.

2012-10-01

The transit method for discovering extra-solar planets relies on detecting regular diminutions of light from stars due to the shadows of planets passing in between the star and the observer. NASA's Kepler Mission has successfully discovered thousands of exoplanet candidates using this technique, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, our research concerns the efficient calculation of geometric probabilities for detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods (e.g., Ragozzine & Holman 2010, Tremaine & Dong 2011), we have constructed an efficient, analytical algorithm which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets are transiting. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere (see Ragozzine & Holman 2010). The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparison with Monte Carlo simulations. Expanding this work, we have also developed semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability two planets will transit each other (Planet-Planet Occultation) and the probability that this transit occurs simultaneously as they transit their star (Overlapping Double Transits; see Ragozzine & Holman 2010). The latter algorithm can also be applied to calculating the probability of observing transiting circumbinary planets (Doyle et al. 2011, Welsh et al. 2012). All of these algorithms have been coded in C and will be made publicly available. We will present and advertise these codes and illustrate their value for studying exoplanetary systems.

Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals.

PubMed

Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua

2016-08-08

A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C₆ point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.

Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure

NASA Astrophysics Data System (ADS)

Łepkowski, S. P.; Bardyszewski, W.

2017-02-01

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure.

PubMed

Łepkowski, S P; Bardyszewski, W

2017-02-08

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

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.

Universality of phase transition dynamics: topological defects from symmetry breaking

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

Zurek, Wojciech H.; Del Campo, Adolfo

In the course of a non-equilibrium continuous phase transition, the dynamics ceases to be adiabatic in the vicinity of the critical point as a result of the critical slowing down (the divergence of the relaxation time in the neighborhood of the critical point). This enforces a local choice of the broken symmetry and can lead to the formation of topological defects. The Kibble-Zurek mechanism (KZM) was developed to describe the associated nonequilibrium dynamics and to estimate the density of defects as a function of the quench rate through the transition. During recent years, several new experiments investigating formation of defectsmore » in phase transitions induced by a quench both in classical and quantum mechanical systems were carried out. At the same time, some established results were called into question. We review and analyze the Kibble-Zurek mechanism focusing in particular on this surge of activity, and suggest possible directions for further progress.« less

Geometric structure and information change in phase transitions

NASA Astrophysics Data System (ADS)

Kim, Eun-jin; Hollerbach, Rainer

2017-06-01

We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L , which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale τ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation γ of a control parameter from the critical state in BPs while increasing logarithmically with γ in FPs. L scales as |lnD | and D-1 /2 in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with γ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).

Geometric structure and information change in phase transitions.

PubMed

Kim, Eun-Jin; Hollerbach, Rainer

2017-06-01

We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale τ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation γ of a control parameter from the critical state in BPs while increasing logarithmically with γ in FPs. L scales as |lnD| and D^{-1/2} in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with γ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).

Andreev rectifier: A nonlocal conductance signature of topological phase transitions

NASA Astrophysics Data System (ADS)

Rosdahl, T. Ö.; Vuik, A.; Kjaergaard, M.; Akhmerov, A. R.

2018-01-01

The proximity effect in hybrid superconductor-semiconductor structures, crucial for realizing Majorana edge modes, is complicated to control due to its dependence on many unknown microscopic parameters. In addition, defects can spoil the induced superconductivity locally in the proximitized system, which complicates measuring global properties with a local probe. We show how to use the nonlocal conductance between two spatially separated leads to probe three global properties of a proximitized system: the bulk superconducting gap, the induced gap, and the induced coherence length. Unlike local conductance spectroscopy, nonlocal conductance measurements distinguish between nontopological zero-energy modes localized around potential inhomogeneities, and true Majorana edge modes that emerge in the topological phase. In addition, we find that the nonlocal conductance is an odd function of bias at the topological phase transition, acting as a current rectifier in the low-bias limit. More generally, we identify conditions for crossed Andreev reflection to dominate the nonlocal conductance and show how to design a Cooper pair splitter in the open regime.

Phonon-induced topological transition to a type-II Weyl semimetal

DOE PAGES

Wang, Lin-Lin; Jo, Na Hyun; Wu, Yun; ...

2017-04-11

Given the importance of crystal symmetry for the emergence of topological quantum states, we have studied here, as exemplified in NbNiTe 2, the interplay of crystal symmetry, atomic displacements (lattice vibration), band degeneracy, and band topology. For the NbNiTe 2 structure in space-group 53 (Pmna)$-$ having an inversion center arising from two glide planes and one mirror plane with a two-fold rotation and screw axis$-$a full gap opening exists between two band manifolds near the Fermi energy. Upon atomic displacements by optical phonons, the symmetry lowers to space-group 28 (Pma2), eliminating one glide plane along c, the associated rotation andmore » screw axis, and the inversion center. As a result, 20 Weyl points emerge, including four type-IIWeyl points in the Γ-X direction at the boundary between a pair of adjacent electron and hole bands. Thus, optical phonons may offer control of the transition to a Weyl fermion state.« less

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

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

On the Axiomatization of Mathematical Understanding: Continuous Functions in the Transition to Topology

ERIC Educational Resources Information Center

Cheshire, Daniel C.

2017-01-01

The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear algebra, and real or complex analysis to fit within a more abstract conceptual system. Students must adopt a new lexicon of…

Cosmic Topology

NASA Astrophysics Data System (ADS)

Luminet, Jean-Pierre

2015-08-01

Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.

A novel transition pathway of ligand-induced topological conversion from hybrid forms to parallel forms of human telomeric G-quadruplexes

PubMed Central

Wang, Zi-Fu; Li, Ming-Hao; Chen, Wei-Wen; Hsu, Shang-Te Danny; Chang, Ta-Chau

2016-01-01

The folding topology of DNA G-quadruplexes (G4s) depends not only on their nucleotide sequences but also on environmental factors and/or ligand binding. Here, a G4 ligand, 3,6-bis(1-methyl-4-vinylpyridium iodide)-9-(1-(1-methyl-piperidinium iodide)-3,6,9-trioxaundecane) carbazole (BMVC-8C3O), can induce topological conversion of non-parallel to parallel forms in human telomeric DNA G4s. Nuclear magnetic resonance (NMR) spectroscopy with hydrogen-deuterium exchange (HDX) reveals the presence of persistent imino proton signals corresponding to the central G-quartet during topological conversion of Tel23 and Tel25 G4s from hybrid to parallel forms, implying that the transition pathway mainly involves local rearrangements. In contrast, rapid HDX was observed during the transition of 22-CTA G4 from an anti-parallel form to a parallel form, resulting in complete disappearance of all the imino proton signals, suggesting the involvement of substantial unfolding events associated with the topological transition. Site-specific imino proton NMR assignments of Tel23 G4 enable determination of the interconversion rates of individual guanine bases and detection of the presence of intermediate states. Since the rate of ligand binding is much higher than the rate of ligand-induced topological conversion, a three-state kinetic model was evoked to establish the associated energy diagram for the topological conversion of Tel23 G4 induced by BMVC-8C3O. PMID:26975658

Quantum spin Hall effect and topological phase transition in InN x Bi y Sb1-x-y /InSb quantum wells

NASA Astrophysics Data System (ADS)

Song, Zhigang; Bose, Sumanta; Fan, Weijun; Zhang, Dao Hua; Zhang, Yan Yang; Shen Li, Shu

2017-07-01

Quantum spin Hall (QSH) effect, a fundamentally new quantum state of matter and topological phase transitions are characteristics of a kind of electronic material, popularly referred to as topological insulators (TIs). TIs are similar to ordinary insulator in terms of their bulk bandgap, but have gapless conducting edge-states that are topologically protected. These edge-states are facilitated by the time-reversal symmetry and they are robust against nonmagnetic impurity scattering. Recently, the quest for new materials exhibiting non-trivial topological state of matter has been of great research interest, as TIs find applications in new electronics and spintronics and quantum-computing devices. Here, we propose and demonstrate as a proof-of-concept that QSH effect and topological phase transitions can be realized in {{InN}}x{{Bi}}y{{Sb}}1-x-y/InSb semiconductor quantum wells (QWs). The simultaneous incorporation of nitrogen and bismuth in InSb is instrumental in lowering the bandgap, while inducing opposite kinds of strain to attain a near-lattice-matching conducive for lattice growth. Phase diagram for bandgap shows that as we increase the QW thickness, at a critical thickness, the electronic bandstructure switches from a normal to an inverted type. We confirm that such transition are topological phase transitions between a traditional insulator and a TI exhibiting QSH effect—by demonstrating the topologically protected edge-states using the bandstructure, edge-localized distribution of the wavefunctions and edge-state spin-momentum locking phenomenon, presence of non-zero conductance in spite of the Fermi energy lying in the bandgap window, crossover points of Landau levels in the zero-mode indicating topological band inversion in the absence of any magnetic field and presence of large Rashba spin-splitting, which is essential for spin-manipulation in TIs.

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.

2013-05-01

Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.

Vertex stability and topological transitions in vertex models of foams and epithelia

NASA Astrophysics Data System (ADS)

Spencer, Meryl; Jabeen, Zahera; Lubensky, David

Vertex models are widely used to computationally simulate dry foams and epithelial tissues. This class of models describes the shape and motion of cells as a function of the forces on vertices where 3 or more cells meet. Despite the widespread use of these models, relatively little is known about their basic theoretical properties. One outstanding issue is the stability of fourfold vertices. In real foams, fourfold vertices are always unstable, but it has been unclear whether vertex models necessarily reflect this behavior. In biological tissues, fourfold vertices arise as an intermediate in T1 transitions, which are one of the fundamental processes by which tissues change topology, and stable fourfold vertices have recently been observed in several different epithelia. We show that, when all edges have the same tension, stationary fourfold vertices in vertex models must always break up. However, when tensions depend on edge orientation, as they might in a planar-polarized tissue, fourfold vertices can become stable. These findings pave the way for studies of more biologically realistic models that couple topological transitions to the dynamics of regulatory proteins. NSF Grant No. DMR-1056456 and NSF-GRFP Grant No. DGE-1256260.

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.

Geometric diffusion of quantum trajectories

PubMed Central

Yang, Fan; Liu, Ren-Bao

2015-01-01

A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745

Topologies on quantum topoi induced by quantization

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

Nakayama, Kunji

2013-07-15

In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantummore » topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.« less

The geometric nature of weights in real complex networks

NASA Astrophysics Data System (ADS)

Allard, Antoine; Serrano, M. Ángeles; García-Pérez, Guillermo; Boguñá, Marián

2017-01-01

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.

Lifshitz topological transitions, induced by doping and deformation in single-crystal bismuth wires

NASA Astrophysics Data System (ADS)

Nikolaeva, A. A.; Konopko, L. A.; Huber, T. E.; Kobylianskaya, A. K.; Para, Gh. I.

2017-02-01

The features associated with the manifestation of Lifshitz electron topological transitions (ETT) in glass-insulated bismuth wires upon qualitative changes to the topology of the Fermi surface are investigated. The variation of the energy spectrum parameters was implemented by doping Bi with an acceptor impurity Sn and using elastic strain of up to 2%, relative to the elongation in the weakly-doped p-type Bi wires. Pure and doped glass-insulated single-crystal bismuth with different diameters and (1011) orientations along the axis were prepared by the Ulitovsky liquid phase casting method. For the first time, ETT-induced anomalies are observed along the temperature dependences of the thermoemf α(T) as triple-changes of the α sign (given heavy doping of Bi wires with an acceptor impurity Sn). The concentration and energy position of the Σ-band given a high degree of bismuth doping with Sn was assessed using the Shubnikov-de Haas effect oscillations, which were detected both from L-electrons and from T-holes in magnetic fields of up to 14 T. It is shown that the Lifshitz electron-topological transitions with elastic deformation of weakly-doped p-type Bi wires are accompanied by anomalies along the deformation dependences of the thermoemf at low temperatures. The effect is interpreted in terms of the formation of a selective scattering channel of L-carriers into the T-band with a high density of states, which is in good agreement with existing theoretical ETT models.

Pressure induced structural, electronic topological, and semiconductor to metal transition in AgBiSe2

NASA Astrophysics Data System (ADS)

Rajaji, V.; Malavi, Pallavi S.; Yamijala, Sharma S. R. K. C.; Sorb, Y. A.; Dutta, Utpal; Guin, Satya N.; Joseph, B.; Pati, Swapan K.; Karmakar, S.; Biswas, Kanishka; Narayana, Chandrabhas

2016-10-01

We report the effect of strong spin orbit coupling inducing electronic topological and semiconductor to metal transitions on the thermoelectric material AgBiSe2 at high pressures. The synchrotron X-ray diffraction and the Raman scattering measurement provide evidence for a pressure induced structural transition from hexagonal (α-AgBiSe2) to rhombohedral (β-AgBiSe2) at a relatively very low pressure of around 0.7 GPa. The sudden drop in the electrical resistivity and clear anomalous changes in the Raman line width of the A1g and Eg(1) modes around 2.8 GPa was observed suggesting a pressure induced electronic topological transition. On further increasing the pressure, anomalous pressure dependence of phonon (A1g and Eg(1)) frequencies and line widths along with the observed temperature dependent electrical resistivity show a pressure induced semiconductor to metal transition above 7.0 GPa in β-AgBiSe2. First principles theoretical calculations reveal that the metallic character of β-AgBiSe2 is induced mainly due to redistributions of the density of states (p orbitals of Bi and Se) near to the Fermi level. Based on its pressure induced multiple electronic transitions, we propose that AgBiSe2 is a potential candidate for the good thermoelectric performance and pressure switches at high pressure.

The formation of topological defects in phase transitions

NASA Technical Reports Server (NTRS)

Hodges, Hardy M.

1989-01-01

It was argued, and fought through numerical work that the results of non-dynamical Monte Carlo computer simulations cannot be applied to describe the formation of topological defects when the correlation length at the Ginzburg temperature is significantly smaller than the horizon size. To test the current hypothesis that infinite strings at formation are essentially described by Brownian walks of size the correlation length at the Ginzburg temperature, fields at the Ginzburg temperature were equilibrated. Infinite structure do not exist in equilibrium for reasonable definitions of the Ginzburg temperature, and horizons must be included in a proper treatment. A phase transition, from small-scale to large-scale string or domain wall structure, is found to occur very close to the Ginzburg temperature, in agreement with recent work. The formation process of domain walls and global strings were investigated through the breaking of initially ordered states. To mimic conditions in the early Universe, cooling times are chosen so that horizons exist in the sample volume when topological structure formation occurs. The classical fields are evolved in real-time by the numerical solution of Langevin equations of motion on a three dimensional spatial lattice. The results indicate that it is possible for most of the string energy to be in small loops, rather than in long strings, at formation.

On Certain Topological Indices of Boron Triangular Nanotubes

NASA Astrophysics Data System (ADS)

Aslam, Adnan; Ahmad, Safyan; Gao, Wei

2017-08-01

The topological index gives information about the whole structure of a chemical graph, especially degree-based topological indices that are very useful. Boron triangular nanotubes are now replacing usual carbon nanotubes due to their excellent properties. We have computed general Randić (Rα), first Zagreb (M1) and second Zagreb (M2), atom-bond connectivity (ABC), and geometric-arithmetic (GA) indices of boron triangular nanotubes. Also, we have computed the fourth version of atom-bond connectivity (ABC4) and the fifth version of geometric-arithmetic (GA5) indices of boron triangular nanotubes.

Topological Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

Zhang, Pengfei; Zhai, Hui

2018-05-01

In this Rapid Communication, we construct a large-N exactly solvable model to study the interplay between interaction and topology, by connecting the Sachdev-Ye-Kitaev (SYK) model with constant hopping. The hopping forms a band structure that can exhibit both topologically trivial and nontrivial phases. Starting from a topologically trivial insulator with zero Hall conductance, we show that the interaction can drive a phase transition to a topologically nontrivial insulator with quantized nonzero Hall conductance, and a single gapless Dirac fermion emerges when the interaction is fine tuned to the critical point. The finite temperature effect is also considered, and we show that the topological phase with a stronger interaction is less stable against temperature. Our model provides a concrete example to illustrate the interacting topological phases and phase transitions, and can shed light on similar problems in physical systems.

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.

Output synchronization of discrete-time dynamical networks based on geometrically incremental dissipativity.

PubMed

Li, Chensong; Zhao, Jun

2017-01-01

In this work, we investigate the output synchronization problem for discrete-time dynamical networks with identical nodes. Firstly, if each node of a network is geometrically incrementally dissipative, the entire network can be viewed as a geometrically dissipative nonlinear system by choosing a particular input-output pair. Then, based on the geometrical dissipativity property, we consider two cases: output synchronization under arbitrary topology and switching topology, respectively. For the first case, we establish several criteria of output synchronization under arbitrary switching between a set of connection topologies by employing a common Lyapunov function. For the other case, we give the design method of a switching signal to achieve output synchronization even if all subnetworks are not synchronous. Finally, an example is provided to illustrate the effectiveness of the main results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Quantum phase transition between cluster and antiferromagnetic states

NASA Astrophysics Data System (ADS)

Son, W.; Amico, L.; Fazio, R.; Hamma, A.; Pascazio, S.; Vedral, V.

2011-09-01

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied and used to investigate the quantum phase transition. Our findings in one dimension corroborate the analysis of the two-dimensional generalization of the system, indicating, at a mean-field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.

Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition

DOE PAGES

Wang, Jing; Zhou, Quan; Lian, Biao; ...

2015-08-31

Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance willmore » be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e 2 /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.« less

Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition

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

Wang, Jing; Zhou, Quan; Lian, Biao

Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance willmore » be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e 2 /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.« less

Geometric effects on surface states in topological insulator Bi2Te3 nanowire

NASA Astrophysics Data System (ADS)

Sengupta, Parijat; Kubis, Tillman; Povolotskyi, Michael; Klimeck, Gerhard

2012-02-01

Bismuth Telluride (BT) is a 3D topological insulator (TI) with surface states that have energy dispersion linear in momentum and forms a Dirac cone at low energy. In this work we investigate the surface properties of a BT nanowire and demonstrate the existence of TI states. We also show how such states vanish under certain geometric conditions. An atomistic model (sp3d5s* TB) is used to compute the energy dispersion in a BT nanowire. Penetration depth of the surface states is estimated by ratio of Fermi velocity and band-gap. BT possesses a tiny band-gap, which creates small localization of surface states and greater penetration in to the bulk. To offset this large spatial penetration, which is undesirable to avoid a direct coupling between surfaces, we expect that bigger cross-sections of BT nanowires would be needed to obtain stable TI states. Our numerical work validates this prediction. Furthermore, geometry of the nanowire is shown to influence the TI states. Using a combined analytical and numerical approach our results reveal that surface roughness impact electronic structure leading to Rashba type splits along z-direction. Cylindrical and square cross-sections are given as illustrative examples.

Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane

NASA Technical Reports Server (NTRS)

Lisle, B. J.

1963-01-01

This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).

Symmetry-protected topological insulator and its symmetry-enriched topologically ordered boundary

NASA Astrophysics Data System (ADS)

Wang, Juven; Wen, Xiao-Gang; Witten, Edward

We propose a mechanism for achieving symmetry-enriched topologically ordered boundaries for symmetry-protected topological states, including those of topological insulators. Several different boundary phases and their phase transitions are considered, including confined phases, deconfined phases, symmetry-breaking, gapped and gapless phases. National Science Foundation PHY-1606531, Corning Glass Works Foundation Fellowship, NSF Grant DMR- 1506475 and NSFC 11274192, the BMO Financial Group and the John Templeton Foundation No. 39901.

The hydrophilic-to-hydrophobic transition in glassy silica is driven by the atomic topology of its surface

NASA Astrophysics Data System (ADS)

Yu, Yingtian; Krishnan, N. M. Anoop; Smedskjaer, Morten M.; Sant, Gaurav; Bauchy, Mathieu

2018-02-01

The surface reactivity and hydrophilicity of silicate materials are key properties for various industrial applications. However, the structural origin of their affinity for water remains unclear. Here, based on reactive molecular dynamics simulations of a series of artificial glassy silica surfaces annealed at various temperatures and subsequently exposed to water, we show that silica exhibits a hydrophilic-to-hydrophobic transition driven by its silanol surface density. By applying topological constraint theory, we show that the surface reactivity and hydrophilic/hydrophobic character of silica are controlled by the atomic topology of its surface. This suggests that novel silicate materials with tailored reactivity and hydrophilicity could be developed through the topological nanoengineering of their surface.

Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator

NASA Astrophysics Data System (ADS)

Sato, T.; Segawa, Kouji; Kosaka, K.; Souma, S.; Nakayama, K.; Eto, K.; Minami, T.; Ando, Yoichi; Takahashi, T.

2011-11-01

The three-dimensional (3D) topological insulator is a novel quantum state of matter where an insulating bulk hosts a linearly dispersing surface state, which can be viewed as a sea of massless Dirac fermions protected by the time-reversal symmetry (TRS). Breaking the TRS by a magnetic order leads to the opening of a gap in the surface state, and consequently the Dirac fermions become massive. It has been proposed theoretically that such a mass acquisition is necessary to realize novel topological phenomena, but achieving a sufficiently large mass is an experimental challenge. Here we report an unexpected discovery that the surface Dirac fermions in a solid-solution system TlBi(S1-xSex)2 acquire a mass without explicitly breaking the TRS. We found that this system goes through a quantum phase transition from the topological to the non-topological phase, and, by tracing the evolution of the electronic states using the angle-resolved photoemission, we observed that the massless Dirac state in TlBiSe2 switches to a massive state before it disappears in the non-topological phase. This result suggests the existence of a condensed-matter version of the `Higgs mechanism' where particles acquire a mass through spontaneous symmetry breaking.

Alloy Engineering of Topological Semimetal Phase Transition in MgTa2 -xNbxN3

NASA Astrophysics Data System (ADS)

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

2018-03-01

Dirac, triple-point, and Weyl fermions represent three topological semimetal phases, characterized with a descending degree of band degeneracy, which have been realized separately in specific crystalline materials with different lattice symmetries. Here we demonstrate an alloy engineering approach to realize all three types of fermions in one single material system of MgTa2 -xNbx N3 . Based on symmetry analysis and first-principles calculations, we map out a phase diagram of topological order in the parameter space of alloy concentration and crystalline symmetry, where the intrinsic MgTa2 N3 with the highest symmetry hosts the Dirac semimetal phase, which transforms into the triple-point and then the Weyl semimetal phases with increasing Nb concentration that lowers the crystalline symmetries. Therefore, alloy engineering affords a unique approach for the experimental investigation of topological transitions of semimetallic phases manifesting different fermionic behaviors.

Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement

NASA Technical Reports Server (NTRS)

Hull, P. V.; Tinker, M. L.

2007-01-01

Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem.

Evolutionary Optimization of a Geometrically Refined Truss

NASA Technical Reports Server (NTRS)

Hull, P. V.; Tinker, M. L.; Dozier, G. V.

2007-01-01

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

(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 }.

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.

Optical isolation with nonlinear topological photonics

NASA Astrophysics Data System (ADS)

Zhou, Xin; Wang, You; Leykam, Daniel; Chong, Y. D.

2017-09-01

It is shown that the concept of topological phase transitions can be used to design nonlinear photonic structures exhibiting power thresholds and discontinuities in their transmittance. This provides a novel route to devising nonlinear optical isolators. We study three representative designs: (i) a waveguide array implementing a nonlinear 1D Su-Schrieffer-Heeger model, (ii) a waveguide array implementing a nonlinear 2D Haldane model, and (iii) a 2D lattice of coupled-ring waveguides. In the first two cases, we find a correspondence between the topological transition of the underlying linear lattice and the power threshold of the transmittance, and show that the transmission behavior is attributable to the emergence of a self-induced topological soliton. In the third case, we show that the topological transition produces a discontinuity in the transmittance curve, which can be exploited to achieve sharp jumps in the power-dependent isolation ratio.

Unified Generic Geometric-Decompositions for Consensus or Flocking Systems of Cooperative Agents and Fast Recalculations of Decomposed Subsystems Under Topology-Adjustments.

PubMed

Li, Wei

2016-06-01

This paper considers a unified geometric projection approach for: 1) decomposing a general system of cooperative agents coupled via Laplacian matrices or stochastic matrices and 2) deriving a centroid-subsystem and many shape-subsystems, where each shape-subsystem has the distinct properties (e.g., preservation of formation and stability of the original system, sufficiently simple structures and explicit formation evolution of agents, and decoupling from the centroid-subsystem) which will facilitate subsequent analyses. Particularly, this paper provides an additional merit of the approach: considering adjustments of coupling topologies of agents which frequently occur in system design (e.g., to add or remove an edge, to move an edge to a new place, and to change the weight of an edge), the corresponding new shape-subsystems can be derived by a few simple computations merely from the old shape-subsystems and without referring to the original system, which will provide further convenience for analysis and flexibility of choice. Finally, such fast recalculations of new subsystems under topology adjustments are provided with examples.

Comprehensible Presentation of Topological Information

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

Weber, Gunther H.; Beketayev, Kenes; Bremer, Peer-Timo

2012-03-05

Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations,more » the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.« less

Transition from nonresonant to resonant random lasers by the geometrical confinement of disorder.

PubMed

Ghofraniha, N; Viola, I; Zacheo, A; Arima, V; Gigli, G; Conti, C

2013-12-01

We report on a transition in random lasers that is induced by the geometrical confinement of the emitting material. Different dye doped paper devices with controlled geometry are fabricated by soft lithography and show two distinguished behaviors in the stimulated emission: in the absence of boundary constraints, the energy threshold decreases for larger laser volumes showing the typical trend of diffusive nonresonant random lasers, while when the same material is lithographed into channels, the walls act as cavity and the resonant behavior typical of standard lasers is observed. The experimental results are consistent with the general theories of random and standard lasers and a clear phase diagram of the transition is reported.

A topological hierarchy for functions on triangulated surfaces.

PubMed

Bremer, Peer-Timo; Edelsbrunner, Herbert; Hamann, Bernd; Pascucci, Valerio

2004-01-01

We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.

The Data Transfer Kit: A geometric rendezvous-based tool for multiphysics data transfer

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

Slattery, S. R.; Wilson, P. P. H.; Pawlowski, R. P.

2013-07-01

The Data Transfer Kit (DTK) is a software library designed to provide parallel data transfer services for arbitrary physics components based on the concept of geometric rendezvous. The rendezvous algorithm provides a means to geometrically correlate two geometric domains that may be arbitrarily decomposed in a parallel simulation. By repartitioning both domains such that they have the same geometric domain on each parallel process, efficient and load balanced search operations and data transfer can be performed at a desirable algorithmic time complexity with low communication overhead relative to other types of mapping algorithms. With the increased development efforts in multiphysicsmore » simulation and other multiple mesh and geometry problems, generating parallel topology maps for transferring fields and other data between geometric domains is a common operation. The algorithms used to generate parallel topology maps based on the concept of geometric rendezvous as implemented in DTK are described with an example using a conjugate heat transfer calculation and thermal coupling with a neutronics code. In addition, we provide the results of initial scaling studies performed on the Jaguar Cray XK6 system at Oak Ridge National Laboratory for a worse-case-scenario problem in terms of algorithmic complexity that shows good scaling on 0(1 x 104) cores for topology map generation and excellent scaling on 0(1 x 105) cores for the data transfer operation with meshes of O(1 x 109) elements. (authors)« less

A Novel Passive Tracking Scheme Exploiting Geometric and Intercept Theorems

PubMed Central

Zhou, Biao; Sun, Chao; Ahn, Deockhyeon; Kim, Youngok

2018-01-01

Passive tracking aims to track targets without assistant devices, that is, device-free targets. Passive tracking based on Radio Frequency (RF) Tomography in wireless sensor networks has recently been addressed as an emerging field. The passive tracking scheme using geometric theorems (GTs) is one of the most popular RF Tomography schemes, because the GT-based method can effectively mitigate the demand for a high density of wireless nodes. In the GT-based tracking scheme, the tracking scenario is considered as a two-dimensional geometric topology and then geometric theorems are applied to estimate crossing points (CPs) of the device-free target on line-of-sight links (LOSLs), which reveal the target’s trajectory information in a discrete form. In this paper, we review existing GT-based tracking schemes, and then propose a novel passive tracking scheme by exploiting the Intercept Theorem (IT). To create an IT-based CP estimation scheme available in the noisy non-parallel LOSL situation, we develop the equal-ratio traverse (ERT) method. Finally, we analyze properties of three GT-based tracking algorithms and the performance of these schemes is evaluated experimentally under various trajectories, node densities, and noisy topologies. Analysis of experimental results shows that tracking schemes exploiting geometric theorems can achieve remarkable positioning accuracy even under rather a low density of wireless nodes. Moreover, the proposed IT scheme can provide generally finer tracking accuracy under even lower node density and noisier topologies, in comparison to other schemes. PMID:29562621

Two-dimensional topological photonic systems

NASA Astrophysics Data System (ADS)

Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

2017-09-01

The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional 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.

Statistical mechanics of two-dimensional shuffled foams: Geometry-topology correlation in small or large disorder limits

NASA Astrophysics Data System (ADS)

Durand, Marc; Kraynik, Andrew M.; van Swol, Frank; Käfer, Jos; Quilliet, Catherine; Cox, Simon; Ataei Talebi, Shirin; Graner, François

2014-06-01

Bubble monolayers are model systems for experiments and simulations of two-dimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M. Durand, Europhys. Lett. 90, 60002 (2010), 10.1209/0295-5075/90/60002] which takes into account Plateau laws. We predict the correlation between geometrical disorder (bubble size dispersity) and topological disorder (width of bubble side number distribution) over an extended range of bubble size dispersities. Extensive data sets arising from shuffled foam experiments, surface evolver simulations, and cellular Potts model simulations all collapse surprisingly well and coincide with the model predictions, even at extremely high size dispersity. At moderate size dispersity, we recover our earlier approximate predictions [M. Durand, J. Kafer, C. Quilliet, S. Cox, S. A. Talebi, and F. Graner, Phys. Rev. Lett. 107, 168304 (2011), 10.1103/PhysRevLett.107.168304]. At extremely low dispersity, when approaching the perfectly regular honeycomb pattern, we study how both geometrical and topological disorders vanish. We identify a crystallization mechanism and explore it quantitatively in the case of bidisperse foams. Due to the deformability of the bubbles, foams can crystallize over a larger range of size dispersities than hard disks. The model predicts that the crystallization transition occurs when the ratio of largest to smallest bubble radii is 1.4.

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

Quantum anomalous Hall effect and topological phase transition in two-dimensional antiferromagnetic Chern insulator NiOsCl6

NASA Astrophysics Data System (ADS)

Yang, Wei-Wei; Li, Lei; Zhao, Jing-Sheng; Liu, Xiao-Xiong; Deng, Jian-Bo; Tao, Xiao-Ma; Hu, Xian-Ru

2018-05-01

By doing calculations based on density functional theory, we predict that the two-dimensional anti-ferromagnetic (AFM) NiOsCl6 as a Chern insulator can realize the quantum anomalous Hall (QAH) effect. We investigate the magnetocrystalline anisotropy energies in different magnetic configurations and the Néel AFM configuration is proved to be ground state. When considering spin–orbit coupling (SOC), this layered material with spins perpendicular to the plane shows properties as a Chern insulator characterized by an inversion band structure and a nonzero Chern number. The nontrivial band gap is 37 meV and the Chern number C  =  ‑1, which are induced by a strong SOC and AFM order. With strong SOC, the NiOsCl6 system performs a continuous topological phase transition from the Chern insulator to the trivial insulator upon the increasing Coulomb repulsion U. The critical U c is indicated as 0.23 eV, at which the system is in a metallic phase with . Upon increasing U, the E g reduces linearly with C  =  ‑1 for 0  <  U  <  U c and increases linearly with C  =  0 for U  >  U c . At last we analysis the QAH properties and this continuous topological phase transition theoretically in a two-band model. This AFM Chern insulator NiOsCl6 proposes not only a promising way to realize the QAH effect, but also a new material to study the continuous topological phase transition.

Topological Privacy: Lattice Structures and Information Bubbles for Inference and Obfuscation

DTIC Science & Technology

2016-12-19

AFRL-AFOSR-VA-TR-2017-0036 Topological Privacy Michael Erdmann CARNEGIE MELLON UNIVERSITY 5000 FORBES AVENUE PITTSBURGH, PA 15213-3815 02/22/2017...PERSON 19b. TELEPHONE NUMBER (Include area code) 19-12-2016 Final 15-10-2013 - 14-10-2016 Topological Privacy Erdmann, Michael, A. Carnegie Mellon...Michael Erdmann Carnegie Mellon University me@cs.cmu.edu December 19, 2016 Abstract Information has intrinsic geometric and topological structure, arising

Pressure-induced topological insulator-to-metal transition and superconductivity in Sn-doped B i1.1S b0.9T e2S

NASA Astrophysics Data System (ADS)

An, Chao; Chen, Xuliang; Wu, Bin; Zhou, Yonghui; Zhou, Ying; Zhang, Ranran; Park, Changyong; Song, Fengqi; Yang, Zhaorong

2018-05-01

Tetradymite-type topological insulator Sn-doped B i1.1S b0.9T e2S (Sn-BSTS), with a surface state Dirac point energy well isolated from the bulk valence and conduction bands, is an ideal platform for studying the topological transport phenomena. Here, we present high-pressure transport studies on single-crystal Sn-BSTS, combined with Raman scattering and synchrotron x-ray diffraction measurements. Over the studied pressure range of 0.7-37.2 GPa, three critical pressure points can be observed: (i) At ˜9 GPa, a pressure-induced topological insulator-to-metal transition is revealed due to closure of the bulk band gap, which is accompanied by changes in slope of the Raman frequencies and a minimum in c /a within the pristine rhombohedral structure (R -3 m ); (ii) at ˜13 GPa, superconductivity is observed to emerge, along with the R -3 m to a C 2 /c (monoclinic) structural transition; (iii) at ˜24 GPa, the superconducting transition onset temperature TC reaches a maximum of ˜12 K , accompanied by a second structural transition from the C 2 /c to a body-centered cubic I m -3 m phase.

Geometric U-folds in four dimensions

NASA Astrophysics Data System (ADS)

Lazaroiu, C. I.; Shahbazi, C. S.

2018-01-01

We describe a general construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion-dilaton model of \

Untangling the mechanics versus topology of overhand knots

NASA Astrophysics Data System (ADS)

Reis, Pedro; Jawed, Mohammad; Dieleman, Peter; Audoly, Basile

2015-03-01

We study the interplay between mechanics and topology of overhand knots in slender elastic rods. We perform precision desktop experiments of overhand knots with increasing values for the crossing number (our measure of topology) and characterize their mechanical response through tension-displacement tests. The tensile force required to tighten the knot is governed by an intricate balance between topology, bending, friction, and contact forces. Digital imaging is employed to characterize the configuration of the contact braid as a function of crossing number. A robust scaling law is found for the pulling force in terms of the geometric and topological parameters of the knot. A reduced theory is developed, which predictively rationalizes the process.

Topological computation based on direct magnetic logic communication.

PubMed

Zhang, Shilei; Baker, Alexander A; Komineas, Stavros; Hesjedal, Thorsten

2015-10-28

Non-uniform magnetic domains with non-trivial topology, such as vortices and skyrmions, are proposed as superior state variables for nonvolatile information storage. So far, the possibility of logic operations using topological objects has not been considered. Here, we demonstrate numerically that the topology of the system plays a significant role for its dynamics, using the example of vortex-antivortex pairs in a planar ferromagnetic film. Utilising the dynamical properties and geometrical confinement, direct logic communication between the topological memory carriers is realised. This way, no additional magnetic-to-electrical conversion is required. More importantly, the information carriers can spontaneously travel up to ~300 nm, for which no spin-polarised current is required. The derived logic scheme enables topological spintronics, which can be integrated into large-scale memory and logic networks capable of complex computations.

Geometrical Description of fractional quantum Hall quasiparticles

NASA Astrophysics Data System (ADS)

Park, Yeje; Yang, Bo; Haldane, F. D. M.

2012-02-01

We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.

Geometrically controlled snapping transitions in shells with curved creases.

PubMed

Bende, Nakul Prabhakar; Evans, Arthur A; Innes-Gold, Sarah; Marin, Luis A; Cohen, Itai; Hayward, Ryan C; Santangelo, Christian D

2015-09-08

Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains to wrinkled membranes and programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities.

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.

Complex quantum network geometries: Evolution and phase transitions

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Complex quantum network geometries: Evolution and phase transitions.

PubMed

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Multiple Types of Topological Fermions in Transition Metal Silicides

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

Tang, Peizhe; Zhou, Quan; Zhang, Shou -Cheng

Exotic massless fermionic excitations with nonzero Berry flux, other than the Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with threefold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using the ab initio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe, and CoGe, when spin-orbit coupling is considered. Their nontrivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on the side surface, whichmore » is confirmed by (001) surface electronic spectra of CoSi. Additionally, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.« less

Multiple Types of Topological Fermions in Transition Metal Silicides

DOE PAGES

Tang, Peizhe; Zhou, Quan; Zhang, Shou -Cheng

2017-11-17

Exotic massless fermionic excitations with nonzero Berry flux, other than the Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with threefold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using the ab initio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe, and CoGe, when spin-orbit coupling is considered. Their nontrivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on the side surface, whichmore » is confirmed by (001) surface electronic spectra of CoSi. Additionally, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.« less

Modeling concepts for communication of geometric shape data

NASA Technical Reports Server (NTRS)

Collins, M. F.; Emnett, R. F.; Magedson, R. L.; Shu, H. H.

1984-01-01

ANSI5, an abbreviation for Section 5 of the American National Standard under Engineering Drawing and Related Documentation Practices (Committee Y14) on Digital Representation for Communication of Product Definition Data (ANSI Y14.26M-1981), allows encoding of a broad range of geometric shapes to be communicated through digital channels. A brief review of its underlying concepts is presented. The intent of ANSI5 is to devise a unified set of concise language formats for transmission of data pertaining to five types of geometric entities in Euclidean 3 space (E(3)). These are regarded as point like, curve like, surface like, solid like, and a combination of these types. For the first four types, ANSI5 makes a distinction between the geometry and topology. Geometry is a description of the spatial occupancy of the entity, and topology discusses the interconnectedness of the entity's boundary components.

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.

Coexistence of tunable Weyl points and topological nodal lines in ternary transition-metal telluride TaIrT e4

NASA Astrophysics Data System (ADS)

Zhou, Xiaoqing; Liu, Qihang; Wu, QuanSheng; Nummy, Tom; Li, Haoxiang; Griffith, Justin; Parham, Stephen; Waugh, Justin; Emmanouilidou, Eve; Shen, Bing; Yazyev, Oleg V.; Ni, Ni; Dessau, Daniel

2018-06-01

We report a combined theoretical and experimental study on TaIrT e4 , a potential candidate for a minimal model of type-II Weyl semimetals. Unexpectedly, an intriguing node structure with 12 Weyl points and a pair of nodal lines protected by mirror symmetry was found by first-principles calculations. Some signatures of the complex electronic structure, such as topologically nontrivial band crossings and topologically trivial Fermi arcs, are cross-validated by angle-resolved photoemission spectroscopy. Through external strain, the number of Weyl points can be reduced to a theoretical minimum of four, and the appearance of the nodal lines can be switched between different mirror planes in momentum space. The coexistence of switchable Weyl points and nodal lines establishes transition-metal chalcogenides as a unique test ground for topological state characterization and engineering.

Topologically and geometrically flexible structural units in seven new organically templated uranyl selenates and selenite–selenates

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

Gurzhiy, Vladislav V., E-mail: vladgeo17@mail.ru; Kovrugin, Vadim M.; Tyumentseva, Olga S.

2015-09-15

was used for investigation of topologies of structural units. • The method of orientation matrices was applied to distinguish geometrical isomers. • The flexibility of structural complexes specifies the undulation of layered structural units.« less

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.

Geometric Defects in Quantum Hall States

NASA Astrophysics Data System (ADS)

Gromov, Andrey

I will describe a geometric analogue of Laughlin quasiholes in fractional quantum Hall (FQH) states. These ``quasiholes'' are generated by an insertion of quantized fluxes of curvature - which can be modeled by branch points of a certain Riemann surface - and, consequently, are related to genons. Unlike quasiholes, the genons are not excitations, but extrinsic defects. Fusion of genons describes the response of an FQH state to a process that changes (effective) topology of the physical space. These defects are abelian for IQH states and non-abelian for FQH states. I will explain how to calculate an electric charge, geometric spin and adiabatic mutual statistics of the these defects. Leo Kadanoff Fellowship.

Spatially-protected Topology and Group Cohomology in Band Insulators

NASA Astrophysics Data System (ADS)

Alexandradinata, A.

This thesis investigates band topologies which rely fundamentally on spatial symmetries. A basic geometric property that distinguishes spatial symmetry regards their transformation of the spatial origin. Point groups consist of spatial transformations that preserve the spatial origin, while un-split extensions of the point groups by spatial translations are referred to as nonsymmorphic space groups. The first part of the thesis addresses topological phases with discretely-robust surface properties: we introduce theories for the Cnv point groups, as well as certain nonsymmorphic groups that involve glide reflections. These band insulators admit a powerful characterization through the geometry of quasimomentum space; parallel transport in this space is represented by the Wilson loop. The non-symmorphic topology we study is naturally described by a further extension of the nonsymmorphic space group by quasimomentum translations (the Wilson loop), thus placing real and quasimomentum space on equal footing -- here, we introduce the language of group cohomology into the theory of band insulators. The second part of the thesis addresses topological phases without surface properties -- their only known physical consequences are discrete signatures in parallel transport. We provide two such case studies with spatial-inversion and discrete-rotational symmetries respectively. One lesson learned here regards the choice of parameter loops in which we carry out transport -- the loop must be chosen to exploit the symmetry that protects the topology. While straight loops are popular for their connection with the geometric theory of polarization, we show that bent loops also have utility in topological band theory.

Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides

NASA Astrophysics Data System (ADS)

Bahramy, M. S.; Clark, O. J.; Yang, B.-J.; Feng, J.; Bawden, L.; Riley, J. M.; Marković, I.; Mazzola, F.; Sunko, V.; Biswas, D.; Cooil, S. P.; Jorge, M.; Wells, J. W.; Leandersson, M.; Balasubramanian, T.; Fujii, J.; Vobornik, I.; Rault, J. E.; Kim, T. K.; Hoesch, M.; Okawa, K.; Asakawa, M.; Sasagawa, T.; Eknapakul, T.; Meevasana, W.; King, P. D. C.

2018-01-01

Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied bulk properties, while their single-layer variants have become one of the most prominent examples of two-dimensional materials beyond graphene. Their disparate ground states largely depend on transition metal d-electron-derived electronic states, on which the vast majority of attention has been concentrated to date. Here, we focus on the chalcogen-derived states. From density-functional theory calculations together with spin- and angle-resolved photoemission, we find that these generically host a co-existence of type-I and type-II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. We demonstrate how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across a large number of compounds. Already, we demonstrate their existence in six separate TMDs, opening routes to tune, and ultimately exploit, their topological physics.

Topological phase transition measured in a dissipative metamaterial

NASA Astrophysics Data System (ADS)

Rosenthal, Eric I.; Ehrlich, Nicole K.; Rudner, Mark S.; Higginbotham, Andrew P.; Lehnert, K. W.

2018-06-01

We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy transport. The impulse response of our circuit is measured and used to reconstruct the band structure and winding number of circuit eigenfunctions around a dark mode. Our results demonstrate that dissipative topological transport can occur in a wider class of physical systems than considered before.

Structural properties of Sb 2S 3 under pressure: Evidence of an electronic topological transition

DOE PAGES

Efthimiopoulos, Ilias; Buchan, Cienna; Wang, Yuejian

2016-04-06

High-pressure Raman spectroscopy and x-ray diffraction of Sb 2S 3 up to 53 GPa reveals two phase transitions at 5 GPa and 15 GPa. The first transition is evidenced by noticeable compressibility changes in distinct Raman-active modes, in the lattice parameter axial ratios, the unit cell volume, as well as in specific interatomic bond lengths and bond angles. By taking into account relevant results from the literature, we assign these effects to a second-order isostructural transition arising from an electronic topological transition in Sb 2S 3 near 5 GPa. Close comparison between Sb 2S 3 and Sb 2S 3 upmore » to 10 GPa reveals a slightly diverse structural behavior for these two compounds after the isostructural transition pressure. This structural diversity appears to account for the different pressure-induced electronic behavior of Sb 2S 3 and Sb 2S 3 up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb 2S 3 up to that pressure. Lastly, the second high-pressure modification appearing above 15 GPa appears to trigger a structural disorder at ~20 GPa; full decompression from 53 GPa leads to the recovery of an amorphous state.« less

Chiralities of spiral waves and their transitions.

PubMed

Pan, Jun-ting; Cai, Mei-chun; Li, Bing-wei; Zhang, Hong

2013-06-01

The chiralities of spiral waves usually refer to their rotation directions (the turning orientations of the spiral temporal movements as time elapses) and their curl directions (the winding orientations of the spiral spatial geometrical structures themselves). Traditionally, they are the same as each other. Namely, they are both clockwise or both counterclockwise. Moreover, the chiralities are determined by the topological charges of spiral waves, and thus they are conserved quantities. After the inwardly propagating spirals were experimentally observed, the relationship between the chiralities and the one between the chiralities and the topological charges are no longer preserved. The chiralities thus become more complex than ever before. As a result, there is now a desire to further study them. In this paper, the chiralities and their transition properties for all kinds of spiral waves are systemically studied in the framework of the complex Ginzburg-Landau equation, and the general relationships both between the chiralities and between the chiralities and the topological charges are obtained. The investigation of some other models, such as the FitzHugh-Nagumo model, the nonuniform Oregonator model, the modified standard model, etc., is also discussed for comparison.

Topologically identical, but geometrically isomeric layers in hydrous α-, β-Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O and anhydrous Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})

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

Yu, Na; Klepov, Vladislav V.; Villa, Eric M.

2014-07-01

The hydrothermal reaction of uranyl nitrate with rubidium nitrate and arsenic (III) oxide results in the formation of polymorphic α- and β-Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O (α-, β-RbUAs) and the anhydrous phase Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] (RbUAs). These phases were structurally, chemically and spectroscopically characterized. The structures of all three compounds are based upon topologically identical, but geometrically isomeric layers. The layers are linked with each other by means of the Rb cations and hydrogen bonding. Dehydration experiments demonstrate that water deintercalation from hydrous α- and β-RbUAs yields anhydrous RbUAs via topotactic reactions. - Graphical abstract: Three differentmore » layer geometries observed in the structures of Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] and α- and β- Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O. Two different coordination environments of uranium polyhedra (types I and II) are shown schematically on the top of the figure. - Highlights: • Three new uranyl arsenates were synthesized from the hydrothermal reactions. • The phases consist of the topologically identical but geometrically different layers. • Topotactic transitions were observed in the processes of mono-hyrates dehydration.« less

The topological Anderson insulator phase in the Kane-Mele model

NASA Astrophysics Data System (ADS)

Orth, Christoph P.; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L.

2016-04-01

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.

Area collapse algorithm computing new curve of 2D geometric objects

NASA Astrophysics Data System (ADS)

Buczek, Michał Mateusz

2017-06-01

The processing of cartographic data demands human involvement. Up-to-date algorithms try to automate a part of this process. The goal is to obtain a digital model, or additional information about shape and topology of input geometric objects. A topological skeleton is one of the most important tools in the branch of science called shape analysis. It represents topological and geometrical characteristics of input data. Its plot depends on using algorithms such as medial axis, skeletonization, erosion, thinning, area collapse and many others. Area collapse, also known as dimension change, replaces input data with lower-dimensional geometric objects like, for example, a polygon with a polygonal chain, a line segment with a point. The goal of this paper is to introduce a new algorithm for the automatic calculation of polygonal chains representing a 2D polygon. The output is entirely contained within the area of the input polygon, and it has a linear plot without branches. The computational process is automatic and repeatable. The requirements of input data are discussed. The author analyzes results based on the method of computing ends of output polygonal chains. Additional methods to improve results are explored. The algorithm was tested on real-world cartographic data received from BDOT/GESUT databases, and on point clouds from laser scanning. An implementation for computing hatching of embankment is described.

Temperature-driven topological quantum phase transitions in a phase-change material Ge2Sb2Te5.

PubMed

Eremeev, S V; Rusinov, I P; Echenique, P M; Chulkov, E V

2016-12-13

The Ge 2 Sb 2 Te 5 is a phase-change material widely used in optical memory devices and is a leading candidate for next generation non-volatile random access memory devices which are key elements of various electronics and portable systems. Despite the compound is under intense investigation its electronic structure is currently not fully understood. The present work sheds new light on the electronic structure of the Ge 2 Sb 2 Te 5 crystalline phases. We demonstrate by predicting from first-principles calculations that stable crystal structures of Ge 2 Sb 2 Te 5 possess different topological quantum phases: a topological insulator phase is realized in low-temperature structure and Weyl semimetal phase is a characteristic of the high-temperature structure. Since the structural phase transitions are caused by the temperature the switching between different topologically non-trivial phases can be driven by variation of the temperature. The obtained results reveal the rich physics of the Ge 2 Sb 2 Te 5 compound and open previously unexplored possibility for spintronics applications of this material, substantially expanding its application potential.

Engineering topological defect patterns of Bose condensates in shaken optical lattices

NASA Astrophysics Data System (ADS)

Feng, Lei; Clark, Logan W.; Gaj, Anita; Chin, Cheng

2017-04-01

Topological defects emerge and play an essential role in the dynamics of systems undergoing continuous, symmetry-breaking phase transitions. Here, we study the topological defects (domain walls) which form when a Bose condensate in a shaken optical lattice undergoes a quantum phase transition and separates into domains of superfluid with finite momentum. Here, we experimentally demonstrate the ability to control the pattern of domain walls using a digital micromirror device. We further explore implementations of this technique to study dynamics near the phase transition and the evolution of topological defects.

Topological phononic insulator with robust pseudospin-dependent transport

NASA Astrophysics Data System (ADS)

Xia, Bai-Zhan; Liu, Ting-Ting; Huang, Guo-Liang; Dai, Hong-Qing; Jiao, Jun-Rui; Zang, Xian-Guo; Yu, De-Jie; Zheng, Sheng-Jie; Liu, Jian

2017-09-01

Topological phononic states, which facilitate unique acoustic transport around defects and disorders, have significantly revolutionized our scientific cognition of acoustic systems. Here, by introducing a zone folding mechanism, we realize the topological phase transition in a double Dirac cone of the rotatable triangular phononic crystal with C3 v symmetry. We then investigate the distinct topological edge states on two types of interfaces of our phononic insulators. The first one is a zigzag interface which simultaneously possesses a symmetric mode and an antisymmetric mode. Hybridization of the two modes leads to a robust pseudospin-dependent one-way propagation. The second one is a linear interface with a symmetric mode or an antisymmetric mode. The type of mode is dependent on the topological phase transition of the phononic insulators. Based on the rotatability of triangular phononic crystals, we consider several complicated contours defined by the topological zigzag interfaces. Along these contours, the acoustic waves can unimpededly transmit without backscattering. Our research develops a route for the exploration of the topological phenomena in experiments and provides an excellent framework for freely steering the acoustic backscattering-immune propagation within topological phononic structures.

Topological phases of topological-insulator thin films

NASA Astrophysics Data System (ADS)

Asmar, Mahmoud M.; Sheehy, Daniel E.; Vekhter, Ilya

2018-02-01

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as a function of both the film thickness and the momentum in the plane of the film for Bi2Se3 and Bi2Te3 . As a result, while the magnitude of the matrix element at the center of the surface Brillouin zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and nontopological phases, separated by semimetallic states, as the film thickness varies. In the topological phase, the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi2Se3 , making Bi2Te3 , where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators.

Entanglement entropy and entanglement spectrum of triplet topological superconductors.

PubMed

Oliveira, T P; Ribeiro, P; Sacramento, P D

2014-10-22

We analyze the entanglement entropy properties of a 2D p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and we find numerical evidence that for this model the derivative with respect to the magnetization provides a sensible signature of each topological phase. Following the area law for the entanglement entropy, we systematically analyze the contributions that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the finite subsystem. For this model, we show that even though the topological entanglement entropy vanishes, it signals the topological phase transitions in a finite system. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state, as in other topological systems.

Hg-Based Epitaxial Materials for Topological Insulators

DTIC Science & Technology

2014-07-01

Research Laboratory for investigation of properties. 15. SUBJECT TERMS EOARD, topological insulator , diluted magnetic ...topological superconductors and spintronics to quantum computation (e.g. see C.L.Kane and J.E.Moore "Topological Insulators " Physics World (2011) 24...tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 which form magnetically ordered insulators when doped with transition metal elements Cr or Fe (Rui Yu et

Magnetic-flux-driven topological quantum phase transition and manipulation of perfect edge states in graphene tube.

PubMed

Lin, S; Zhang, G; Li, C; Song, Z

2016-08-24

We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.

Topological Phenotypes Constitute a New Dimension in the Phenotypic Space of Leaf Venation Networks

PubMed Central

Ronellenfitsch, Henrik; Lasser, Jana; Daly, Douglas C.; Katifori, Eleni

2015-01-01

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested loops. This phenotypic trait encodes information orthogonal to widely used geometric phenotypic traits, and thus constitutes a new dimension in the leaf venation phenotypic space. We apply our metric to a database of 186 leaves and leaflets representing 137 species, predominantly from the Burseraceae family, revealing diverse topological network traits even within this single family. We show that topological information significantly improves identification of leaves from fragments by calculating a “leaf venation fingerprint” from topology and geometry. Further, we present a phenomenological model suggesting that the topological traits can be explained by noise effects unique to specimen during development of each leaf which leave their imprint on the final network. This work opens the path to new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and is directly applicable to other planar or sub-planar networks such as blood vessels in the brain. PMID:26700471

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.

Classification and characterization of topological insulators and superconductors

NASA Astrophysics Data System (ADS)

Mong, Roger

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

Topological order and thermal equilibrium in polariton condensates

NASA Astrophysics Data System (ADS)

Caputo, Davide; Ballarini, Dario; Dagvadorj, Galbadrakh; Sánchez Muñoz, Carlos; de Giorgi, Milena; Dominici, Lorenzo; West, Kenneth; Pfeiffer, Loren N.; Gigli, Giuseppe; Laussy, Fabrice P.; Szymańska, Marzena H.; Sanvitto, Daniele

2018-02-01

The Berezinskii-Kosterlitz-Thouless phase transition from a disordered to a quasi-ordered state, mediated by the proliferation of topological defects in two dimensions, governs seemingly remote physical systems ranging from liquid helium, ultracold atoms and superconducting thin films to ensembles of spins. Here we observe such a transition in a short-lived gas of exciton-polaritons, bosonic light-matter particles in semiconductor microcavities. The observed quasi-ordered phase, characteristic for an equilibrium two-dimensional bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. This is made possible thanks to long polariton lifetimes in high-quality samples and in a reservoir-free region. Our results show that the joint measurement of coherence both in space and time is required to characterize driven-dissipative phase transitions and enable the investigation of topological ordering in open systems.

Thermodynamic precursors, liquid-liquid transitions, dynamic and topological anomalies in densified liquid germania

NASA Astrophysics Data System (ADS)

Pacaud, F.; Micoulaut, M.

2015-08-01

The thermodynamic, dynamic, structural, and rigidity properties of densified liquid germania (GeO2) have been investigated using classical molecular dynamics simulation. We construct from a thermodynamic framework an analytical equation of state for the liquid allowing the possible detection of thermodynamic precursors (extrema of the derivatives of the free energy), which usually indicate the possibility of a liquid-liquid transition. It is found that for the present germania system, such precursors and the possible underlying liquid-liquid transition are hidden by the slowing down of the dynamics with decreasing temperature. In this respect, germania behaves quite differently when compared to parent tetrahedral systems such as silica or water. We then detect a diffusivity anomaly (a maximum of diffusion with changing density/volume) that is strongly correlated with changes in coordinated species, and the softening of bond-bending (BB) topological constraints that decrease the liquid rigidity and enhance transport. The diffusivity anomaly is finally substantiated from a Rosenfeld-type scaling law linked to the pair correlation entropy, and to structural relaxation.

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.

Global topological dominance in the left hemisphere.

PubMed

Wang, Bo; Zhou, Tian Gang; Zhuo, Yan; Chen, Lin

2007-12-26

A series of experiments with right-handers demonstrated that the left hemisphere (LH) is reliably and consistently superior to the right hemisphere (RH) for global topological perception. These experiments generalized the topological account of lateralization to different kinds of topological properties (including holes, inside/outside relation, and "presence vs. absence") in comparison with a broad spectrum of geometric properties, including orientation, distance, size, mirror-symmetry, parallelism, collinearity, etc. The stimuli and paradigms used were also designed to prevent subjects from using various nontopological properties in performing the tasks of topological discrimination. Furthermore, task factors commonly considered in the study of hemispheric asymmetry, such as response latency vs. accuracy, vertical vs. horizontal presentation, detection vs. recognition, and simultaneous vs. sequential judgment, were manipulated to not be confounding factors. Moreover, left-handed subjects were tested and showed the right lateralization of topological perception, in the opposite direction of lateralization compared with right-handers. In addition, the functional magnetic resonance imaging measure revealed that only a region in the left temporal gyrus was consistently more activated across subjects in the task of topological discrimination, consistent with the behavioral results. In summary, the global topological dominance in the LH is well supported by the converging evidence from the variety of paradigms and techniques, and it suggests a unified solution to the current major controversies on visual lateralization.

Machine learning topological states

NASA Astrophysics Data System (ADS)

Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.

2017-11-01

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.

Topological Superconductivity on the Surface of Fe-Based Superconductors.

PubMed

Xu, Gang; Lian, Biao; Tang, Peizhe; Qi, Xiao-Liang; Zhang, Shou-Cheng

2016-07-22

As one of the simplest systems for realizing Majorana fermions, the topological superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calculations and the analysis of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe_{1+y}Se_{0.5}Te_{0.5} have a metallic topologically nontrivial band structure, and exhibit a normal-topological-normal superconductivity phase transition on the (001) surface by tuning the bulk carrier doping level. In the topological superconductivity (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topological phase transition driven by the temperature, which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.

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 Anderson insulator induced by inter-cell hopping disorder

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

Lv, Shu-Hui; College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018; Song, Juntao, E-mail: jtsong@mail.hebtu.edu.cn

We have studied in detail the influence of same-orbit and different-orbit hopping disorders in HgTe/CdTe quantum wells. Intriguingly, similar to the behavior of the on-site Anderson disorder, a phase transition from a topologically trivial phase to a topological phase is induced at a proper strength of the same-orbit hopping disorder. For different-orbit hopping disorder, however, the phase transition does not occur. The results have been analytically verified by using effective medium theory. A consistent conclusion can be obtained by comparing phase diagrams, conductance, and conductance fluctuations. In addition, the influence of Rashba spin-orbit interaction (RSOI) on the system has beenmore » studied for different types of disorder, and the RSOI shows different influence on topological phase at different disorders. The topological phase induced by same-orbit hopping disorder is more robust against the RSOI than that induced by on-site Anderson disorder. For different-orbit hopping disorder, no matter whether the RSOI is included or not, the phase transition does not occur. The results indicate, whether or not the topological Anderson insulator can be observed depends on a competition between the different types of the disorder as well as the strength of the RSOI in a system.« less

Finite Topological Spaces as a Pedagogical Tool

ERIC Educational Resources Information Center

Helmstutler, Randall D.; Higginbottom, Ryan S.

2012-01-01

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

Topological magnons in a one-dimensional itinerant flatband ferromagnet

NASA Astrophysics Data System (ADS)

Su, Xiao-Fei; Gu, Zhao-Long; Dong, Zhao-Yang; Li, Jian-Xin

2018-06-01

Different from previous scenarios that topological magnons emerge in local spin models, we propose an alternative that itinerant electron magnets can host topological magnons. A one-dimensional Tasaki model with a flatband is considered as the prototype. This model can be viewed as a quarter-filled periodic Anderson model with impurities located in between and hybridizing with the nearest-neighbor conducting electrons, together with a Hubbard repulsion for these electrons. By increasing the Hubbard interaction, the gap between the acoustic and optical magnons closes and reopens while the Berry phase of the acoustic band changes from 0 to π , leading to the occurrence of a topological transition. After this transition, there always exist in-gap edge magnonic modes, which is consistent with the bulk-edge correspondence. The Hubbard interaction-driven transition reveals a new mechanism to realize nontrivial magnon bands.

Pressure variation of Rashba spin splitting toward topological transition in the polar semiconductor BiTeI

NASA Astrophysics Data System (ADS)

Ideue, T.; Checkelsky, J. G.; Bahramy, M. S.; Murakawa, H.; Kaneko, Y.; Nagaosa, N.; Tokura, Y.

2014-10-01

BiTeI is a polar semiconductor with gigantic Rashba spin-split bands in bulk. We have investigated the effect of pressure on the electronic structure of this material via magnetotransport. Periods of Shubunikov-de Haas (SdH) oscillations originating from the spin-split outer Fermi surface and inner Fermi surface show disparate responses to pressure, while the carrier number derived from the Hall effect is unchanged with pressure. The associated parameters which characterize the spin-split band structure are strongly dependent on pressure, reflecting the pressure-induced band deformation. We find the SdH oscillations and transport response are consistent with the theoretically proposed pressure-induced band deformation leading to a topological phase transition. Our analysis suggests the critical pressure for the quantum phase transition near Pc=3.5 GPa.

Interplay between topology and disorder in a two-dimensional semi-Dirac material

NASA Astrophysics Data System (ADS)

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2018-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes—single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.

Universalities of thermodynamic signatures in topological phases

PubMed Central

Kempkes, S. N.; Quelle, A.; Smith, C. Morais

2016-01-01

Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase transition the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter. PMID:27929041

Universalities of thermodynamic signatures in topological phases.

PubMed

Kempkes, S N; Quelle, A; Smith, C Morais

2016-12-08

Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase transition the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter.

Electronic Topological Transitions in CuNiMnAl and CuNiMnSn under pressure from first principles study

NASA Astrophysics Data System (ADS)

Rambabu, P.; Kanchana, V.

2018-06-01

A detailed study on quaternary ordered full Heusler alloys CuNiMnAl and CuNiMnSn at ambient and under different compressions is presented using first principles electronic structure calculations. Both the compounds are found to possess ferromagnetic nature at ambient with magnetic moment of Mn being 3.14 μB and 3.35 μB respectively in CuNiMnAl and CuNiMnSn. The total magnetic moment for both the compounds is found to decrease under compression. Fermi surface (FS) topology change is observed in both compounds under pressure at V/V0 = 0.90, further leading to Electronic Topological Transitions (ETTs) and is evidenced by the anomalies visualized in density of states and elastic constants under compression.

Geometric control of capillary architecture via cell-matrix mechanical interactions.

PubMed

Sun, Jian; Jamilpour, Nima; Wang, Fei-Yue; Wong, Pak Kin

2014-03-01

Capillary morphogenesis is a multistage, multicellular activity that plays a pivotal role in various developmental and pathological situations. In-depth understanding of the regulatory mechanism along with the capability of controlling the morphogenic process will have direct implications on tissue engineering and therapeutic angiogenesis. Extensive research has been devoted to elucidate the biochemical factors that regulate capillary morphogenesis. The roles of geometric confinement and cell-matrix mechanical interactions on the capillary architecture, nevertheless, remain largely unknown. Here, we show geometric control of endothelial network topology by creating physical confinements with microfabricated fences and wells. Decreasing the thickness of the matrix also results in comparable modulation of the network architecture, supporting the boundary effect is mediated mechanically. The regulatory role of cell-matrix mechanical interaction on the network topology is further supported by alternating the matrix stiffness by a cell-inert PEG-dextran hydrogel. Furthermore, reducing the cell traction force with a Rho-associated protein kinase inhibitor diminishes the boundary effect. Computational biomechanical analysis delineates the relationship between geometric confinement and cell-matrix mechanical interaction. Collectively, these results reveal a mechanoregulation scheme of endothelial cells to regulate the capillary network architecture via cell-matrix mechanical interactions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Free-form geometric modeling by integrating parametric and implicit PDEs.

PubMed

Du, Haixia; Qin, Hong

2007-01-01

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDE-based geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.

Identifying and Fostering Higher Levels of Geometric Thinking

ERIC Educational Resources Information Center

Škrbec, Maja; Cadež, Tatjana Hodnik

2015-01-01

Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…

Topological Spin Glass in Diluted Spin Ice

NASA Astrophysics Data System (ADS)

Sen, Arnab; Moessner, R.

2015-06-01

It is a salient experimental fact that a large fraction of candidate spin liquid materials freeze as the temperature is lowered. The question naturally arises whether such freezing is intrinsic to the spin liquid ("disorder-free glassiness") or extrinsic, in the sense that a topological phase simply coexists with standard freezing of impurities. Here, we demonstrate a surprising third alternative, namely, that freezing and topological liquidity are inseparably linked. The topological phase reacts to the introduction of disorder by generating degrees of freedom of a new type (along with interactions between them), which in turn undergo a freezing transition while the topological phase supporting them remains intact.

Topological Spin Glass in Diluted Spin Ice.

PubMed

Sen, Arnab; Moessner, R

2015-06-19

It is a salient experimental fact that a large fraction of candidate spin liquid materials freeze as the temperature is lowered. The question naturally arises whether such freezing is intrinsic to the spin liquid ("disorder-free glassiness") or extrinsic, in the sense that a topological phase simply coexists with standard freezing of impurities. Here, we demonstrate a surprising third alternative, namely, that freezing and topological liquidity are inseparably linked. The topological phase reacts to the introduction of disorder by generating degrees of freedom of a new type (along with interactions between them), which in turn undergo a freezing transition while the topological phase supporting them remains intact.

Mathematics and morphogenesis of cities: A geometrical approach

NASA Astrophysics Data System (ADS)

Courtat, Thomas; Gloaguen, Catherine; Douady, Stephane

2011-03-01

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city’s current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of the traditional models, from random graphs, complex networks theory, or stochastic geometry, takes into account the geometrical, functional, and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating, and explaining cities’ overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division or extension of space. We propose a dynamical model that mimics this logic and that, from simple general rules and a few parameters, succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.

Topological phase transitions and chiral inelastic transport induced by the squeezing of light

PubMed Central

Peano, Vittorio; Houde, Martin; Brendel, Christian; Marquardt, Florian; Clerk, Aashish A.

2016-01-01

There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits. PMID:26931620

Topological phase transitions and chiral inelastic transport induced by the squeezing of light

NASA Astrophysics Data System (ADS)

Peano, Vittorio; Houde, Martin; Brendel, Christian; Marquardt, Florian; Clerk, Aashish A.

2016-03-01

There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits.

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.

Lateral topological crystalline insulator heterostructure

NASA Astrophysics Data System (ADS)

Sun, Qilong; Dai, Ying; Niu, Chengwang; Ma, Yandong; Wei, Wei; Yu, Lin; Huang, Baibiao

2017-06-01

The emergence of lateral heterostructures fabricated by two-dimensional building blocks brings many exciting realms in material science and device physics. Enriching available nanomaterials for creating such heterostructures and enabling the underlying new physics is highly coveted for the integration of next-generation devices. Here, we report a breakthrough in lateral heterostructure based on the monolayer square transition-metal dichalcogenides MX2 (M  =  W, X  =  S/Se) modules. Our results reveal that the MX2 lateral heterostructure (1S-MX2 LHS) can possess excellent thermal and dynamical stability. Remarkably, the highly desired two-dimensional topological crystalline insulator phase is confirmed by the calculated mirror Chern number {{n}\\text{M}}=-1 . A nontrivial band gap of 65 meV is obtained with SOC, indicating the potential for room-temperature observation and applications. The topologically protected edge states emerge at the edges of two different nanoribbons between the bulk band gap, which is consistent with the mirror Chern number. In addition, a strain-induced topological phase transition in 1S-MX2 LHS is also revealed, endowing the potential utilities in electronics and spintronics. Our predictions not only introduce new member and vitality into the studies of lateral heterostructures, but also highlight the promise of lateral heterostructure as appealing topological crystalline insulator platforms with excellent stability for future devices.

Closed geometric models in medical applications

NASA Astrophysics Data System (ADS)

Jagannathan, Lakshmipathy; Nowinski, Wieslaw L.; Raphel, Jose K.; Nguyen, Bonnie T.

1996-04-01

Conventional surface fitting methods give twisted surfaces and complicates capping closures. This is a typical character of surfaces that lack rectangular topology. We suggest an algorithm which overcomes these limitations. The analysis of the algorithm is presented with experimental results. This algorithm assumes the mass center lying inside the object. Both capping closure and twisting are results of inadequate information on the geometric proximity of the points and surfaces which are proximal in the parametric space. Geometric proximity at the contour level is handled by mapping the points along the contour onto a hyper-spherical space. The resulting angular gradation with respect to the centroid is monotonic and hence avoids the twisting problem. Inter-contour geometric proximity is achieved by partitioning the point set based on the angle it makes with the respective centroids. Avoidance of capping complications is achieved by generating closed cross curves connecting curves which are reflections about the abscissa. The method is of immense use for the generation of the deep cerebral structures and is applied to the deep structures generated from the Schaltenbrand- Wahren brain atlas.

Topological Classification of Crystalline Insulators through Band Structure Combinatorics

NASA Astrophysics Data System (ADS)

Kruthoff, Jorrit; de Boer, Jan; van Wezel, Jasper; Kane, Charles L.; Slager, Robert-Jan

2017-10-01

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented match the mathematical structure underlying the topological classification of these crystals in terms of K -theory and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify all allowed topological phases of spinless particles in crystals in class A . Employing this classification, we study transitions between topological phases within class A that are driven by band inversions at high-symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure and to identify whether or not they give rise to intermediate Weyl semimetallic phases.

Electronic properties of new topological quantum materials

NASA Astrophysics Data System (ADS)

Kaminski, Adam

Topological materials are characterized by the presence of nontrivial quantum electronic states, where often the electron spin is locked to its momentum. This opens up the possibility for developing new devices in which information is processed or stored by means of spin rather than charge. In this talk we will discuss the electronic properties of several of newly discovered topological quantum materials. In WTe2 we have observed a topological transition involving a change of the Fermi surface topology (known as a Lifshitz transition) driven by temperature. The strong temperature-dependence of the chemical potential that is at the heart of this phenomenon is also important for understanding the thermoelectric properties of such semimetals. Both WTe2 and MoTe2 were proposed to host type II Weyl semimetalic state. Indeed our data provides first experimental confirmation of such state in both of these materials. We will also present evidence for a new topological state in PtSn4 where pairs of extended Dirac node arcs rather are present rather than Dirac points, that is so far not understood theoretically. Our research opens up new directions on enhancing topological responsiveness of new quantum materials. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division (ARPES measurements), Center for Emergent Materials, an NSF MRSEC, under Grant DMR-1420451 (theory and data anal.

On Topological Indices of Certain Dendrimer Structures

NASA Astrophysics Data System (ADS)

Aslam, Adnan; Bashir, Yasir; Ahmad, Safyan; Gao, Wei

2017-05-01

A topological index can be considered as transformation of chemical structure in to real number. In QSAR/QSPR study, physicochemical properties and topological indices such as Randić, Zagreb, atom-bond connectivity ABC, and geometric-arithmetic GA index are used to predict the bioactivity of chemical compounds. Dendrimers are highly branched, star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper we determine generalised Randić, general Zagreb, general sum-connectivity indices of poly(propyl) ether imine, porphyrin, and zinc-Porphyrin dendrimers. We also compute ABC and GA indices of these families of dendrimers.

Discrete elastic model for two-dimensional melting.

PubMed

Lansac, Yves; Glaser, Matthew A; Clark, Noel A

2006-04-01

We present a network model for the study of melting and liquid structure in two dimensions, the first in which the presence and energy of topological defects (dislocations and disclinations) and of geometrical defects (elemental voids) can be independently controlled. Interparticle interaction is via harmonic springs and control is achieved by Monte Carlo moves which springs can either be orientationally "flipped" between particles to generate topological defects, or can be "popped" in force-free shape, to generate geometrical defects. With the geometrical defects suppressed the transition to the liquid phase occurs via disclination unbinding, as described by the Kosterlitz-Thouless-Halperin-Nelson-Young model and found in soft potential two-dimensional (2D) systems, such as the dipole-dipole potential [H. H. von Grünberg, Phys. Rev. Lett. 93, 255703 (2004)]. By contrast, with topological defects suppressed, a disordering transition, the Glaser-Clark condensation of geometrical defects [M. A. Glaser and N. A. Clark, Adv. Chem. Phys. 83, 543 (1993); M. A. Glaser, (Springer-Verlag, Berlin, 1990), Vol. 52, p. 141], produces a state that accurately characterizes the local liquid structure and first-order melting observed in hard-potential 2D systems, such as hard disk and the Weeks-Chandler-Andersen (WCA) potentials (M. A. Glaser and co-workers, see above). Thus both the geometrical and topological defect systems play a role in melting. The present work introduces a system in which the relative roles of topological and geometrical defects and their interactions can be explored. We perform Monte Carlo simulations of this model in the isobaric-isothermal ensemble, and present the phase diagram as well as various thermodynamic, statistical, and structural quantities as a function of the relative populations of geometrical and topological defects. The model exhibits a rich phase behavior including hexagonal and square crystals, expanded crystal, dodecagonal quasicrystal

On the topology of chromatin fibres

PubMed Central

Barbi, Maria; Mozziconacci, Julien; Victor, Jean-Marc; Wong, Hua; Lavelle, Christophe

2012-01-01

The ability of cells to pack, use and duplicate DNA remains one of the most fascinating questions in biology. To understand DNA organization and dynamics, it is important to consider the physical and topological constraints acting on it. In the eukaryotic cell nucleus, DNA is organized by proteins acting as spools on which DNA can be wrapped. These proteins can subsequently interact and form a structure called the chromatin fibre. Using a simple geometric model, we propose a general method for computing topological properties (twist, writhe and linking number) of the DNA embedded in those fibres. The relevance of the method is reviewed through the analysis of magnetic tweezers single molecule experiments that revealed unexpected properties of the chromatin fibre. Possible biological implications of these results are discussed. PMID:24098838

Nonequilibrium Floquet States in Topological Kondo Insulators

DTIC Science & Technology

2016-02-04

increase in an insulating crystal of SmB6. However, extrinsic heating effects are a potential source of the observation, which would act to reduce...the first known topological Kondo insulator , Samarium Hexaboride, we investigated the possibility of realizing a moving cascade of topological... insulator -to-metal transitions to obtain bulk-like conduction through the Kondo insulator . Experiments in collaboration with Prof. T. Yanagisawa at

Urbanisation and 3d Spatial - a Geometric Approach

NASA Astrophysics Data System (ADS)

Duncan, E. E.; Rahman, A. Abdul

2013-09-01

Urbanisation creates immense competition for space, this may be attributed to an increase in population owing to domestic and external tourism. Most cities are constantly exploring all avenues in maximising its limited space. Hence, urban or city authorities need to plan, expand and use such three dimensional (3D) space above, on and below the city space. Thus, difficulties in property ownership and the geometric representation of the 3D city space is a major challenge. This research, investigates the concept of representing a geometric topological 3D spatial model capable of representing 3D volume parcels for man-made constructions above and below the 3D surface volume parcel. A review of spatial data models suggests that the 3D TIN (TEN) model is significant and can be used as a unified model. The concepts, logical and physical models of 3D TIN for 3D volumes using tetrahedrons as the base geometry is presented and implemented to show man-made constructions above and below the surface parcel within a user friendly graphical interface. Concepts for 3D topology and 3D analysis are discussed. Simulations of this model for 3D cadastre are implemented. This model can be adopted by most countries to enhance and streamline geometric 3D property ownership for urban centres. 3D TIN concept for spatial modelling can be adopted for the LA_Spatial part of the Land Administration Domain Model (LADM) (ISO/TC211, 2012), this satisfies the concept of 3D volumes.

Local characterization of one-dimensional topologically ordered states

NASA Astrophysics Data System (ADS)

Cui, Jian; Amico, Luigi; Fan, Heng; Gu, Mile; Hamma, Alioscia; Vedral, Vlatko

2013-09-01

We consider one-dimensional Hamiltonian systems whose ground states display symmetry-protected topological order. We show that ground states within the topological phase cannot be connected with each other through local operations and classical communication between a bipartition of the system. Our claim is demonstrated by analyzing the entanglement spectrum and Rényi entropies of different physical systems that provide examples for symmetry-protected topological phases. Specifically, we consider the spin-1/2 cluster-Ising model and a class of spin-1 models undergoing quantum phase transitions to the Haldane phase. Our results provide a probe for symmetry-protected topological order. Since the picture holds even at the system's local scale, our analysis can serve as a local experimental test for topological order.

Geometries in Soft Matter From Geometric Frustration, Liquid Droplets to Electrostatics in Solution

NASA Astrophysics Data System (ADS)

Yao, Zhenwei

This thesis explores geometric aspects of soft matter systems. The topics covered fall into three categories: (i) geometric frustrations, including the interplay of geometry and topological defects in two dimensional systems, and the frustration of a planar sheet attached to a curved surface; (ii) geometries of liquid droplets, including the curvature driven instabilities of toroidal liquid droplets and the self-propulsion of droplets on a spatially varying surface topography; (iii) the study of the electric double layer structure around charged spherical interfaces by a geometric method. In (i), we study the crystalline order on capillary bridges with varying Gaussian curvature. Energy requires the appearance of topological defects on the surface, which are natural spots for biological activity and chemical functionalization. We further study how liquid crystalline order deforms flexible structured vesicles. In particular we find faceted tetrahedral vesicle as the ground state, which may lead to the design of supra-molecular structures with tetrahedral symmetry and new classes of nano-carriers. Furthermore, by a simple paper model we explore the geometric frustration on a planar sheet when brought to a negative curvature surface in a designed elasto-capillary system. In (ii), motivated by the idea of realizing crystalline order on a stable toroidal droplet and a beautiful experiment on toroidal droplets, we study the Rayleigh instability and the shrinking instability of thin and fat toroidal droplets, where the toroidal geometry plays an essential role. In (iii), by a geometric mapping we construct an approximate analytic spherical solution to the nonlinear Poisson-Boltzmann equation, and identify the applicability regime of the solution. The derived geometric solution enables further analytical study of spherical electrostatic systems such as colloidal suspensions.

Augmented Topological Descriptors of Pore Networks for Material Science.

PubMed

Ushizima, D; Morozov, D; Weber, G H; Bianchi, A G C; Sethian, J A; Bethel, E W

2012-12-01

One potential solution to reduce the concentration of carbon dioxide in the atmosphere is the geologic storage of captured CO2 in underground rock formations, also known as carbon sequestration. There is ongoing research to guarantee that this process is both efficient and safe. We describe tools that provide measurements of media porosity, and permeability estimates, including visualization of pore structures. Existing standard algorithms make limited use of geometric information in calculating permeability of complex microstructures. This quantity is important for the analysis of biomineralization, a subsurface process that can affect physical properties of porous media. This paper introduces geometric and topological descriptors that enhance the estimation of material permeability. Our analysis framework includes the processing of experimental data, segmentation, and feature extraction and making novel use of multiscale topological analysis to quantify maximum flow through porous networks. We illustrate our results using synchrotron-based X-ray computed microtomography of glass beads during biomineralization. We also benchmark the proposed algorithms using simulated data sets modeling jammed packed bead beds of a monodispersive material.

Integrated Design Engineering Analysis (IDEA) Environment Automated Generation of Structured CFD Grids using Topology Methods

NASA Technical Reports Server (NTRS)

Kamhawi, Hilmi N.

2012-01-01

This report documents the work performed from March 2010 to March 2012. The Integrated Design and Engineering Analysis (IDEA) environment is a collaborative environment based on an object-oriented, multidisciplinary, distributed framework using the Adaptive Modeling Language (AML) as a framework and supporting the configuration design and parametric CFD grid generation. This report will focus on describing the work in the area of parametric CFD grid generation using novel concepts for defining the interaction between the mesh topology and the geometry in such a way as to separate the mesh topology from the geometric topology while maintaining the link between the mesh topology and the actual geometry.

Quantum friction in two-dimensional topological materials

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

Farias, M. Belén; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.

In this paper, we develop the theory of quantum friction in two-dimensional topological materials. The quantum drag force on a metallic nanoparticle moving above such systems is sensitive to the nontrivial topology of their electronic phases, shows a novel distance scaling law, and can be manipulated through doping or via the application of external fields. We use the developed framework to investigate quantum friction due to the quantum Hall effect in magnetic field biased graphene, and to topological phase transitions in the graphene family materials. Finally, it is shown that topologically nontrivial states in two-dimensional materials enable an increase ofmore » two orders of magnitude in the quantum drag force with respect to conventional neutral graphene systems.« less

Quantum friction in two-dimensional topological materials

DOE PAGES

Farias, M. Belén; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.

2018-04-24

In this paper, we develop the theory of quantum friction in two-dimensional topological materials. The quantum drag force on a metallic nanoparticle moving above such systems is sensitive to the nontrivial topology of their electronic phases, shows a novel distance scaling law, and can be manipulated through doping or via the application of external fields. We use the developed framework to investigate quantum friction due to the quantum Hall effect in magnetic field biased graphene, and to topological phase transitions in the graphene family materials. Finally, it is shown that topologically nontrivial states in two-dimensional materials enable an increase ofmore » two orders of magnitude in the quantum drag force with respect to conventional neutral graphene systems.« less

Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions

NASA Astrophysics Data System (ADS)

Dyachenko, P. N.; Molesky, S.; Petrov, A. Yu; Störmer, M.; Krekeler, T.; Lang, S.; Ritter, M.; Jacob, Z.; Eich, M.

2016-06-01

Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C.

Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions

PubMed Central

Dyachenko, P. N.; Molesky, S.; Petrov, A. Yu; Störmer, M.; Krekeler, T.; Lang, S.; Ritter, M.; Jacob, Z.; Eich, M.

2016-01-01

Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C. PMID:27263653

A Novel Paradigm for Computer-Aided Design: TRIZ-Based Hybridization of Topologically Optimized Density Distributions

NASA Astrophysics Data System (ADS)

Cardillo, A.; Cascini, G.; Frillici, F. S.; Rotini, F.

In a recent project the authors have proposed the adoption of Optimization Systems [1] as a bridging element between Computer-Aided Innovation (CAI) and PLM to identify geometrical contradictions [2], a particular case of the TRIZ physical contradiction [3]. A further development of the research [4] has revealed that the solutions obtained from several topological optimizations can be considered as elementary customized modeling features for a specific design task. The topology overcoming the arising geometrical contradiction can be obtained through a manipulation of the density distributions constituting the conflicting pair. Already two strategies of density combination have been identified as capable to solve geometrical contradictions and several others are under extended testing. The paper illustrates the most recent results of the ongoing research mainly related to the extension of the algorithms from 2D to 3D design spaces. The whole approach is clarified by means of two detailed examples, where the proposed technique is compared with classical multi-goal optimization.

Emancipating traditional channel network types: quantification of topology and geometry, and relation to geologic boundary conditions

NASA Astrophysics Data System (ADS)

Temme, A.; Langston, A. L.

2017-12-01

Traditional classification of channel networks is helpful for qualitative geologic and geomorphic inference. For instance, a dendritic network indicates no strong lithological control on where channels flow. However, an approach where channel network structure is quantified, is required to be able to indicate for instance how increasing levels of lithological control lead, gradually or suddenly, to a trellis-type drainage network Our contribution aims to aid this transition to a quantitative analysis of channel networks. First, to establish the range of typically occurring channel network properties, we selected 30 examples of traditional drainage network types from around the world. For each of these, we calculated a set of topological and geometric properties, such as total drainage length, average length of a channel segment and the average angle of intersection of channel segments. A decision tree was used to formalize the relation between these newly quantified properties on the one hand, and traditional network types on the other hand. Then, to explore how variations in lithological and geomorphic boundary conditions affect channel network structure, we ran a set of experiments with landscape evolution model Landlab. For each simulated channel network, the same set of topological and geometric properties was calculated as for the 30 real-world channel networks. The latter were used for a first, visual evaluation to find out whether a simulated network that looked, for instance, rectangular, also had the same set of properties as real-world rectangular channel networks. Ultimately, the relation between these properties and the imposed lithological and geomorphic boundary conditions was explored using simple bivariate statistics.

A quantized microwave quadrupole insulator with topologically protected corner states

NASA Astrophysics Data System (ADS)

Peterson, Christopher W.; Benalcazar, Wladimir A.; Hughes, Taylor L.; Bahl, Gaurav

2018-03-01

The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state. This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator and the quantum spin Hall insulator, as well as quantized adiabatic pumping processes. A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments, revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials—a quantized quadrupole topological insulator—produced using a gigahertz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase using spectroscopic measurements and by identifying corner states that result from the bulk topology. In addition, we test the critical prediction that these corner states are protected by the topology of the bulk, and are not due to surface artefacts, by deforming the edges of the crystal lattice from the topological to the trivial regime. Our results provide conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topological insulators.

Topological Maxwell Metal Bands in a Superconducting Qutrit

NASA Astrophysics Data System (ADS)

Tan, Xinsheng; Zhang, Dan-Wei; Liu, Qiang; Xue, Guangming; Yu, Hai-Feng; Zhu, Yan-Qing; Yan, Hui; Zhu, Shi-Liang; Yu, Yang

2018-03-01

We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits. An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Threefold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one.

Disordered topological wires in a momentum-space lattice

NASA Astrophysics Data System (ADS)

Meier, Eric; An, Fangzhao; Gadway, Bryce

2017-04-01

One of the most interesting aspects of topological systems is the presence of boundary modes which remain robust in the presence of weak disorder. We explore this feature in the context of one-dimensional (1D) topological wires where staggered tunneling strengths lead to the creation of a mid-gap state in the lattice band structure. Using Bose-condensed 87Rb atoms in a 1D momentum-space lattice, we probe the robust topological character of this model when subjected to both site energy and tunneling disorder. We observe a transition to a topologically trivial phase when tailored disorder is applied, which we detect through both charge-pumping and Hamiltonian-quenching protocols. In addition, we report on efforts to probe the influence of interactions in topological momentum-space lattices.

Effects of electronic interactions near the topological semimetal-insulator quantum phase transition in two dimensions

NASA Astrophysics Data System (ADS)

Roy, Bitan; Foster, Matthew

The quasiparticle dispersion of gapless excitations residing at the quantum critical point (QCP) separating a two dimensional topological Dirac semimetal and a symmetry preserving band insulator, displays distinct power-law dependence with various components of spatial momenta. In this talk first I will review scaling of various thermodynamic and transport quantities at this QCP. Next I will demonstrate that even though such noninteracting QCP is stable against sufficiently weak but generic short-range interaction, the direct transition between the Dirac semimetal and band insulator can either (i) become a fluctuation driven first order transition, or (ii) get eliminated by an intervening broken symmetry phase, with staggered pattern in charge or spin being two prominent candidates, for sufficiently strong interactions. The novel quantum critical phenomena associated with the instability of critical excitations toward the formation of various broken symmetry phases will be discussed. Relevance of our study in strained graphene, black phosphorus, pressured organic compounds and oxide heterostructure will be highlighted. Welch Foundation Grant No. C-1809, NSF CAREER Grant No. DMR-1552327.

Visualizing nD Point Clouds as Topological Landscape Profiles to Guide Local Data Analysis

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

Oesterling, Patrick; Heine, Christian; Weber, Gunther H.

2012-05-04

Analyzing high-dimensional point clouds is a classical challenge in visual analytics. Traditional techniques, such as projections or axis-based techniques, suffer from projection artifacts, occlusion, and visual complexity.We propose to split data analysis into two parts to address these shortcomings. First, a structural overview phase abstracts data by its density distribution. This phase performs topological analysis to support accurate and non-overlapping presentation of the high-dimensional cluster structure as a topological landscape profile. Utilizing a landscape metaphor, it presents clusters and their nesting as hills whose height, width, and shape reflect cluster coherence, size, and stability, respectively. A second local analysis phasemore » utilizes this global structural knowledge to select individual clusters or point sets for further, localized data analysis. Focusing on structural entities significantly reduces visual clutter in established geometric visualizations and permits a clearer, more thorough data analysis. In conclusion, this analysis complements the global topological perspective and enables the user to study subspaces or geometric properties, such as shape.« less

Attribute and topology based change detection in a constellation of previously detected objects

DOEpatents

Paglieroni, David W.; Beer, Reginald N.

2016-01-19

A system that applies attribute and topology based change detection to networks of objects that were detected on previous scans of a structure, roadway, or area of interest. The attributes capture properties or characteristics of the previously detected objects, such as location, time of detection, size, elongation, orientation, etc. The topology of the network of previously detected objects is maintained in a constellation database that stores attributes of previously detected objects and implicitly captures the geometrical structure of the network. A change detection system detects change by comparing the attributes and topology of new objects detected on the latest scan to the constellation database of previously detected objects.

Geometry, topology, and string theory

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

Varadarajan, Uday

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

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.

Fundamental Fermions (e.g. Neutrinos) as Topological Objects

NASA Astrophysics Data System (ADS)

Fitzpatrick, Gerald L.

1999-05-01

A new internal ``macroscopic'' description of fundamental fermions based on a matrix-generalization (F) of the scalar fermion-number f, predicts that only three families of quarks and leptons, and their associated neutrinos (ν_e, ν_μ and ν_τ), exist [1]. Moreover, this description places important phtopological constraints on neutrino mixtures [2]. With respect to F, the topology of the νe (ν_μ or ν_τ) is that of a cylinder (Möbius strip). Assuming that topology-changing neutrino-neutrino transitions are suppressed (e.g., one cannot continuously deform a donut into a sphere), while topology-maintaining transitions are relatively enhanced, one may have an explanation for short-distance observations of (nearly) maximal ν_μ-ν_τ mixing [3]. To test this idea, simple topological arguments were used to deduce a matrix describing long-distance neutrino mixtures, which is phidentical to that proposed by Georgi and Glashow on different grounds [4]. Experimental confirmation of this prediction would support the new description, which requires the νe and (ν_μ or ν_τ) to start ``life'' as topologically-distinct quantum objects.l [1] http://www.amazon.com/exec/obidos/ISBN=0965569500, [2] G. L. Fitzpatrick, aps1999feb12\\underbar001 at http://publish.aps.org/eprint/, [3] hep-ex/981001, [4] hep-ph/9808293, p. 5, Eq. 20.

Topological defects in two-dimensional liquid crystals confined by a box

NASA Astrophysics Data System (ADS)

Yao, Xiaomei; Zhang, Hui; Chen, Jeff Z. Y.

2018-05-01

When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.

Renormalization group approach to symmetry protected topological phases

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Schnyder, Andreas P.; Chen, Wei

2018-04-01

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Multifractality and Network Analysis of Phase Transition

PubMed Central

Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang

2017-01-01

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414

A geometric projection method for designing three-dimensional open lattices with inverse homogenization

DOE PAGES

Watts, Seth; Tortorelli, Daniel A.

2017-04-13

Topology optimization is a methodology for assigning material or void to each point in a design domain in a way that extremizes some objective function, such as the compliance of a structure under given loads, subject to various imposed constraints, such as an upper bound on the mass of the structure. Geometry projection is a means to parameterize the topology optimization problem, by describing the design in a way that is independent of the mesh used for analysis of the design's performance; it results in many fewer design parameters, necessarily resolves the ill-posed nature of the topology optimization problem, andmore » provides sharp descriptions of the material interfaces. We extend previous geometric projection work to 3 dimensions and design unit cells for lattice materials using inverse homogenization. We perform a sensitivity analysis of the geometric projection and show it has smooth derivatives, making it suitable for use with gradient-based optimization algorithms. The technique is demonstrated by designing unit cells comprised of a single constituent material plus void space to obtain light, stiff materials with cubic and isotropic material symmetry. Here, we also design a single-constituent isotropic material with negative Poisson's ratio and a light, stiff material comprised of 2 constituent solids plus void space.« less

A geometric projection method for designing three-dimensional open lattices with inverse homogenization

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

Watts, Seth; Tortorelli, Daniel A.

Topology optimization is a methodology for assigning material or void to each point in a design domain in a way that extremizes some objective function, such as the compliance of a structure under given loads, subject to various imposed constraints, such as an upper bound on the mass of the structure. Geometry projection is a means to parameterize the topology optimization problem, by describing the design in a way that is independent of the mesh used for analysis of the design's performance; it results in many fewer design parameters, necessarily resolves the ill-posed nature of the topology optimization problem, andmore » provides sharp descriptions of the material interfaces. We extend previous geometric projection work to 3 dimensions and design unit cells for lattice materials using inverse homogenization. We perform a sensitivity analysis of the geometric projection and show it has smooth derivatives, making it suitable for use with gradient-based optimization algorithms. The technique is demonstrated by designing unit cells comprised of a single constituent material plus void space to obtain light, stiff materials with cubic and isotropic material symmetry. Here, we also design a single-constituent isotropic material with negative Poisson's ratio and a light, stiff material comprised of 2 constituent solids plus void space.« less

Knot soliton in DNA and geometric structure of its free-energy density.

PubMed

Wang, Ying; Shi, Xuguang

2018-03-01

In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.

Laser-irradiated Kondo insulators: Controlling the Kondo effect and topological phases

NASA Astrophysics Data System (ADS)

Takasan, Kazuaki; Nakagawa, Masaya; Kawakami, Norio

2017-09-01

We investigate theoretically the nature of laser-irradiated Kondo insulators. Using Floquet theory and the slave-boson approach, we study a periodic Anderson model and derive an effective model that describes laser-irradiated Kondo insulators. In this model, we find two generic effects induced by laser light. One is dynamical localization, which suppresses hopping and hybridization. The other is laser-induced hopping and hybridization, which can be interpreted as synthetic spin-orbit coupling or a magnetic field. The first effect drastically changes the behavior of the Kondo effect. In particular, the Kondo effect under laser light qualitatively changes its character depending on whether the hybridization is on-site or off-site. The second effect triggers topological phase transitions. In topological Kondo insulators, linearly polarized laser light realizes phase transitions between trivial, weak topological, and strong topological Kondo insulators. Moreover, circularly polarized laser light breaks time-reversal symmetry and induces Weyl semimetallic phases. Our results make it possible to dynamically control the Kondo effect and topological phases in heavy-fermion systems. We also discuss experimental setups to detect the signatures.

Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators

NASA Astrophysics Data System (ADS)

Mohanta, Narayan; Kampf, Arno P.; Kopp, Thilo

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like ``spin'' texture in momentum space. Here, we apply the previously formulated low-energy model for Bi2Se3, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transition between two topologically distinct phases. The topological phase transition takes place without energy gap closing at the Fermi level and leaves the transverse Hall conductance unchanged and quantized to e2 / 2 h . The momentum-space skyrmion texture persists in a finite field range. It may find its realization in hybrid heterostructures with an interface between a three-dimensional topological insulator and a ferromagnetic insulator. The work was supported by the Deutsche Forschungsgemeinschaft through TRR 80.

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.

Floquet topological polaritons in semiconductor microcavities

NASA Astrophysics Data System (ADS)

Ge, R.; Broer, W.; Liew, T. C. H.

2018-05-01

We propose and model Floquet topological polaritons in semiconductor microcavities, using the interference of frequency-detuned coherent fields to provide a time-periodic potential. For arbitrarily weak field strength, where the Floquet frequency is larger than the relevant bandwidth of the system, a Chern insulator is obtained. As the field strength is increased, a topological phase transition is observed with an unpaired Dirac cone proclaiming the anomalous Floquet topological insulator. As the relevant bandwidth increases even further, an exotic Chern insulator with flatband is observed with unpaired Dirac cone at the second critical point. Considering the polariton spin degree of freedom, we find that the choice of field polarization allows oppositely polarized polaritons to either copropagate or counterpropagate in chiral edge states.

A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology

PubMed Central

Dabaghian, Y.; Mémoli, F.; Frank, L.; Carlsson, G.

2012-01-01

An animal's ability to navigate through space rests on its ability to create a mental map of its environment. The hippocampus is the brain region centrally responsible for such maps, and it has been assumed to encode geometric information (distances, angles). Given, however, that hippocampal output consists of patterns of spiking across many neurons, and downstream regions must be able to translate those patterns into accurate information about an animal's spatial environment, we hypothesized that 1) the temporal pattern of neuronal firing, particularly co-firing, is key to decoding spatial information, and 2) since co-firing implies spatial overlap of place fields, a map encoded by co-firing will be based on connectivity and adjacency, i.e., it will be a topological map. Here we test this topological hypothesis with a simple model of hippocampal activity, varying three parameters (firing rate, place field size, and number of neurons) in computer simulations of rat trajectories in three topologically and geometrically distinct test environments. Using a computational algorithm based on recently developed tools from Persistent Homology theory in the field of algebraic topology, we find that the patterns of neuronal co-firing can, in fact, convey topological information about the environment in a biologically realistic length of time. Furthermore, our simulations reveal a “learning region” that highlights the interplay between the parameters in combining to produce hippocampal states that are more or less adept at map formation. For example, within the learning region a lower number of neurons firing can be compensated by adjustments in firing rate or place field size, but beyond a certain point map formation begins to fail. We propose that this learning region provides a coherent theoretical lens through which to view conditions that impair spatial learning by altering place cell firing rates or spatial specificity. PMID:22912564

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

Generalized GW+Boltzmann Approach for the Description of Ultrafast Electron Dynamics in Topological Insulators

PubMed Central

Battiato, Marco; Sánchez-Barriga, Jaime

2017-01-01

Quantum-phase transitions between trivial insulators and topological insulators differ from ordinary metal-insulator transitions in that they arise from the inversion of the bulk band structure due to strong spin–orbit coupling. Such topological phase transitions are unique in nature as they lead to the emergence of topological surface states which are characterized by a peculiar spin texture that is believed to play a central role in the generation and manipulation of dissipationless surface spin currents on ultrafast timescales. Here, we provide a generalized GW+Boltzmann approach for the description of ultrafast dynamics in topological insulators driven by electron–electron and electron–phonon scatterings. Taking the prototypical insulator Bi2Te3 as an example, we test the robustness of our approach by comparing the theoretical prediction to results of time- and angle-resolved photoemission experiments. From this comparison, we are able to demonstrate the crucial role of the excited spin texture in the subpicosecond relaxation of transient electrons, as well as to accurately obtain the magnitude and strength of electron–electron and electron–phonon couplings. Our approach could be used as a generalized theory for three-dimensional topological insulators in the bulk-conducting transport regime, paving the way for the realization of a unified theory of ultrafast dynamics in topological materials. PMID:28773171

Generalized GW+Boltzmann Approach for the Description of Ultrafast Electron Dynamics in Topological Insulators.

PubMed

Battiato, Marco; Aguilera, Irene; Sánchez-Barriga, Jaime

2017-07-17

Quantum-phase transitions between trivial insulators and topological insulators differ from ordinary metal-insulator transitions in that they arise from the inversion of the bulk band structure due to strong spin-orbit coupling. Such topological phase transitions are unique in nature as they lead to the emergence of topological surface states which are characterized by a peculiar spin texture that is believed to play a central role in the generation and manipulation of dissipationless surface spin currents on ultrafast timescales. Here, we provide a generalized G W +Boltzmann approach for the description of ultrafast dynamics in topological insulators driven by electron-electron and electron-phonon scatterings. Taking the prototypical insulator Bi 2 Te 3 as an example, we test the robustness of our approach by comparing the theoretical prediction to results of time- and angle-resolved photoemission experiments. From this comparison, we are able to demonstrate the crucial role of the excited spin texture in the subpicosecond relaxation of transient electrons, as well as to accurately obtain the magnitude and strength of electron-electron and electron-phonon couplings. Our approach could be used as a generalized theory for three-dimensional topological insulators in the bulk-conducting transport regime, paving the way for the realization of a unified theory of ultrafast dynamics in topological materials.

Topological quantum pump in serpentine-shaped semiconducting narrow channels

NASA Astrophysics Data System (ADS)

Pandey, Sudhakar; Scopigno, Niccoló; Gentile, Paola; Cuoco, Mario; Ortix, Carmine

2018-06-01

We propose and analyze theoretically a one-dimensional solid-state electronic setup that operates as a topological charge pump in the complete absence of superimposed oscillating local voltages. The system consists of a semiconducting narrow channel with a strong Rashba spin-orbit interaction patterned in a mesoscale serpentine shape. A rotating planar magnetic field serves as the external ac perturbation, and cooperates with the Rashba spin-orbit interaction, which is modulated by the geometric curvature of the electronic channel to realize the topological pumping protocol, originally introduced by Thouless, in a different fashion. We expect the precise pumping of electric charges in our mesoscopic quantum device to be relevant for quantum metrology purposes.

Generalized hedgehog ansatz and Gribov copies in regions with nontrivial topologies

NASA Astrophysics Data System (ADS)

Canfora, Fabrizio; Salgado-Rebolledo, Patricio

2013-02-01

In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with nontrivial topologies but flat metric, (such as closed tubes S1×D2, or R×T2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond spherical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with nontrivial topologies.

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.

Entropy in Spacetime and Topological Hair

NASA Astrophysics Data System (ADS)

Hyun, Young-Hwan; Kim, Yoonbai

2018-01-01

Global topological soliton of the hedgehog ansatz is added to de Sitter spacetime in arbitrary dimensions larger than three, and then thermodynamic law is checked at the cosmological horizon. All geometric and thermodynamic quantities are varied in the presence of a long-range interacting matter distribution with negative pressure, however the entropy-area relation is satisfied in the exact form. Its geometry involves deficit solid angle but maintains a single horizon which allows unique temperature normalization, different from the case of Schwarzschild-de Sitter spacetime.

Accurate airway centerline extraction based on topological thinning using graph-theoretic analysis.

PubMed

Bian, Zijian; Tan, Wenjun; Yang, Jinzhu; Liu, Jiren; Zhao, Dazhe

2014-01-01

The quantitative analysis of the airway tree is of critical importance in the CT-based diagnosis and treatment of popular pulmonary diseases. The extraction of airway centerline is a precursor to identify airway hierarchical structure, measure geometrical parameters, and guide visualized detection. Traditional methods suffer from extra branches and circles due to incomplete segmentation results, which induce false analysis in applications. This paper proposed an automatic and robust centerline extraction method for airway tree. First, the centerline is located based on the topological thinning method; border voxels are deleted symmetrically to preserve topological and geometrical properties iteratively. Second, the structural information is generated using graph-theoretic analysis. Then inaccurate circles are removed with a distance weighting strategy, and extra branches are pruned according to clinical anatomic knowledge. The centerline region without false appendices is eventually determined after the described phases. Experimental results show that the proposed method identifies more than 96% branches and keep consistency across different cases and achieves superior circle-free structure and centrality.

Geometrical and topological methods in optimal control theory

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

Vakhrameev, S.A.

1995-10-05

The present article will appear 30 years after Hermann`s report was published; in that report, the foundations of a new direction in optimal control theory, later called geometrical, were laid. The main purpose of this article is to present an overview of some of the basic results obtained in this direction. Each survey is subjective, and our work is no exception: the choice of themes and the degree of detail of their presentation are determined mainly by the author`s own interests (and by his own knowledge); the brief exposition, or, in general, the neglect of some aspects of the theorymore » does not reflect their significance. As some compensation for these gaps (which refer mainly to discrete-time systems, to algebraic aspects of the theory, and, partially, to structural theory) there is a rather long reference list presented in the article (it goes up to 1993 and consists, basically, of papers reviewed in the review journal {open_quotes}Matematika{close_quotes} during last 30 years).« less

Topological Phases in the Real World

NASA Astrophysics Data System (ADS)

Hsu, Yi-Ting

The experimental discovery and subsequent theoretical understanding of the integer quantum Hall effect, the first known topological phase, has started a revolutionary breakthrough in understanding states of matter since its discovery four decades ago. Topological phases are predicted to have many generic signatures resulting from their underlying topological nature, such as quantized Hall transport, robust boundary states, and possible fractional excitations. The intriguing nature of these signatures and their potential applications in quantum computation has intensely fueled the efforts of the physics community to materialize topological phases. Among various topological phases initially predicted on theoretical grounds, chiral topological superconductors and time-reversal symmetric topological insulators (TI) in three dimension (3D) are two promising candidates for experimental realization and application. The family of materials, Bi2X3 (X = Se, Te), has been predicted and shown experimentally to be time-reversal symmetric 3D TIs through the observation of robust Dirac surface states with Rashba-type spin-winding. Due to their robust surface states with spin-windings, these 3D TIs are expected to be promising materials for producing large spin-transfer torques which are advantageous for spintronics application. As for topological superconductors, despite the exotic excitations that have been extensively proposed as qubits for topological quantum computing, materials hosting topological superconductivity are rare to date and the leading candidate in two dimensions (2D), Sr 2RuO4, has a low transition temperature (Tc ). The goal of my phd study is to push forward the current status of realization of topological phases by materializing higher Tc topological superconductors and investigating the stability of Dirac surface states in 3D TIs. In the first part of this thesis, I will discuss our double-pronged objective for topological superconductors: to propose how to

Realizing high-quality ultralarge momentum states and ultrafast topological transitions using semiconductor hyperbolic metamaterials

DOE PAGES

Campione, Salvatore; Liu, Sheng; Luk, Ting S.; ...

2015-08-05

We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation ofmore » the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.« less

Phonon-Induced Topological Transition to a Type-II Weyl Semimetal

NASA Astrophysics Data System (ADS)

Wang, Lin-Lin; Jo, Na Hyun; Wu, Yun; Kaminski, Adam; Canfield, Paul C.; Johnson, Duane D.

The emergence of topological quantum states requires certain combinations of crystalline symmetry with or without time reversal symmetry. Without restricting to searches for crystal structures with non-symmorphic symmetry operations in the space groups, we have studied the interplay between crystal symmetry, atomic displacements (lattice vibration), band degeneracy and topology. For a system with a full gap opening between the two band manifolds near the Fermi energy, we show that small atomic displacements (accessible via optical phonons near room temperature) can lower the symmetry to induce type-II Weyl points at the boundary between a pair of closely-lying electron and hole pockets. DOE Ames Laboratory LDRD.

Superconductivity in a Misfit Phase That Combines the Topological Crystalline Insulator Pb 1-xSn xSe with the CDW-Bearing Transition Metal Dichalcogenide TiSe 2

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

Luo, H.; Yan, K.; Pletikosic, I.

We report the characterization of the misfit compound (Pb 1-xSn xSe 2)1.16(TiSe 2) 2 for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally nonsuperconducting transition metal dichalcogenide TiSe 2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topological transition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductormore » at x = 0.4, for which the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol -1 K -2, the Debye temperature Θ D = 161 K, the normalized specific heat jump value ΔC/γT c = 1.38 and the electron-phonon constant value γ ep = 0.72, suggesting that (Pb 0.6Sn 0.4Se) 1.16(TiSe 2) 2 is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.« less

Superconductivity in a Misfit Phase That Combines the Topological Crystalline Insulator Pb 1-xSn xSe with the CDW-Bearing Transition Metal Dichalcogenide TiSe 2

DOE PAGES

Luo, H.; Yan, K.; Pletikosic, I.; ...

2016-05-13

We report the characterization of the misfit compound (Pb 1-xSn xSe 2)1.16(TiSe 2) 2 for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally nonsuperconducting transition metal dichalcogenide TiSe 2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topological transition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductormore » at x = 0.4, for which the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol -1 K -2, the Debye temperature Θ D = 161 K, the normalized specific heat jump value ΔC/γT c = 1.38 and the electron-phonon constant value γ ep = 0.72, suggesting that (Pb 0.6Sn 0.4Se) 1.16(TiSe 2) 2 is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.« less

Manipulating topological-insulator properties using quantum confinement

NASA Astrophysics Data System (ADS)

Kotulla, M.; Zülicke, U.

2017-07-01

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This work considers the specific case of quantum-well confinement defining two-dimensional layers. Based on the effective-Hamiltonian description of bulk topological insulators, and using a harmonic-oscillator potential as an example for a softer-than-hard-wall confinement, we have studied the interplay of band inversion and size quantization. Our model system provides a useful platform for systematic study of the transition between the normal and topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron-hole asymmetry are disentangled and their respective physical consequences elucidated.

Topological characters in Fe (Te1 -xSex ) thin films

NASA Astrophysics Data System (ADS)

Wu, Xianxin; Qin, Shengshan; Liang, Yi; Fan, Heng; Hu, Jiangping

2016-03-01

We investigate topological properties in the Fe(Te,Se) thin films. We find that the single layer FeTe1 -xSex has nontrivial Z2 topological invariance which originates from the parity exchange at the Γ point of the Brillouin zone. The nontrivial topology is mainly controlled by the Te(Se) height. Adjusting the anion height, which can be realized as the function of lattice constants and x in FeTe1 -xSex , can drive a topological phase transition. In a bulk material, the two-dimensional Z2 topology invariance is extended to a strong three-dimensional one. In a thin film, we predict that the topological invariance oscillates with the number of layers. The results can also be applied to iron pnictides. Our research establishes FeTe1 -xSex as a unique system to integrate high-Tc superconductivity and topological properties in a single electronic structure.

Geometrical model for martensitic phase transitions: Understanding criticality and weak universality during microstructure growth.

PubMed

Torrents, Genís; Illa, Xavier; Vives, Eduard; Planes, Antoni

2017-01-01

A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size L×L and in the thermodynamic limit L→∞, where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.

Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges

NASA Astrophysics Data System (ADS)

Cerjan, Alexander; Xiao, Meng; Yuan, Luqi; Fan, Shanhui

2018-02-01

We provide a systematic study of non-Hermitian topologically charged systems. Starting from a Hermitian Hamiltonian supporting Weyl points with arbitrary topological charge, adding a non-Hermitian perturbation transforms the Weyl points to one-dimensional exceptional contours. We analytically prove that the topological charge is preserved on the exceptional contours. In contrast to Hermitian systems, the addition of gain and loss allows for a new class of topological phase transition: when two oppositely charged exceptional contours touch, the topological charge can dissipate without opening a gap. These effects can be demonstrated in realistic photonics and acoustics systems.

Optical and Casimir effects in topological materials

NASA Astrophysics Data System (ADS)

Wilson, Justin H.

Two major electromagnetic phenomena, magneto-optical effects and the Casimir effect, have seen much theoretical and experimental use for many years. On the other hand, recently there has been an explosion of theoretical and experimental work on so-called topological materials, and a natural question to ask is how such electromagnetic phenomena change with these novel materials. Specifically, we will consider are topological insulators and Weyl semimetals. When Dirac electrons on the surface of a topological insulator are gapped or Weyl fermions in the bulk of a Weyl semimetal appear due to time-reversal symmetry breaking, there is a resulting quantum anomalous Hall effect (2D in one case and bulk 3D in the other, respectively). For topological insulators, we investigate the role of localized in-gap states which can leave their own fingerprints on the magneto-optics and can therefore be probed. We have shown that these states resonantly contribute to the Hall conductivity and are magneto-optically active. For Weyl semimetals we investigate the Casimir force and show that with thickness, chemical potential, and magnetic field, a repulsive and tunable Casimir force can be obtained. Additionally, various values of the parameters can give various combinations of traps and antitraps. We additionally probe the topological transition called a Lifshitz transition in the band structure of a material and show that in a Casimir experiment, one can observe a non-analytic "kink'' in the Casimir force across such a transition. The material we propose is a spin-orbit coupled semiconductor with large g-factor that can be magnetically tuned through such a transition. Additionally, we propose an experiment with a two-dimensional metal where weak localization is tuned with an applied field in order to definitively test the effect of diffusive electrons on the Casimir force---an issue that is surprisingly unresolved to this day. Lastly, we show how the time-continuous coherent state

Multiple topological electronic phases in superconductor MoC

NASA Astrophysics Data System (ADS)

Huang, Angus; Smith, Adam D.; Schwinn, Madison; Lu, Qiangsheng; Chang, Tay-Rong; Xie, Weiwei; Jeng, Horng-Tay; Bian, Guang

2018-05-01

The search for a superconductor with non-s -wave pairing is important not only for understanding unconventional mechanisms of superconductivity but also for finding new types of quasiparticles such as Majorana bound states. Materials with both topological band structure and superconductivity are promising candidates as p +i p superconducting states can be generated through pairing the spin-polarized topological surface states. In this work, the electronic and phonon properties of the superconductor molybdenum carbide (MoC) are studied with first-principles methods. Our calculations show that nontrivial band topology and s -wave Bardeen-Cooper-Schrieffer superconductivity coexist in two structural phases of MoC, namely the cubic α and hexagonal γ phases. The α phase is a strong topological insulator and the γ phase is a topological nodal-line semimetal with drumhead surface states. In addition, hole doping can stabilize the crystal structure of the α phase and elevate the transition temperature in the γ phase. Therefore, MoC in different structural forms can be a practical material platform for studying topological superconductivity.

Spin-polarized surface resonances accompanying topological surface state formation

DOE PAGES

Jozwiak, Chris; Sobota, Jonathan A.; Gotlieb, Kenneth; ...

2016-10-14

Topological insulators host spin-polarized surface states born out of the energetic inversion of bulk bands driven by the spin-orbit interaction. Here we discover previously unidentified consequences of band-inversion on the surface electronic structure of the topological insulator Bi 2Se 3. By performing simultaneous spin, time, and angle-resolved photoemission spectroscopy, we map the spin-polarized unoccupied electronic structure and identify a surface resonance which is distinct from the topological surface state, yet shares a similar spin-orbital texture with opposite orientation. Its momentum dependence and spin texture imply an intimate connection with the topological surface state. Calculations show these two distinct states canmore » emerge from trivial Rashba-like states that change topology through the spin-orbit-induced band inversion. As a result, this work thus provides a compelling view of the coevolution of surface states through a topological phase transition, enabled by the unique capability of directly measuring the spin-polarized unoccupied band structure.« less

Spin-polarized surface resonances accompanying topological surface state formation

PubMed Central

Jozwiak, Chris; Sobota, Jonathan A.; Gotlieb, Kenneth; Kemper, Alexander F.; Rotundu, Costel R.; Birgeneau, Robert J.; Hussain, Zahid; Lee, Dung-Hai; Shen, Zhi-Xun; Lanzara, Alessandra

2016-01-01

Topological insulators host spin-polarized surface states born out of the energetic inversion of bulk bands driven by the spin-orbit interaction. Here we discover previously unidentified consequences of band-inversion on the surface electronic structure of the topological insulator Bi2Se3. By performing simultaneous spin, time, and angle-resolved photoemission spectroscopy, we map the spin-polarized unoccupied electronic structure and identify a surface resonance which is distinct from the topological surface state, yet shares a similar spin-orbital texture with opposite orientation. Its momentum dependence and spin texture imply an intimate connection with the topological surface state. Calculations show these two distinct states can emerge from trivial Rashba-like states that change topology through the spin-orbit-induced band inversion. This work thus provides a compelling view of the coevolution of surface states through a topological phase transition, enabled by the unique capability of directly measuring the spin-polarized unoccupied band structure. PMID:27739428

Roots and decompositions of three-dimensional topological objects

NASA Astrophysics Data System (ADS)

Matveev, Sergei V.

2012-06-01

In 1942 M.H.A. Newman formulated and proved a simple lemma of great importance for various fields of mathematics, including algebra and the theory of Gröbner-Shirshov bases. Later it was called the Diamond Lemma, since its key construction was illustrated by a diamond-shaped diagram. In 2005 the author suggested a new version of this lemma suitable for topological applications. This paper gives a survey of results on the existence and uniqueness of prime decompositions of various topological objects: three-dimensional manifolds, knots in thickened surfaces, knotted graphs, three-dimensional orbifolds, and knotted theta-curves in three-dimensional manifolds. As it turned out, all these topological objects admit a prime decomposition, although it is not unique in some cases (for example, in the case of orbifolds). For theta-curves and knots of geometric degree 1 in a thickened torus, the algebraic structure of the corresponding semigroups can be completely described. In both cases the semigroups are quotients of free groups by explicit commutation relations. Bibliography: 33 titles.

Topological and trivial magnetic oscillations in nodal loop semimetals

NASA Astrophysics Data System (ADS)

Oroszlány, László; Dóra, Balázs; Cserti, József; Cortijo, Alberto

2018-05-01

Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi-Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is identified from purely trivial oscillations, arising from the Landau levels of a normal two dimensional (2D) electron gas, to a phase where oscillations of topological and trivial origin coexist, originating from 2D massless Dirac and semi-Dirac points, respectively. These could in principle be directly identified in current experiments.

Mechanical Model of Geometric Cell and Topological Algorithm for Cell Dynamics from Single-Cell to Formation of Monolayered Tissues with Pattern

PubMed Central

Kachalo, Sëma; Naveed, Hammad; Cao, Youfang; Zhao, Jieling; Liang, Jie

2015-01-01

Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly

Control of defect localization in crystalline wrinkling by curvature and topology

NASA Astrophysics Data System (ADS)

Lopez Jimenez, Francisco

We investigate the influence of curvature and topology on crystalline wrinkling patterns in generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling or folding processes. Generally, this study suggests that bilayer systems provide an inexpensive yet valuable experimental test-bed for exploring the effects of geometrically induced forces on assemblies of topological charges. Joint work with Norbert Stoop, Romain Lagrange, Jorn Dunkel and Pedro M. Reis.

Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions

PubMed Central

Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi

2015-01-01

In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models. PMID:25775452

Wire constructions of Abelian topological phases in three or more dimensions

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher

2016-05-01

Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theoretical tools available to study such systems. In three dimensions, however, much less is known about topological phases. Since the theoretical arsenal in this case is smaller, it stands to reason that wire constructions, which are based on one-dimensional physics, could play a useful role in developing a greater microscopic understanding of three-dimensional topological phases. In this paper, we provide a comprehensive strategy, based on the geometric arrangement of commuting projectors in the toric code, to generate and characterize coupled-wire realizations of strongly interacting three-dimensional topological phases. We show how this method can be used to construct pointlike and linelike excitations, and to determine the topological degeneracy. We also point out how, with minor modifications, the machinery already developed in two dimensions can be naturally applied to study the surface states of these systems, a fact that has implications for the study of surface topological order. Finally, we show that the strategy developed for the construction of three-dimensional topological phases generalizes readily to arbitrary dimensions, vastly expanding the existing landscape of coupled-wire theories. Throughout the paper, we discuss Zm topological order in three and four dimensions as a concrete example of this approach, but the approach itself is not limited to this type of topological order.

Geometrical force constraint method for vessel and x-ray angiogram simulation.

PubMed

Song, Shuang; Yang, Jian; Fan, Jingfan; Cong, Weijian; Ai, Danni; Zhao, Yitian; Wang, Yongtian

2016-01-01

This study proposes a novel geometrical force constraint method for 3-D vasculature modeling and angiographic image simulation. For this method, space filling force, gravitational force, and topological preserving force are proposed and combined for the optimization of the topology of the vascular structure. The surface covering force and surface adhesion force are constructed to drive the growth of the vasculature on any surface. According to the combination effects of the topological and surface adhering forces, a realistic vasculature can be effectively simulated on any surface. The image projection of the generated 3-D vascular structures is simulated according to the perspective projection and energy attenuation principles of X-rays. Finally, the simulated projection vasculature is fused with a predefined angiographic mask image to generate a realistic angiogram. The proposed method is evaluated on a CT image and three generally utilized surfaces. The results fully demonstrate the effectiveness and robustness of the proposed method.

Topological structure of dictionary graphs

NASA Astrophysics Data System (ADS)

Fukś, Henryk; Krzemiński, Mark

2009-09-01

We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.

Geometric constraints for shape and topology optimization in architectural design

NASA Astrophysics Data System (ADS)

Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael

2017-06-01

This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

NASA Astrophysics Data System (ADS)

Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang

2017-10-01

The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

Classification of topological insulators and superconductors in three spatial dimensions

NASA Astrophysics Data System (ADS)

Ryu, Shinsei; Schnyder, Andreas; Furusaki, Akira; Ludwig, Andreas

2009-03-01

We systematically study topological phases of insulators and superconductors (or superfluids) in 3D. We find that there exist 3D topologically non-trivial 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 there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in 3D, 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 non-trivial phases can be realized as time-reversal invariant superconductors, and 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 2D surface, they support stable surface Dirac (Majorana) fermion modes.

Topology Change and the Unity of Space

NASA Astrophysics Data System (ADS)

Callender, Craig; Weingard, Robert

Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general relativity (modulo considerations about energy conditions) allows virtually unrestrained spatial topology change in four dimensions. We also survey the situation in many other dimensions of interest. However, topology change comes with a cost: a famous theorem by Robert Geroch shows that, for many interesting types of such change, transitions of spatial topology imply the existence of closed timelike curves or temporal non-orientability. Ways of living with this theorem and of evading it are discussed.

Supersymmetrical bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states

PubMed Central

Afzal, Muhammad Imran; Lee, Yong Tak

2016-01-01

Von Neumann and Wigner theorized the bounding and anti-crossing of eigenstates. Experiments have demonstrated that owing to anti-crossing and similar radiation rates, the graphene-like resonance of inhomogeneously strained photonic eigenstates can generate a pseudomagnetic field, bandgaps and Landau levels, whereas exponential or dissimilar rates induce non-Hermicity. Here, we experimentally demonstrate higher-order supersymmetry and quantum phase transitions by resonance between similar one-dimensional lattices. The lattices consisted of inhomogeneous strain-like phases of triangular solitons. The resonance created two-dimensional, inhomogeneously deformed photonic graphene. All parent eigenstates were annihilated. Eigenstates of mildly strained solitons were annihilated at similar rates through one tail and generated Hermitian bounded eigenstates. The strongly strained solitons with positive phase defects were annihilated at exponential rates through one tail, which bounded eigenstates through non-Hermitianally generated exceptional points. Supersymmetry was evident, with preservation of the shapes and relative phase differences of the parent solitons. Localizations of energies generated from annihilations of mildly and strongly strained soliton eigenstates were responsible for geometrical (Berry) and topological phase transitions, respectively. Both contributed to generating a quantum Zeno phase, whereas only strong twists generated topological (Anderson) localization. Anti-bunching-like condensation was also observed. PMID:27966596

Elastic and failure response of imperfect three-dimensional metallic lattices: the role of geometric defects induced by Selective Laser Melting

NASA Astrophysics Data System (ADS)

Liu, Lu; Kamm, Paul; García-Moreno, Francisco; Banhart, John; Pasini, Damiano

2017-10-01

This paper examines three-dimensional metallic lattices with regular octet and rhombicuboctahedron units fabricated with geometric imperfections via Selective Laser Sintering. We use X-ray computed tomography to capture morphology, location, and distribution of process-induced defects with the aim of studying their role in the elastic response, damage initiation, and failure evolution under quasi-static compression. Testing results from in-situ compression tomography show that each lattice exhibits a distinct failure mechanism that is governed not only by cell topology but also by geometric defects induced by additive manufacturing. Extracted from X-ray tomography images, the statistical distributions of three sets of defects, namely strut waviness, strut thickness variation, and strut oversizing, are used to develop numerical models of statistically representative lattices with imperfect geometry. Elastic and failure responses are predicted within 10% agreement from the experimental data. In addition, a computational study is presented to shed light into the relationship between the amplitude of selected defects and the reduction of elastic properties compared to their nominal values. The evolution of failure mechanisms is also explained with respect to strut oversizing, a parameter that can critically cause failure mode transitions that are not visible in defect-free lattices.

Spectral statistics of random geometric graphs

NASA Astrophysics Data System (ADS)

Dettmann, C. P.; Georgiou, O.; Knight, G.

2017-04-01

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short-range correlations in the level spacings of the spectrum via the nearest-neighbour and next-nearest-neighbour spacing distribution and long-range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter-dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdős-Rényi, Barabási-Albert and Watts-Strogatz random graphs.

EDITORIAL: Topological data analysis Topological data analysis

NASA Astrophysics Data System (ADS)

Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert

2011-12-01

Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide

EDITORIAL: Topological data analysis Topological data analysis

NASA Astrophysics Data System (ADS)

2011-12-01

Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide

Infrared spectroscopic characterization of dehydration and accompanying phase transition behaviors in NAT-topology zeolites

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

Wang, Hsiu-Wen; Bishop, David

2012-01-01

Relative humidity (PH2O, partial pressure of water)-dependent dehydration and accompanying phase transitions in NAT-topology zeolites (natrolite, scolecite, and mesolite) were studied under controlled temperature and known PH2O conditions by in situ diffuse-reflectance infrared Fourier transform spectroscopy and parallel X-ray powder diffraction. Dehydration was characterized by the disappearance of internal H2O vibrational modes. The loss of H2O molecules caused a sequence of structural transitions in which the host framework transformation path was coupled primarily via the thermal motion of guest Na?/Ca2? cations and H2O molecules. The observation of different interactions of H2O molecules and Na?/Ca2? cations with host aluminosilicate frameworks undermore » highand low-PH2O conditions indicated the development of different local strain fields, arising from cation H2O interactions in NAT-type channels. These strain fields influence the Si O/Al O bond strength and tilting angles within and between tetrahedra as the dehydration temperature is approached. The newly observed infrared bands (at 2,139 cm-1 in natrolite, 2,276 cm-1 in scolecite, and 2,176 and 2,259 cm-1 in mesolite) result from strong cation H2O Al Si framework interactions in NAT-type channels, and these bands can be used to evaluate the energetic evolution of Na?/Ca2? cations before and after phase transitions, especially for scolecite and mesolite. The 2,176 and 2,259 cm-1 absorption bands in mesolite also appear to be related to Na?/Ca2? order disorder that occur when mesolite loses its Ow4 H2O molecules.« less

Efficiently computing and deriving topological relation matrices between complex regions with broad boundaries

NASA Astrophysics Data System (ADS)

Du, Shihong; Guo, Luo; Wang, Qiao; Qin, Qimin

The extended 9-intersection matrix is used to formalize topological relations between uncertain regions while it is designed to satisfy the requirements at a concept level, and to deal with the complex regions with broad boundaries (CBBRs) as a whole without considering their hierarchical structures. In contrast to simple regions with broad boundaries, CBBRs have complex hierarchical structures. Therefore, it is necessary to take into account the complex hierarchical structure and to represent the topological relations between all regions in CBBRs as a relation matrix, rather than using the extended 9-intersection matrix to determine topological relations. In this study, a tree model is first used to represent the intrinsic configuration of CBBRs hierarchically. Then, the reasoning tables are presented for deriving topological relations between child, parent and sibling regions from the relations between two given regions in CBBRs. Finally, based on the reasoning, efficient methods are proposed to compute and derive the topological relation matrix. The proposed methods can be incorporated into spatial databases to facilitate geometric-oriented applications.

Pressure induced Ag 2Te polymorphs in conjunction with topological non trivial to metal transition

DOE PAGES

Zhu, J.; Oganov, A. R.; Feng, W. X.; ...

2016-08-01

Silver telluride (Ag 2Te) is well known as superionic conductor and topologica insulator with polymorphs. Pressure induced three phase transitions in Ag 2Te hav been reported in previous. Here, we experimentally identified high pressure phas above 13 GPa of Ag 2Te by using high pressure synchrotron x ray diffraction metho in combination with evolutionary crystal structure prediction, showing it crystallize into a monoclinic structure of space group C2/m with lattice parameters a = 6.081Å b = 5.744Å, c = 6.797 Å, β = 105.53°. The electronic properties measurements of Ag 2Te reveal that the topologically non-trivial semiconducting phase I andmore » semimetalli phase II previously predicated by theory transformed into bulk metals fo high pressure phases in consistent with the first principles calculations« less

Topology of polymer chains under nanoscale confinement.

PubMed

Satarifard, Vahid; Heidari, Maziar; Mashaghi, Samaneh; Tans, Sander J; Ejtehadi, Mohammad Reza; Mashaghi, Alireza

2017-08-24

topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.

Topologically protected bound states in one-dimensional Floquet acoustic waveguide systems

NASA Astrophysics Data System (ADS)

Peng, Yu-Gui; Geng, Zhi-Guo; Zhu, Xue-Feng

2018-03-01

Topological manipulation of sound has recently been a hot spot in acoustics due to the fascinating property of defect immune transport. To the best of our knowledge, the studies on one-dimensional (1D) topological acoustic systems hitherto mainly focus on the case of the Su-Schrieffer-Heeger model. Here, we show that topologically protected bound states may also exist in 1D periodically modulated acoustic waveguide systems, viz., 1D Floquet topological insulators. The results show that tuning the coupling strength in a waveguide lattice could trigger topological phase transition, which gives rise to topologically protected interface states as we put together two waveguide lattices featured with different topological phases or winding numbers. However, for the combined lattice, input at the waveguides other than the interfacial ones will excite bulk states. We have further verified the robustness of interface bound states against the variation of coupling strengths between the two distinct waveguide lattices. This work extends the scope of topological acoustics and may promote potential applications for acoustic devices with topological functionalities.

Pressure-induced electronic topological transitions in the charge-density-wave material In 4 Se 3

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

Zhang, Yuhang; Song, Liyan; Shao, Xuecheng

2017-08-01

High-pressure in situ angle dispersive X-ray diffraction (ADXRD) measurements were performed on the charge-density-wave (CDW) material In4Se3 up to 48.8 GPa. Pressure-induced structural changes were observed at 7.0 and 34.2 GPa, respectively. Using the CALYPSO methodology, the first high-pressure phase was solved as an exotic Pca21 structure. The compressional behaviors of the initial Pnnm and the Pca21 phases were all determined. Combined with first-principle calculations, we find that, unexpectedly, the Pnnm phase probably experiences twice electronic topological transitions (ETTs), from the initial possible CDW state to a semimetallic state at about 2.3 GPa and then back to a possible CDWmore » state at around 3.5 GPa, which was uncovered for the first time in CDW systems. In the both possible CDW states, pressure provokes a decrease of band-gap. The observation of a bulk metallic state was ascribed to structural transition to the Pca21 phase. Besides, based on electronic band structure calculations, the thermoelectric property of the Pnnm phase under compression was discussed. Our results show that pressure play a dramatic role in tuning In4Se3's structure and transport properties.« less

Quantum anomalous Hall effect in magnetic topological insulators

DOE PAGES

Wang, Jing; Lian, Biao; Zhang, Shou -Cheng

2015-08-25

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We presentmore » the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.« less

A novel algorithm using an orthotropic material model for topology optimization

NASA Astrophysics Data System (ADS)

Tong, Liyong; Luo, Quantian

2017-09-01

This article presents a novel algorithm for topology optimization using an orthotropic material model. Based on the virtual work principle, mathematical formulations for effective orthotropic material properties of an element containing two materials are derived. An algorithm is developed for structural topology optimization using four orthotropic material properties, instead of one density or area ratio, in each element as design variables. As an illustrative example, minimum compliance problems for linear and nonlinear structures are solved using the present algorithm in conjunction with the moving iso-surface threshold method. The present numerical results reveal that: (1) chequerboards and single-node connections are not present even without filtering; (2) final topologies do not contain large grey areas even using a unity penalty factor; and (3) the well-known numerical issues caused by low-density material when considering geometric nonlinearity are resolved by eliminating low-density elements in finite element analyses.

Three dimensional magnetic solutions in massive gravity with (non)linear field

NASA Astrophysics Data System (ADS)

Hendi, S. H.; Eslam Panah, B.; Panahiyan, S.; Momennia, M.

2017-12-01

The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.

Observation of topological edge states of acoustic metamaterials at subwavelength scale

NASA Astrophysics Data System (ADS)

Dai, Hongqing; Jiao, Junrui; Xia, Baizhan; Liu, Tingting; Zheng, Shengjie; Yu, Dejie

2018-05-01

Topological states are of key importance for acoustic wave systems owing to their unique transport properties. In this study, we develop a hexagonal array of hexagonal columns with Helmholtz resonators to obtain subwavelength Dirac cones. Rotation operations are performed to open the Dirac cones and obtain acoustic valley vortex states. In addition, we calculate the angular-dependent frequencies for the band edges at the K-point. Through a topological phase transition, the topological phase of pattern A can change into that of pattern B. The calculations for the bulk dispersion curves show that the acoustic metamaterials exhibit BA-type and AB-type topological edge states. Experimental results demonstrate that a sound wave can transmit well along the topological path. This study could reveal a simple approach to create acoustic topological edge states at the subwavelength scale.

Synthetic topological Kondo insulator in a pumped optical cavity

NASA Astrophysics Data System (ADS)

Zheng, Zhen; Zou, Xu-Bo; Guo, Guang-Can

2018-02-01

Motivated by experimental advances on ultracold atoms coupled to a pumped optical cavity, we propose a scheme for synthesizing and observing the Kondo insulator in Fermi gases trapped in optical lattices. The synthetic Kondo phase arises from the screening of localized atoms coupled to mobile ones, which in our proposal is generated via the pumping laser as well as the cavity. By designing the atom-cavity coupling, it can engineer a nearest-neighbor-site Kondo coupling that plays an essential role for supporting topological Kondo phase. Therefore, the cavity-induced Kondo transition is associated with a nontrivial topological features, resulting in the coexistence of the superradiant and topological Kondo state. Our proposal can be realized with current technique, and thus has potential applications in quantum simulation of the topological Kondo insulator in ultracold atoms.

Dial-in Topological Metamaterials Based on Bistable Stewart Platform.

PubMed

Wu, Ying; Chaunsali, Rajesh; Yasuda, Hiromi; Yu, Kaiping; Yang, Jinkyu

2018-01-08

Recently, there have been significant efforts to guide mechanical energy in structures by relying on a novel topological framework popularized by the discovery of topological insulators. Here, we propose a topological metamaterial system based on the design of the Stewart Platform, which can not only guide mechanical waves robustly in a desired path, but also can be tuned in situ to change this wave path at will. Without resorting to any active materials, the current system harnesses bistablilty in its unit cells, such that tuning can be performed simply by a dial-in action. Consequently, a topological transition mechanism inspired by the quantum valley Hall effect can be achieved. We show the possibility of tuning in a variety of topological and traditional waveguides in the same system, and numerically investigate key qualitative and quantitative differences between them. We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range, topological waveguides are distinctive as they support robust, back scattering immune, one-way wave propagation.

Geometry of complex networks and topological centrality

NASA Astrophysics Data System (ADS)

Ranjan, Gyan; Zhang, Zhi-Li

2013-09-01

We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L). The squared distance of a node i to the origin in this n-dimensional space (lii+), yields a topological centrality index, defined as C∗(i)=1/lii+. In turn, the sum of reciprocals of individual node centralities, ∑i1/C∗(i)=∑ilii+, or the trace of L, yields the well-known Kirchhoff index (K), an overall structural descriptor for the network. To put into context this geometric definition of centrality, we provide alternative interpretations of the proposed indices that connect them to meaningful topological characteristics - first, as forced detour overheads and frequency of recurrences in random walks that has an interesting analogy to voltage distributions in the equivalent electrical network; and then as the average connectedness of i in all the bi-partitions of the graph. These interpretations respectively help establish the topological centrality (C∗(i)) of node i as a measure of its overall position as well as its overall connectedness in the network; thus reflecting the robustness of i to random multiple edge failures. Through empirical evaluations using synthetic and real world networks, we demonstrate how the topological centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchhoff index, is appropriately sensitive to perturbations/re-wirings in the network.

Rényi-Fisher entropy product as a marker of topological phase transitions

NASA Astrophysics Data System (ADS)

Bolívar, J. C.; Nagy, Ágnes; Romera, Elvira

2018-05-01

The combined Rényi-Fisher entropy product of electrons plus holes displays a minimum at the charge neutrality points. The Stam-Rényi difference and the Stam-Rényi uncertainty product of the electrons plus holes, show maxima at the charge neutrality points. Topological quantum numbers capable of detecting the topological insulator and the band insulator phases, are defined. Upper and lower bounds for the position and momentum space Rényi-Fisher entropy products are derived.

Probing lattice dynamics and electron-phonon coupling in the topological nodal-line semimetal ZrSiS

NASA Astrophysics Data System (ADS)

Singha, Ratnadwip; Samanta, Sudeshna; Chatterjee, Swastika; Pariari, Arnab; Majumdar, Dipanwita; Satpati, Biswarup; Wang, Lin; Singha, Achintya; Mandal, Prabhat

2018-03-01

Topological materials provide an exclusive platform to study the dynamics of relativistic particles in table-top experiments and offer the possibility of wide-scale technological applications. ZrSiS is a newly discovered topological nodal-line semimetal and has drawn enormous interests. In this paper, we have investigated the lattice dynamics and electron-phonon interaction in single-crystalline ZrSiS using Raman spectroscopy. Polarization and angle-resolved Raman data have been analyzed using crystal symmetries and theoretically calculated atomic vibrational patterns along with phonon dispersion spectra. Wavelength- and temperature-dependent measurements show the complex interplay of electron and phonon degrees of freedom, resulting in resonant phonon and quasielastic electron scattering through interband transition. Our high-pressure Raman studies reveal vibrational anomalies, which are the signature of structural phase transitions. Further investigations through high-pressure synchrotron x-ray diffraction clearly show pressure-induced structural transitions and coexistence of multiple phases, which also indicate possible electronic topological transitions in ZrSiS. This study not only provides the fundamental information on the phonon subsystem, but also sheds some light in understanding the topological nodal-line phase in ZrSiS and other isostructural systems.

Crystallographic Topology 2: Overview and Work in Progress

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

Johnson, C.K.

1999-08-01

This overview describes an application of contemporary geometric topology and stochastic process concepts to structural crystallography. In this application, crystallographic groups become orbifolds, crystal structures become Morse functions on orbifolds, and vibrating atoms in a crystal become vector valued Gaussian measures with the Radon-Nikodym property. Intended crystallographic benefits include new methods for visualization of space groups and crystal structures, analysis of the thermal motion patterns seen in ORTEP drawings, and a classification scheme for crystal structures based on their Heegaard splitting properties.

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.

Learning phase transitions by confusion

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D.

2017-02-01

Classifying phases of matter is key to our understanding of many problems in physics. For quantum-mechanical systems in particular, the task can be daunting due to the exponentially large Hilbert space. With modern computing power and access to ever-larger data sets, classification problems are now routinely solved using machine-learning techniques. Here, we propose a neural-network approach to finding phase transitions, based on the performance of a neural network after it is trained with data that are deliberately labelled incorrectly. We demonstrate the success of this method on the topological phase transition in the Kitaev chain, the thermal phase transition in the classical Ising model, and the many-body-localization transition in a disordered quantum spin chain. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to the development of a generic tool for identifying unexplored phase transitions.

Learning phase transitions by confusion

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert; Liu, Ye-Hua; Huber, Sebastian

Classifying phases of matter is a central problem in physics. For quantum mechanical systems, this task can be daunting owing to the exponentially large Hilbert space. Thanks to the available computing power and access to ever larger data sets, classification problems are now routinely solved using machine learning techniques. Here, we propose to use a neural network based approach to find transitions depending on the performance of the neural network after training it with deliberately incorrectly labelled data. We demonstrate the success of this method on the topological phase transition in the Kitaev chain, the thermal phase transition in the classical Ising model, and the many-body-localization transition in a disordered quantum spin chain. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to a generic tool to identify unexplored transitions.

Neural Representation of Spatial Topology in the Rodent Hippocampus

PubMed Central

Chen, Zhe; Gomperts, Stephen N.; Yamamoto, Jun; Wilson, Matthew A.

2014-01-01

Pyramidal cells in the rodent hippocampus often exhibit clear spatial tuning in navigation. Although it has been long suggested that pyramidal cell activity may underlie a topological code rather than a topographic code, it remains unclear whether an abstract spatial topology can be encoded in the ensemble spiking activity of hippocampal place cells. Using a statistical approach developed previously, we investigate this question and related issues in greater details. We recorded ensembles of hippocampal neurons as rodents freely foraged in one and two-dimensional spatial environments, and we used a “decode-to-uncover” strategy to examine the temporally structured patterns embedded in the ensemble spiking activity in the absence of observed spatial correlates during periods of rodent navigation or awake immobility. Specifically, the spatial environment was represented by a finite discrete state space. Trajectories across spatial locations (“states”) were associated with consistent hippocampal ensemble spiking patterns, which were characterized by a state transition matrix. From this state transition matrix, we inferred a topology graph that defined the connectivity in the state space. In both one and two-dimensional environments, the extracted behavior patterns from the rodent hippocampal population codes were compared against randomly shuffled spike data. In contrast to a topographic code, our results support the efficiency of topological coding in the presence of sparse sample size and fuzzy space mapping. This computational approach allows us to quantify the variability of ensemble spiking activity, to examine hippocampal population codes during off-line states, and to quantify the topological complexity of the environment. PMID:24102128

Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves

NASA Astrophysics Data System (ADS)

Carpentier, David; Le Doussal, Pierre

2000-11-01

We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the transition at which frozen topological defects (vortices) proliferate. This RG approach is constructed both from the replicated Coulomb gas and, equivalently without the use of replicas, using the probability distribution of the local disorder (random defect core energy). By taking into account the fusion of environments (i.e., charge fusion in the replicated Coulomb gas) this distribution is shown to obey a Kolmogorov's type (KPP) non linear RG equation which admits traveling wave solutions and exhibits a freezing phenomenon analogous to glassy freezing in Derrida's random energy models. The resulting physical picture is that the distribution of local disorder becomes broad below a freezing temperature and that the transition is controlled by rare favorable regions for the defects, the density of which can be used as the new perturbative parameter. The determination of marginal directions at the disorder induced transition is shown to be related to the well studied front velocity selection problem in the KPP equation and the universality of the novel critical behaviour obtained here to the known universality of the corrections to the front velocity. Applications to other two dimensional problems are mentioned at the end.

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

Photoinduced Nonequilibrium Topological States in Strained Black Phosphorus

NASA Astrophysics Data System (ADS)

Liu, Hang; Sun, Jia-Tao; Cheng, Cai; Liu, Feng; Meng, Sheng

2018-06-01

Black phosphorus (BP), an elemental semiconductor, has attracted tremendous interest because it exhibits a wealth of interesting electronic and optoelectronic properties in equilibrium condition. The nonequilibrium electronic structures of bulk BP under a periodic field of laser remain unexplored, but can lead to intriguing topological optoelectronic properties. Here we show that, under the irradiation of circularly polarized light (CPL), BP exhibits a photon-dressed Floquet-Dirac semimetal state, which can be continuously tuned by changing the direction, intensity, and frequency of the incident laser. The topological phase transition from type-I to type-II Floquet-Dirac fermions manifests a new form of type-III phase, which exists in a wide range of intensities and frequencies of the incident laser. Furthermore, topological surface states exhibit nonequilibrium electron transport in a direction locked by the helicity of CPL. Our findings not only deepen our understanding of fundamental properties of BP in relation to topology but also extend optoelectronic device applications of BP to the nonequilibrium regime.

Fermi surfaces and electronic topological transitions in metallic solid solutions

NASA Astrophysics Data System (ADS)

Bruno, E.; Ginatempo, B.; Guiliano, E. S.; Ruban, A. V.; Vekilov, Yu. Kh.

1994-12-01

Notwithstanding the substitutional disorder, the Fermi surface of metallic alloys can be measured and computed. We show that, from the theoretical point of view, it is defined as the locus of the peaks of the Bloch Spectral Function (BSF). Such Fermi surfaces, on varying the atomic concentrations, may undergo changes of their topology, known as Electronic Topological Transitions (ETT). Thus, for instance, pockets of electrons or holes may appear or disappear, necks may open or close. ETTs cause anomalous behaviours of thermodynamic, transport and elastic properties of metals and constitute a fascinating field in the study of Fermi liquid systems. Although ETTs could be studied on pure systems as a function of the thermodynamic variables, nevertheless such a study would often require extreme conditions, and would lead to experimental difficulties. On the other hand, it is possible to explore the variations of atomic concentration, i.e. the valence electron per atom ratio, in metallic solid solutions with a relative experimental ease. In this paper we review the theoretical techniques for the determination of Fermi surfaces in metallic solid solutions and discuss some examples of ETTs, namely LiMg, ZrNb, NbMo, MoRe, AgPd, CdMg, NiW and NiTi alloys, also in connection with experimental data as thermoelectric power, resistivity, elastic constants and electron-phonon coupling and with the determinations of the electron momentum distribution function from Compton scattering and positron annihilation experiments. We show that the ab initio calculations of the electronic structure for the quoted systems, together with a careful determination of the BSF, are able to predict quantitatively ETTs at those concentrations where physical quantities display anomalies, so confirming directly ETT theory. Although it is not the purpose of the present review to give a full account of electronic structure calculation schemes, however, we briefly discuss the

Novel Phases from the Interplay of Topology and Strong Interactions

NASA Astrophysics Data System (ADS)

Hickey, Ciaran

In recent years, topology has become increasingly prevalent in condensed matter physics. It has allowed us to understand, and even predict, a variety of striking and remarkable physical phenomena. The study of strongly interacting systems has similarly lavished us with a diverse range of exotic phases and unconventional transitions, many of which are still poorly understood. In this thesis we will explore the interplay between topology and interactions in an effort to uncover new and novel phases. First we study how interactions impact the quantum phase transition between a topologically non-trivial phase and a trivial phase. The combination of interactions and the low-energy degrees of freedom associated with the transition leads to the emergence of a dome of lattice-symmetry breaking nematic order. Such behaviour is reminiscent of a number of strongly correlated electronic systems. We move on to study the strongly interacting limit of one of the earliest and best-known non-interacting topological phases, Haldane's model of a Chern insulator. Recently realized with ultracold atoms in a shaken optical lattice, the model has a non-trivial topological invariant associated with its band structure. In the strongly interacting limit the spin degrees of freedom are all that survive and we find a rich phase diagram of magnetically ordered phases, using a combination of both classical and quantum techniques. Supplementing the model with an additional term we can 'quantum-melt' one of these ordered states to produce a disordered, liquid state that we positively identify as a chiral spin liquid, a highly entangled state of matter with fractionalised excitations. We generalise this mechanism to other two dimensional lattices, uncovering a possible unifying framework with which to understand the emergence of chiral spin liquids in lattice spin models. Finally, motivated by groundbreaking experiments in the ultracold atoms community, we investigate a model of two

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).

Beyond Group: Multiple Person Tracking via Minimal Topology-Energy-Variation.

PubMed

Gao, Shan; Ye, Qixiang; Xing, Junliang; Kuijper, Arjan; Han, Zhenjun; Jiao, Jianbin; Ji, Xiangyang

2017-12-01

Tracking multiple persons is a challenging task when persons move in groups and occlude each other. Existing group-based methods have extensively investigated how to make group division more accurately in a tracking-by-detection framework; however, few of them quantify the group dynamics from the perspective of targets' spatial topology or consider the group in a dynamic view. Inspired by the sociological properties of pedestrians, we propose a novel socio-topology model with a topology-energy function to factor the group dynamics of moving persons and groups. In this model, minimizing the topology-energy-variance in a two-level energy form is expected to produce smooth topology transitions, stable group tracking, and accurate target association. To search for the strong minimum in energy variation, we design the discrete group-tracklet jump moves embedded in the gradient descent method, which ensures that the moves reduce the energy variation of group and trajectory alternately in the varying topology dimension. Experimental results on both RGB and RGB-D data sets show the superiority of our proposed model for multiple person tracking in crowd scenes.

Geometrical Phases in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Christian, Joy Julius

In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a

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).

Converting topological insulators into topological metals within the tetradymite family

NASA Astrophysics Data System (ADS)

Chen, K.-W.; Aryal, N.; Dai, J.; Graf, D.; Zhang, S.; Das, S.; Le Fèvre, P.; Bertran, F.; Yukawa, R.; Horiba, K.; Kumigashira, H.; Frantzeskakis, E.; Fortuna, F.; Balicas, L.; Santander-Syro, A. F.; Manousakis, E.; Baumbach, R. E.

2018-04-01

We report the electronic band structures and concomitant Fermi surfaces for a family of exfoliable tetradymite compounds with the formula T2C h2P n , obtained as a modification to the well-known topological insulator binaries Bi2(Se,Te ) 3 by replacing one chalcogen (C h ) with a pnictogen (P n ) and Bi with the tetravalent transition metals T = Ti, Zr, or Hf. This imbalances the electron count and results in layered metals characterized by relatively high carrier mobilities and bulk two-dimensional Fermi surfaces whose topography is well-described by first-principles calculations. Intriguingly, slab electronic structure calculations predict Dirac-like surface states. In contrast to Bi2Se3 , where the surface Dirac bands are at the Γ point, for (Zr,Hf ) 2Te2 (P,As) there are Dirac cones of strong topological character around both the Γ ¯ and M ¯ points, which are above and below the Fermi energy, respectively. For Ti2Te2P , the surface state is predicted to exist only around the M ¯ point. In agreement with these predictions, the surface states that are located below the Fermi energy are observed by angle-resolved photoemission spectroscopy measurements, revealing that they coexist with the bulk metallic state. Thus this family of materials provides a foundation upon which to develop novel phenomena that exploit both the bulk and surface states (e.g., topological superconductivity).

Spin and topological order in a periodically driven spin chain

NASA Astrophysics Data System (ADS)

Russomanno, Angelo; Friedman, Bat-el; Dalla Torre, Emanuele G.

2017-07-01

The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In this work, we systematically explore its quantum phase diagram by examining the properties of its Floquet ground state. We specifically focus on driving protocols with time-reversal invariant points, and demonstrate the existence of an infinite number of distinct phases. These phases are separated by second-order quantum phase transitions, accompanied by continuous changes of local and string order parameters, as well as sudden changes of a topological winding number and of the number of protected edge states. When one of these phase transitions is adiabatically crossed, the correlator associated to the order parameter is nonvanishing over a length scale which shows a Kibble-Zurek scaling. In some phases, the Floquet ground state spontaneously breaks the discrete time-translation symmetry of the Hamiltonian. Our findings provide a better understanding of topological phases in periodically driven clean integrable models.

Topology and Edge Modes in Quantum Critical Chains

NASA Astrophysics Data System (ADS)

Verresen, Ruben; Jones, Nick G.; Pollmann, Frank

2018-02-01

We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases. This is possible even without gapped degrees of freedom in the bulk—in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of noninteracting spinless fermions with time-reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the noninteracting BDI class is obtained: Each phase is labeled by the central charge of the CFT, c ∈1/2 N , and the topological invariant, ω ∈Z . Moreover, c is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder.

Pressure driven topological semi metallic phase in SrTe

NASA Astrophysics Data System (ADS)

Kunduru, Lavanya; Roshan, S. C. Rakesh; Yedukondalu, N.; Sainath, M.

2018-05-01

We have investigated the structural, electronic properties and Fermi surface topology of SrTe under high pressure up to 50 GPa based on density functional theory calculations. We predict that SrTe undergoes a structural phase transition from NaCl (B1) to CsCl (B2)-type structure at 14.7 GPa which is consistent with the experimental observations as well as with previous theoretical studies. The ambient (B1) and high pressure (B2) phases are found to be indirect band gap semiconductors and upon further compression B2 phase turns into a nontrivial topological semimetal. Interestingly, we have observed that B2 phase of SrTe has band inversion at Γ and M symmetry directions which lead to formation of 3D topological nodal line semimetal at high pressure which is analogous to CaTe and Cu3PdN due to nontrivial band topology.

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins.

PubMed

Ahmed, Aqeel; Rippmann, Friedrich; Barnickel, Gerhard; Gohlke, Holger

2011-07-25

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 Å) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.

Controlling the Topological Sector of Magnetic Solitons in Exfoliated Cr 1 / 3 NbS 2 Crystals

DOE PAGES

Wang, Lin; Chepiga, N.; Ki, D. -K.; ...

2017-06-23

Here, we investigate manifestations of topological order in monoaxial helimagnet Cr 1/3NbS 2 by performing transport measurements on ultrathin crystals. Upon sweeping the magnetic field perpendicularly to the helical axis, crystals thicker than one helix pitch (48 nm) but much thinner than the magnetic domain size (similar to 1 mu m) are found to exhibit sharp and hysteretic resistance jumps. We also show that these phenomena originate from transitions between topological sectors with a different number of magnetic solitons. This is confirmed by measurements on crystals thinner than 48 nm-in which the topological sector cannot change-that do not exhibit anymore » jump or hysteresis. These results show the ability to deterministically control the topological sector of finite-size Cr 1/3NbS 2 and to detect intersector transitions by transport measurements.« less

Controlling the Topological Sector of Magnetic Solitons in Exfoliated Cr 1 / 3 NbS 2 Crystals

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

Wang, Lin; Chepiga, N.; Ki, D. -K.

Here, we investigate manifestations of topological order in monoaxial helimagnet Cr 1/3NbS 2 by performing transport measurements on ultrathin crystals. Upon sweeping the magnetic field perpendicularly to the helical axis, crystals thicker than one helix pitch (48 nm) but much thinner than the magnetic domain size (similar to 1 mu m) are found to exhibit sharp and hysteretic resistance jumps. We also show that these phenomena originate from transitions between topological sectors with a different number of magnetic solitons. This is confirmed by measurements on crystals thinner than 48 nm-in which the topological sector cannot change-that do not exhibit anymore » jump or hysteresis. These results show the ability to deterministically control the topological sector of finite-size Cr 1/3NbS 2 and to detect intersector transitions by transport measurements.« less

Topological quantum error correction in the Kitaev honeycomb model

NASA Astrophysics Data System (ADS)

Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.

2017-08-01

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.

The topology of geology 1: Topological analysis

NASA Astrophysics Data System (ADS)

Thiele, Samuel T.; Jessell, Mark W.; Lindsay, Mark; Ogarko, Vitaliy; Wellmann, J. Florian; Pakyuz-Charrier, Evren

2016-10-01

Topology has been used to characterise and quantify the properties of complex systems in a diverse range of scientific domains. This study explores the concept and applications of topological analysis in geology. We have developed an automatic system for extracting first order 2D topological information from geological maps, and 3D topological information from models built with the Noddy kinematic modelling system, and equivalent analyses should be possible for other implicit modelling systems. A method is presented for describing the spatial and temporal topology of geological models using a set of adjacency relationships that can be expressed as a topology network, thematic adjacency matrix or hive diagram. We define three types of spatial topology (cellular, structural and lithological) that allow us to analyse different aspects of the geology, and then apply them to investigate the geology of the Hamersley Basin, Western Australia.

Topology optimization in acoustics and elasto-acoustics via a level-set method

NASA Astrophysics Data System (ADS)

Desai, J.; Faure, A.; Michailidis, G.; Parry, G.; Estevez, R.

2018-04-01

Optimizing the shape and topology (S&T) of structures to improve their acoustic performance is quite challenging. The exact position of the structural boundary is usually of critical importance, which dictates the use of geometric methods for topology optimization instead of standard density approaches. The goal of the present work is to investigate different possibilities for handling topology optimization problems in acoustics and elasto-acoustics via a level-set method. From a theoretical point of view, we detail two equivalent ways to perform the derivation of surface-dependent terms and propose a smoothing technique for treating problems of boundary conditions optimization. In the numerical part, we examine the importance of the surface-dependent term in the shape derivative, neglected in previous studies found in the literature, on the optimal designs. Moreover, we test different mesh adaptation choices, as well as technical details related to the implicit surface definition in the level-set approach. We present results in two and three-space dimensions.

Observation of zone folding induced acoustic topological insulators and the role of spin-mixing defects

NASA Astrophysics Data System (ADS)

Deng, Yuanchen; Ge, Hao; Tian, Yuan; Lu, Minghui; Jing, Yun

2017-11-01

This article reports on the experimental realization of a flow-free, pseudospin-based acoustic topological insulator designed using the strategy of zone folding. Robust sound one-way propagation is demonstrated with the presence of non-spin-mixing defects. On the other hand, it is shown that spin-mixing defects, which break the geometric symmetry and therefore the pseudo-time-reversal symmetry, can open up nontrivial band gaps within the edge state frequency band, and their width can be tailored by the extent of the defect. This provides a possible route for realizing tunable acoustic topological insulators.

Numerical simulation of phase transition problems with explicit interface tracking

DOE PAGES

Hu, Yijing; Shi, Qiangqiang; de Almeida, Valmor F.; ...

2015-12-19

Phase change is ubiquitous in nature and industrial processes. Started from the Stefan problem, it is a topic with a long history in applied mathematics and sciences and continues to generate outstanding mathematical problems. For instance, the explicit tracking of the Gibbs dividing surface between phases is still a grand challenge. Our work has been motivated by such challenge and here we report on progress made in solving the governing equations of continuum transport in the presence of a moving interface by the front tracking method. The most pressing issue is the accounting of topological changes suffered by the interfacemore » between phases wherein break up and/or merge takes place. The underlying physics of topological changes require the incorporation of space-time subscales not at reach at the moment. Therefore we use heuristic geometrical arguments to reconnect phases in space. This heuristic approach provides new insight in various applications and it is extensible to include subscale physics and chemistry in the future. We demonstrate the method on applications such as simulating freezing, melting, dissolution, and precipitation. The later examples also include the coupling of the phase transition solution with the Navier-Stokes equations for the effect of flow convection.« less

Geometrizing adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Rezakhani, Ali; Kuo, Wan-Jung; Hamma, Alioscia; Lidar, Daniel; Zanardi, Paolo

2010-03-01

A time-optimal approach to adiabatic quantum computation (AQC) is formulated. The corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. We demonstrate this geometrization through some examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance. The underlying connection with quantum phase transitions is also explored.

Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS.

PubMed

Ali, Mazhar N; Schoop, Leslie M; Garg, Chirag; Lippmann, Judith M; Lara, Erik; Lotsch, Bettina; Parkin, Stuart S P

2016-12-01

Magnetoresistance (MR), the change of a material's electrical resistance in response to an applied magnetic field, is a technologically important property that has been the topic of intense study for more than a quarter century. We report the observation of an unusual "butterfly"-shaped titanic angular magnetoresistance (AMR) in the nonmagnetic Dirac material, ZrSiS, which we find to be the most conducting sulfide known, with a 2-K resistivity as low as 48(4) nΩ⋅cm. The MR in ZrSiS is large and positive, reaching nearly 1.8 × 10 5 percent at 9 T and 2 K at a 45° angle between the applied current ( I || a ) and the applied field (90° is H || c ). Approaching 90°, a "dip" is seen in the AMR, which, by analyzing Shubnikov de Haas oscillations at different angles, we find to coincide with a very sharp topological phase transition unlike any seen in other known Dirac/Weyl materials. We find that ZrSiS has a combination of two-dimensional (2D) and 3D Dirac pockets comprising its Fermi surface and that the combination of high-mobility carriers and multiple pockets in ZrSiS allows for large property changes to occur as a function of angle between applied fields. This makes it a promising platform to study the physics stemming from the coexistence of 2D and 3D Dirac electrons as well as opens the door to creating devices focused on switching between different parts of the Fermi surface and different topological states.

Global Phase Diagram of a Three-Dimensional Dirty Topological Superconductor

NASA Astrophysics Data System (ADS)

Roy, Bitan; Alavirad, Yahya; Sau, Jay D.

2017-06-01

We investigate the phase diagram of a three-dimensional, time-reversal symmetric topological superconductor in the presence of charge impurities and random s -wave pairing. Combining complimentary field theoretic and numerical methods, we show that the quantum phase transition between two topologically distinct paired states (or thermal insulators), described by thermal Dirac semimetal, remains unaffected in the presence of sufficiently weak generic randomness. At stronger disorder, however, these two phases are separated by an intervening thermal metallic phase of diffusive Majorana fermions. We show that across the insulator-insulator and metal-insulator transitions, normalized thermal conductance displays single parameter scaling, allowing us to numerically extract the critical exponents across them. The pertinence of our study in strong spin-orbit coupled, three-dimensional doped narrow gap semiconductors, such as CuxBi2Se3 , is discussed.

X-cube model on generic lattices: Fracton phases and geometric order

NASA Astrophysics Data System (ADS)

Slagle, Kevin; Kim, Yong Baek

2018-04-01

Fracton order is a new kind of quantum order characterized by topological excitations that exhibit remarkable mobility restrictions and a robust ground-state degeneracy (GSD) which can increase exponentially with system size. In this paper, we present a generic lattice construction (in three dimensions) for a generalized X-cube model of fracton order, where the mobility restrictions of the subdimensional particles inherit the geometry of the lattice. This helps explain a previous result that lattice curvature can produce a robust GSD, even on a manifold with trivial topology. We provide explicit examples to show that the (zero-temperature) phase of matter is sensitive to the lattice geometry. In one example, the lattice geometry confines the dimension-1 particles to small loops, which allows the fractons to be fully mobile charges, and the resulting phase is equivalent to (3+1)-dimensional toric code. However, the phase is sensitive to more than just lattice curvature; different lattices without curvature (e.g., cubic or stacked kagome lattices) also result in different phases of matter, which are separated by phase transitions. Unintuitively, however, according to a previous definition of phase [X. Chen et al., Phys. Rev. B 82, 155138 (2010), 10.1103/PhysRevB.82.155138], even just a rotated or rescaled cubic results in different phases of matter, which motivates us to propose a coarser definition of phase for gapped ground states and fracton order. This equivalence relation between ground states is given by the composition of a local unitary transformation and a quasi-isometry (which can rotate and rescale the lattice); equivalently, ground states are in the same phase if they can be adiabatically connected by varying both the Hamiltonian and the positions of the degrees of freedom (via a quasi-isometry). In light of the importance of geometry, we further propose that fracton orders should be regarded as a geometric order.

Mesh quality oriented 3D geometric vascular modeling based on parallel transport frame.

PubMed

Guo, Jixiang; Li, Shun; Chui, Yim Pan; Qin, Jing; Heng, Pheng Ann

2013-08-01

While a number of methods have been proposed to reconstruct geometrically and topologically accurate 3D vascular models from medical images, little attention has been paid to constantly maintain high mesh quality of these models during the reconstruction procedure, which is essential for many subsequent applications such as simulation-based surgical training and planning. We propose a set of methods to bridge this gap based on parallel transport frame. An improved bifurcation modeling method and two novel trifurcation modeling methods are developed based on 3D Bézier curve segments in order to ensure the continuous surface transition at furcations. In addition, a frame blending scheme is implemented to solve the twisting problem caused by frame mismatch of two successive furcations. A curvature based adaptive sampling scheme combined with a mesh quality guided frame tilting algorithm is developed to construct an evenly distributed, non-concave and self-intersection free surface mesh for vessels with distinct radius and high curvature. Extensive experiments demonstrate that our methodology can generate vascular models with better mesh quality than previous methods in terms of surface mesh quality criteria. Copyright © 2013 Elsevier Ltd. All rights reserved.

Oliver E. Buckley Condensed Matter Prize: Quantum-topological phases of matter

NASA Astrophysics Data System (ADS)

Wen, Xiao-Gang

For a long time, we thought that symmetry breaking patterns describe all phases and phase transitions. The featureless disordered liquids correspond to trivial phase. But in fact disordered liquids have very rich features, with amazing emergent phenomena, such as fractional quantum numbers, fractional and non-abelian statistics, perfect conducting boundary even in presence of magnetic impurities, etc. All those are due to many-body entanglement. In this talk, I will first discuss topological phases that have topological order (ie with long range entanglement). Then I will cover topological phases that have no topological order (ie with only short-range entanglement). I will stress on how to understand and describe many-body entanglement, which is a very new phenomenon. This research is supported by NSF Grant No. DMR-1506475.

Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions

PubMed Central

Hankiewicz, Ewelina M.; Culcer, Dimitrie

2017-01-01

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal

On the Certain Topological Indices of Titania Nanotube TiO2[m, n

NASA Astrophysics Data System (ADS)

Javaid, M.; Liu, Jia-Bao; Rehman, M. A.; Wang, Shaohui

2017-07-01

A numeric quantity that characterises the whole structure of a molecular graph is called the topological index that predicts the physical features, chemical reactivities, and boiling activities of the involved chemical compound in the molecular graph. In this article, we give new mathematical expressions for the multiple Zagreb indices, the generalised Zagreb index, the fourth version of atom-bond connectivity (ABC4) index, and the fifth version of geometric-arithmetic (GA5) index of TiO2[m, n]. In addition, we compute the latest developed topological index called by Sanskruti index. At the end, a comparison is also included to estimate the efficiency of the computed indices. Our results extended some known conclusions.

Measurement of the topological charge and index of vortex vector optical fields with a space-variant half-wave plate.

PubMed

Liu, Gui-Geng; Wang, Ke; Lee, Yun-Han; Wang, Dan; Li, Ping-Ping; Gou, Fangwang; Li, Yongnan; Tu, Chenghou; Wu, Shin-Tson; Wang, Hui-Tian

2018-02-15

Vortex vector optical fields (VVOFs) refer to a kind of vector optical field with an azimuth-variant polarization and a helical phase, simultaneously. Such a VVOF is defined by the topological index of the polarization singularity and the topological charge of the phase vortex. We present a simple method to measure the topological charge and index of VVOFs by using a space-variant half-wave plate (SV-HWP). The geometric phase grating of the SV-HWP diffracts a VVOF into ±1 orders with orthogonally left- and right-handed circular polarizations. By inserting a polarizer behind the SV-HWP, the two circular polarization states project into the linear polarization and then interfere with each other to form the interference pattern, which enables the direct measurement of the topological charge and index of VVOFs.

No-go theorem for boson condensation in topologically ordered quantum liquids

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

Neupert, Titus; He, Huan; Keyserlingk, Curt von

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

No-go theorem for boson condensation in topologically ordered quantum liquids

DOE PAGES

Neupert, Titus; He, Huan; Keyserlingk, Curt von; ...

2016-12-07

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics

PubMed Central

Dziarmaga, Jacek; Zurek, Wojciech H.

2014-01-01

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. PMID:25091996

Particle signatures of magnetic topology at the magnetopause: AMPTE/CCE observations

NASA Technical Reports Server (NTRS)

Fuselier, S. A.; Anderson, B. J.; Onsager, T. G.

1995-01-01

Electron distributions at energies above 50 eV have been found to be a sensitive indicator of magnetic topology for magnetopause crossings of the AMPTE/CCE spacecraft. Progressing from the magnetosheath to the magnetosphere two abrupt transitions occur. First, the magnetosheath electron population directed either parallel or antiparallel to the magnetic field is replaced by a streaming, heated magnetosheath electron population. The other half of the distribution is unchanged. The region with unidirectional, heated magnetosheath electrons is identified as the magnetosheath boundary layer (MSBL). Second, the unheated magnetosheath electron population is replaced by a heated population nearly identical to the population encountered in the MSBL, resulting in a symmetric counterstreaming distribution. The region populated by the bidirectional heated magnetosheath electrons is identified as the low-latitude boundary layer (LLBL). The MSBL and LLBL identified by the electron transitions are the same as the regions identified using ion composition measurements. The magnetosheath-MSBL transition reflects a change in magnetic topology from a solar wind field line to one that threads the magnetopause, and the existence of a magnetosheath-MSBL transition implies that the magnetopause is open. When the current layer is easily identified, the MSBL-LLBL transition coincides with the magnetopause current layer, indicating that the magnetosheath electrons are heated in the current layer. Both magnetosheath-MSBL and MSBL-LLBL transitions are observed for low as well as high magnetic shears. Moreover, the transitions are particularly clear for low shear implying that magnetic topology boundaries are sharp even when abrupt changes in the field and other plasma parameters are absent. Furthermore, for low magnetic shear, solar wind ions with low parallel drift speeds make up the majority of the LLBL population indicating that the magnetosheath plasma has convected directly across the

Aperiodic topological order in the domain configurations of functional materials

NASA Astrophysics Data System (ADS)

Huang, Fei-Ting; Cheong, Sang-Wook

2017-03-01

In numerous functional materials, such as steels, ferroelectrics and magnets, new functionalities can be achieved through the engineering of the domain structures, which are associated with the ordering of certain parameters within the material. The recent progress in technologies that enable imaging at atomic-scale spatial resolution has transformed our understanding of domain topology, revealing that, along with simple stripe-like or irregularly shaped domains, intriguing vortex-type topological domain configurations also exist. In this Review, we present a new classification scheme of 'Zm Zn domains with Zl vortices' for 2D macroscopic domain structures with m directional variants and n translational antiphases. This classification, together with the concepts of topological protection and topological charge conservation, can be applied to a wide range of materials, such as multiferroics, improper ferroelectrics, layered transition metal dichalcogenides and magnetic superconductors, as we discuss using selected examples. The resulting topological considerations provide a new basis for the understanding of the formation, kinetics, manipulation and property optimization of domains and domain boundaries in functional materials.

Feasibility of self-correcting quantum memory and thermal stability of topological order

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

Yoshida, Beni, E-mail: rouge@mit.edu

2011-10-15

Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as discussed in quantum information science. Here, with this correspondence in mind, we propose a model of quantum codes that may cover a large class of physically realizable quantum memory. The model is supported by a certain class of gapped spin Hamiltonians, called stabilizer Hamiltonians, with translation symmetries and a small number of ground states that does not grow with the system size. We show that themore » model does not work as self-correcting quantum memory due to a certain topological constraint on geometric shapes of its logical operators. This quantum coding theoretical result implies that systems covered or approximated by the model cannot have thermally stable topological order, meaning that systems cannot be stable against both thermal fluctuations and local perturbations simultaneously in two and three spatial dimensions. - Highlights: > We define a class of physically realizable quantum codes. > We determine their coding and physical properties completely. > We establish the connection between topological order and self-correcting memory. > We find they do not work as self-correcting quantum memory. > We find they do not have thermally stable topological order.« less

Surface operators from M -strings

NASA Astrophysics Data System (ADS)

Mori, Hironori; Sugimoto, Yuji

2017-01-01

It has been found that surface operators have a significant role in Alday-Gaiotto-Tachikawa (AGT) relation. This duality is an outstanding consequence of M -theory, but it is actually encoded into the brane web for which the topological string can work. From this viewpoint, the surface defect in AGT relation is geometrically engineered as a toric brane realization. Also, there is a class of the brane configuration in M -theory called M -strings which can be translated into the language of the topological string. In this work, we propose a new M -string configuration which can realize AGT relation in the presence of the surface defect by utilizing the geometric transition in the refined topological string.

From Majorana fermions to topological order.

PubMed

Terhal, Barbara M; Hassler, Fabian; DiVincenzo, David P

2012-06-29

We consider a system consisting of a 2D network of links between Majorana fermions on superconducting islands. We show that the fermionic Hamiltonian modeling this system is topologically ordered in a region of parameter space: we show that Kitaev's toric code emerges in fourth-order perturbation theory. By using a Jordan-Wigner transformation we can map the model onto a family of signed 2D Ising models in a transverse field where the signs, ferromagnetic or antiferromagnetic, are determined by additional gauge bits. Our mapping allows an understanding of the nonperturbative regime and the phase transition to a nontopological phase. We discuss the physics behind a possible implementation of this model and argue how it can be used for topological quantum computation by adiabatic changes in the Hamiltonian.

Dynamical mechanism of atrial fibrillation: A topological approach

NASA Astrophysics Data System (ADS)

Marcotte, Christopher D.; Grigoriev, Roman O.

2017-09-01

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets' hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead, this complexity is maintained as a dynamical balance between wave coalescence—a unique, previously unidentified, topological process that increases the number of wavelets—and wave collapse—a different topological process that decreases their number.

Topological defects in extended inflation

NASA Technical Reports Server (NTRS)

Copeland, Edmund J.; Kolb, Edward W.; Liddle, Andrew R.

1990-01-01

The production of topological defects, especially cosmic strings, in extended inflation models was considered. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large scale structure via cosmic strings.

Dissolution of topological Fermi arcs in a dirty Weyl semimetal

NASA Astrophysics Data System (ADS)

Slager, Robert-Jan; Juričić, Vladimir; Roy, Bitan

2017-11-01

Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide a condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states, and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) drives the system into a metallic phase. We here numerically demonstrate that with increasing strength of disorder, the Fermi arc gradually loses its sharpness, and close to the WSM-metal QPT it completely dissolves into the metallic bath of the bulk. The predicted topological nature of the WSM-metal QPT and the resulting bulk-boundary correspondence across this transition can be directly observed in angle-resolved photoemission spectroscopy (ARPES) and Fourier transformed scanning tunneling microscopy (STM) measurements by following the continuous deformation of the Fermi arcs with increasing disorder in recently discovered Weyl materials.

Distributed fault detection over sensor networks with Markovian switching topologies

NASA Astrophysics Data System (ADS)

Ge, Xiaohua; Han, Qing-Long

2014-05-01

This paper deals with the distributed fault detection for discrete-time Markov jump linear systems over sensor networks with Markovian switching topologies. The sensors are scatteredly deployed in the sensor field and the fault detectors are physically distributed via a communication network. The system dynamics changes and sensing topology variations are modeled by a discrete-time Markov chain with incomplete mode transition probabilities. Each of these sensor nodes firstly collects measurement outputs from its all underlying neighboring nodes, processes these data in accordance with the Markovian switching topologies, and then transmits the processed data to the remote fault detector node. Network-induced delays and accumulated data packet dropouts are incorporated in the data transmission between the sensor nodes and the distributed fault detector nodes through the communication network. To generate localized residual signals, mode-independent distributed fault detection filters are proposed. By means of the stochastic Lyapunov functional approach, the residual system performance analysis is carried out such that the overall residual system is stochastically stable and the error between each residual signal and the fault signal is made as small as possible. Furthermore, a sufficient condition on the existence of the mode-independent distributed fault detection filters is derived in the simultaneous presence of incomplete mode transition probabilities, Markovian switching topologies, network-induced delays, and accumulated data packed dropouts. Finally, a stirred-tank reactor system is given to show the effectiveness of the developed theoretical results.

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.

Geometrically thin, hot accretion disks - Topology of the thermal equilibrium curves

NASA Technical Reports Server (NTRS)

Kusunose, Masaaki; Mineshige, Shin

1992-01-01

All the possible thermal equilibrium states of geometrically thin alpha-disks around stellar-mass black holes are presented. A (vertically) one-zone disk model is employed and it is assumed that a main energy source is viscous heating of protons and that cooling is due to bremsstrahlung and Compton scattering. There exist various branches of the thermal equilibrium solution, depending on whether disks are effectively optically thick or thin, radiation pressure-dominated or gas pressure-dominated, composed of one-temperature plasmas or of two-temperature plasmas, and with high concentration of e(+)e(-) pairs or without pairs. The thermal equilibrium curves at high temperatures (greater than or approximately equal to 10 exp 8 K) are substantially modified by the presence of e(+)e(-) pairs. The thermal stability of these branches are examined.

Topological insulating phases from two-dimensional nodal loop semimetals

NASA Astrophysics Data System (ADS)

Li, Linhu; Araújo, Miguel A. N.

2016-10-01

Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase-winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.

Geometry and Topology of Two-Dimensional Dry Foams: Computer Simulation and Experimental Characterization.

PubMed

Tong, Mingming; Cole, Katie; Brito-Parada, Pablo R; Neethling, Stephen; Cilliers, Jan J

2017-04-18

Pseudo-two-dimensional (2D) foams are commonly used in foam studies as it is experimentally easier to measure the bubble size distribution and other geometric and topological properties of these foams than it is for a 3D foam. Despite the widespread use of 2D foams in both simulation and experimental studies, many important geometric and topological relationships are still not well understood. Film size, for example, is a key parameter in the stability of bubbles and the overall structure of foams. The relationship between the size distribution of the films in a foam and that of the bubbles themselves is thus a key relationship in the modeling and simulation of unstable foams. This work uses structural simulation from Surface Evolver to statistically analyze this relationship and to ultimately formulate a relationship for the film size in 2D foams that is shown to be valid across a wide range of different bubble polydispersities. These results and other topological features are then validated using digital image analysis of experimental pseudo-2D foams produced in a vertical Hele-Shaw cell, which contains a monolayer of bubbles between two plates. From both the experimental and computational results, it is shown that there is a distribution of sizes that a film can adopt and that this distribution is very strongly dependent on the sizes of the two bubbles to which the film is attached, especially the smaller one, but that it is virtually independent of the underlying polydispersity of the foam.

Topological phase transition in the two-dimensional anisotropic Heisenberg model: A study using the Replica Exchange Wang-Landau sampling

NASA Astrophysics Data System (ADS)

Figueiredo, T. P.; Rocha, J. C. S.; Costa, B. V.

2017-12-01

Although the topological Berezinskii-Kosterlitz-Thouless transition was for the first time described by 40 years ago, it is still a matter of discussion. It has been used to explain several experiments in the most diverse physical systems. In contrast with the ordinary continuous phase transitions the BKT-transition does not break any symmetry. However, in some contexts it can easily be confused with other continuous transitions, in general due to an insufficient data analysis. The two-dimensional XY (or sometimes called planar rotator) spin model is the fruit fly model describing the BKT transition. As demonstrated by Bramwell and Holdsworth (1993) the finite-size effects are more important in two-dimensions than in others due to the logarithmic system size dependence of the properties of the system. Closely related is the anisotropic two dimensional Heisenberg model (AH). Although they have the same Hamiltonian the spin variable in the former has only two degrees of freedom while the AH has three. Many works treat the AH model as undergoing a transition in the same universality class as the XY model. However, its characterization as being in the BKT class of universality deserve some investigation. This paper has two goals. First, we describe an analytical evidence showing that the AH model is in the BKT class of universality. Second, we make an extensive simulation, using the numerical Replica Exchange Wang-Landau method that corroborate our analytical calculations. From our simulation we obtain the BKT transition temperature as TBKT = 0 . 6980(10) by monitoring the susceptibility, the two point correlation function and the helicity modulus. We discuss the misuse of the fourth order Binder's cumulant to locate the transition temperature. The specific heat is shown to have a non-critical behavior as expected in the BKT transition. An analysis of the two point correlation function at low temperature, C(r) ∝r - η(T), shows that the exponent, η, is consistent

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).

Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS

PubMed Central

Ali, Mazhar N.; Schoop, Leslie M.; Garg, Chirag; Lippmann, Judith M.; Lara, Erik; Lotsch, Bettina; Parkin, Stuart S. P.

2016-01-01

Magnetoresistance (MR), the change of a material’s electrical resistance in response to an applied magnetic field, is a technologically important property that has been the topic of intense study for more than a quarter century. We report the observation of an unusual “butterfly”-shaped titanic angular magnetoresistance (AMR) in the nonmagnetic Dirac material, ZrSiS, which we find to be the most conducting sulfide known, with a 2-K resistivity as low as 48(4) nΩ⋅cm. The MR in ZrSiS is large and positive, reaching nearly 1.8 × 105 percent at 9 T and 2 K at a 45° angle between the applied current (I || a) and the applied field (90° is H || c). Approaching 90°, a “dip” is seen in the AMR, which, by analyzing Shubnikov de Haas oscillations at different angles, we find to coincide with a very sharp topological phase transition unlike any seen in other known Dirac/Weyl materials. We find that ZrSiS has a combination of two-dimensional (2D) and 3D Dirac pockets comprising its Fermi surface and that the combination of high-mobility carriers and multiple pockets in ZrSiS allows for large property changes to occur as a function of angle between applied fields. This makes it a promising platform to study the physics stemming from the coexistence of 2D and 3D Dirac electrons as well as opens the door to creating devices focused on switching between different parts of the Fermi surface and different topological states. PMID:28028541

A new class of non-topological solitons

NASA Technical Reports Server (NTRS)

Frieman, Joshua A.; Lynn, Bryan W.

1989-01-01

A class of non-topological solitons was constructed in renormalizable scalar field theories with nonlinear self-interactions. For large charge Q, the soliton mass increases linearly with Q, i.e., the soliton mass density is approximately independent of charge. Such objects could be naturally produced in a phase transition in the early universe or in the decay of superconducting cosmic strings.

Modifier constraint in alkali borophosphate glasses using topological constraint theory

NASA Astrophysics Data System (ADS)

Li, Xiang; Zeng, Huidan; Jiang, Qi; Zhao, Donghui; Chen, Guorong; Wang, Zhaofeng; Sun, Luyi; Chen, Jianding

2016-12-01

In recent years, composition-dependent properties of glasses have been successfully predicted using the topological constraint theory. The constraints of the glass network are derived from two main parts: network formers and network modifiers. The constraints of the network formers can be calculated on the basis of the topological structure of the glass. However, the latter cannot be accurately calculated in this way, because of the existing of ionic bonds. In this paper, the constraints of the modifier ions in phosphate glasses were thoroughly investigated using the topological constraint theory. The results show that the constraints of the modifier ions are gradually increased with the addition of alkali oxides. Furthermore, an improved topological constraint theory for borophosphate glasses is proposed by taking the composition-dependent constraints of the network modifiers into consideration. The proposed theory is subsequently evaluated by analyzing the composition dependence of the glass transition temperature in alkali borophosphate glasses. This method is supposed to be extended to other similar glass systems containing alkali ions.

Metal-Insulator Transition in Epitaxial Pyrochlore Iridates Bi2Ir2O7 thin Films

NASA Astrophysics Data System (ADS)

Chu, Jiun-Haw; Liu, Jian; Yi, Di; Rayan-Serrao, C.; Suresha, S.; Marti, Xavi; Riggs, Scott; Shapiro, Max; Ian, Fisher; Ramesh, R.

2013-03-01

Recently there is a surge of interest in searching for topological order in correlated electronic systems such as transition metal oxides. The strong spin-orbit interaction of 5d electrons and the geometric frustration in the crystal lattice make the pyrochlore iridate(A2Ir2O7) an ideal candidate to achieve this goal. Pioneering experiments on bulk polycrystalline and single crystal samples revealed a temperature dependent metal-insulator transition coupled to a long range magnetic order, and the transition temperature can be tuned by either A-site ionic radius or an external pressure. In this talk we present our efforts to understand and control the metal-insulator transition and the underlying electronic structure of pyrochlore iridates via epitaxial Bi2Ir2O7 thin films. Bulk Bi2Ir2O7 is located at the metallic side of the phase diagram. However as the film's thickness decreases the transport evolves from a metallic to a strongly localized character. Resonant X-ray spectroscopy suggests that the density of states near Fermi level is dominated by the Ir Je ff =1/2 states. Intriguingly, the magnetoresistance shows a linear field dependence over a wide range of fields at low temperatures, which is possibly consistent with the existence of Dirac nodes.

Observation of topological superconductivity on the surface of an iron-based superconductor

NASA Astrophysics Data System (ADS)

Zhang, Peng; Yaji, Koichiro; Hashimoto, Takahiro; Ota, Yuichi; Kondo, Takeshi; Okazaki, Kozo; Wang, Zhijun; Wen, Jinsheng; Gu, G. D.; Ding, Hong; Shin, Shik

2018-04-01

Topological superconductors are predicted to host exotic Majorana states that obey non-Abelian statistics and can be used to implement a topological quantum computer. Most of the proposed topological superconductors are realized in difficult-to-fabricate heterostructures at very low temperatures. By using high-resolution spin-resolved and angle-resolved photoelectron spectroscopy, we find that the iron-based superconductor FeTe1–xSex (x = 0.45; superconducting transition temperature Tc = 14.5 kelvin) hosts Dirac-cone–type spin-helical surface states at the Fermi level; the surface states exhibit an s-wave superconducting gap below Tc. Our study shows that the surface states of FeTe0.55Se0.45 are topologically superconducting, providing a simple and possibly high-temperature platform for realizing Majorana states.

Aging and rejuvenation of active matter under topological constraints

DOE PAGES

Janssen, Liesbeth M. C.; Kaiser, Andreas; Lowen, Hartmut

2017-07-18

The coupling of active, self-motile particles to topological constraints can give rise to novel nonequilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these nonequilibrium processes,more » and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. In conclusion, our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.« less

Topological Dirac semimetal phase in Pd and Pt oxides

NASA Astrophysics Data System (ADS)

Li, Gang; Yan, Binghai; Wang, Zhijun; Held, Karsten

2017-01-01

Topological Dirac semimetals (DSMs) exhibit nodal points through which energy bands disperse linearly in three-dimensional (3D) momentum space, a 3D analog of graphene. The first experimentally confirmed DSMs with a pair of Dirac points (DPs), Na3Bi and Cd3As2 , show topological surface Fermi arc states and exotic magnetotransport properties, boosting the interest in the search for stable and nontoxic DSM materials. Based on density-functional theory and dynamical mean-field theory calculations, we predict a family of palladium and platinum oxides to be robust 3D DSMs with three pairs of Dirac points that are well separated from bulk bands. The Fermi arcs at the surface display a Lifshitz transition upon a continuous change of the chemical potential. Corresponding oxides are already available as high-quality single crystals, an excellent precondition for the verification of our predictions by photoemission and magnetotransport experiments, extending DSMs to the versatile family of transition-metal oxides.

Aging and rejuvenation of active matter under topological constraints

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

Janssen, Liesbeth M. C.; Kaiser, Andreas; Lowen, Hartmut

The coupling of active, self-motile particles to topological constraints can give rise to novel nonequilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these nonequilibrium processes,more » and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. In conclusion, our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.« less

Aging and rejuvenation of active matter under topological constraints.

PubMed

Janssen, Liesbeth M C; Kaiser, Andreas; Löwen, Hartmut

2017-07-18

The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these non-equilibrium processes, and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. Our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.

Calculating degree-based topological indices of dominating David derived networks

NASA Astrophysics Data System (ADS)

Ahmad, Muhammad Saeed; Nazeer, Waqas; Kang, Shin Min; Imran, Muhammad; Gao, Wei

2017-12-01

An important area of applied mathematics is the Chemical reaction network theory. The behavior of real world problems can be modeled by using this theory. Due to applications in theoretical chemistry and biochemistry, it has attracted researchers since its foundation. It also attracts pure mathematicians because it involves interesting mathematical structures. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the dominating David derived networks [1, 2, 3, 4, 5].

Microscopic effects of Dy doping in the topological insulator Bi2Te3

NASA Astrophysics Data System (ADS)

Duffy, L. B.; Steinke, N.-J.; Krieger, J. A.; Figueroa, A. I.; Kummer, K.; Lancaster, T.; Giblin, S. R.; Pratt, F. L.; Blundell, S. J.; Prokscha, T.; Suter, A.; Langridge, S.; Strocov, V. N.; Salman, Z.; van der Laan, G.; Hesjedal, T.

2018-05-01

Magnetic doping with transition metal ions is the most widely used approach to break time-reversal symmetry in a topological insulator (TI)—a prerequisite for unlocking the TI's exotic potential. Recently, we reported the doping of Bi2Te3 thin films with rare-earth ions, which, owing to their large magnetic moments, promise commensurately large magnetic gap openings in the topological surface states. However, only when doping with Dy has a sizable gap been observed in angle-resolved photoemission spectroscopy, which persists up to room temperature. Although disorder alone could be ruled out as a cause of the topological phase transition, a fundamental understanding of the magnetic and electronic properties of Dy-doped Bi2Te3 remained elusive. Here, we present an x-ray magnetic circular dichroism, polarized neutron reflectometry, muon-spin rotation, and resonant photoemission study of the microscopic magnetic and electronic properties. We find that the films are not simply paramagnetic but that instead the observed behavior can be well explained by the assumption of slowly fluctuating, inhomogeneous, magnetic patches with increasing volume fraction as the temperature decreases. At liquid helium temperatures, a large effective magnetization can be easily introduced by the application of moderate magnetic fields, implying that this material is very suitable for proximity coupling to an underlying ferromagnetic insulator or in a heterostructure with transition-metal-doped layers. However, the introduction of some charge carriers by the Dy dopants cannot be excluded at least in these highly doped samples. Nevertheless, we find that the magnetic order is not mediated via the conduction channel in these samples and therefore magnetic order and carrier concentration are expected to be independently controllable. This is not generally the case for transition-metal-doped topological insulators, and Dy doping should thus allow for improved TI quantum devices.

Exploring the origins of topological frustration: Design of a minimally frustrated model of fragment B of protein A

PubMed Central

Shea, Joan-Emma; Onuchic, José N.; Brooks, Charles L.

1999-01-01

Topological frustration in an energetically unfrustrated off-lattice model of the helical protein fragment B of protein A from Staphylococcus aureus was investigated. This Gō-type model exhibited thermodynamic and kinetic signatures of a well-designed two-state folder with concurrent collapse and folding transitions and single exponential kinetics at the transition temperature. Topological frustration is determined in the absence of energetic frustration by the distribution of Fersht φ values. Topologically unfrustrated systems present a unimodal distribution sharply peaked at intermediate φ, whereas highly frustrated systems display a bimodal distribution peaked at low and high φ values. The distribution of φ values in protein A was determined both thermodynamically and kinetically. Both methods yielded a unimodal distribution centered at φ = 0.3 with tails extending to low and high φ values, indicating the presence of a small amount of topological frustration. The contacts with high φ values were located in the turn regions between helices I and II and II and III, intimating that these hairpins are in large part required in the transition state. Our results are in good agreement with all-atom simulations of protein A, as well as lattice simulations of a three- letter code 27-mer (which can be compared with a 60-residue helical protein). The relatively broad unimodal distribution of φ values obtained from the all-atom simulations and that from the minimalist model for the same native fold suggest that the structure of the transition state ensemble is determined mostly by the protein topology and not energetic frustration. PMID:10535953

Two-component quantum Hall effects in topological flat bands

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

Zeng, Tian-Sheng; Zhu, Wei; Sheng, D. N.

2017-03-27

Here in this paper, we study quantum Hall states for two-component particles (hardcore bosons and fermions) loading in topological lattice models. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that two-component fractional quantum Hall states emerge at certain fractional filling factors ν = 1/2 for fermions (ν = 2/3 for bosons) in the lowest Chern band, classified by features from ground states including the unique Chern number matrix (inverse of the K matrix), the fractional charge and spin pumpings, and two parallel propagating edge modes. Moreover, we also apply our strategy to two-component fermions at integer fillingmore » factor ν = 2 , where a possible topological Neel antiferromagnetic phase is under intense debate very recently. For the typical π -flux checkerboard lattice, by tuning the onsite Hubbard repulsion, we establish a first-order phase transition directly from a two-component fermionic ν = 2 quantum Hall state at weak interaction to a topologically trivial antiferromagnetic insulator at strong interaction, and therefore exclude the possibility of an intermediate topological phase for our system.« less

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

Simulating quantum spin Hall effect in the topological Lieb lattice of a linear circuit network

NASA Astrophysics Data System (ADS)

Zhu, Weiwei; Hou, Shanshan; Long, Yang; Chen, Hong; Ren, Jie

2018-02-01

Inspired by the topological insulator circuit experimentally proposed by Jia Ningyuan et al. [Phys. Rev. X 5, 021031 (2015), 10.1103/PhysRevX.5.021031], we theoretically realize the topological Lieb lattice, a line-centered square lattice with rich topological properties, in a radio-frequency circuit. We design a specific capacitor-inductor connection to resemble the intrinsic spin-orbit coupling and construct the analog spin by mixing degrees of freedom of voltages. As such, we are able to simulate the quantum spin Hall effect in the topological Lieb lattice of linear circuits. We then investigate the spin-resolved topological edge mode and the topological phase transition of the band structure varied with capacitances. Finally, we discuss the extension of the π /2 phase change of hopping between sites to arbitrary phase values. Our results may find implications in engineering microwave topological metamaterials for signal transmission and energy harvesting.

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.

Effects of Structural and Electronic Disorder in Topological Insulator Sb2Te3 Thin Films

NASA Astrophysics Data System (ADS)

Korzhovska, Inna

Topological quantum matter is a unique and potentially transformative protectorate against disorder-induced backscattering. The ultimate disorder limits to the topological state, however, are still not known - understanding these limits is critical to potential applications in the fields of spintronics and information processing. In topological insulators spin-orbit interaction and time-reversal-symmetry invariance guarantees - at least up to a certain disorder strength - that charge transport through 2D gapless Dirac surface states is robust against backscattering by non-magnetic disorder. Strong disorder may destroy topological protection and gap out Dirac surface states, although recent theories predict that under severe electronic disorder a quantized topological conductance might yet reemerge. Very strong electronic disorder, however, is not trivial to install and quantify, and topological matter under such conditions thus far has not been experimentally tested. This thesis addresses the behavior of three-dimensional (3D) topological insulator (TI) films in a wide range of structural and electronic disorder. We establish strong positional disorder in thin (20-50 nm) Sb2Te 3 films, free of extrinsic magnetic dopants. Sb 2Te3 is a known 2nd generation topological insulator in the low-disorder crystalline state. It is also a known phase-change material that undergoes insulator-to-metal transition with the concurrent orders of magnitude resistive drop, where a huge range of disorder could be controllably explored. In this work we show that even in the absence of magnetic dopants, disorder may induce spin correlations detrimental to the topological state. Chapter 1 contains a brief introduction to the topological matter and describes the role played by disorder. This is followed by theory considerations and a survey of prior experimental work. Next we describe the motivation for our experiments and explain the choice of the material. Chapter 2 describes deposition

Off-equilibrium sphaleron transitions in the Glasma

DOE PAGES

Mace, Mark; Schlichting, Soren; Venugopalan, Raju

2016-04-28

We perform the first, to our knowledge, classical-statistical real time lattice simulations of topological transitions in the nonequilibrium glasma of weakly coupled but highly occupied gauge fields created immediately after the collision of ultrarelativistic nuclei. Simplifying our description by employing SU(2) gauge fields, and neglecting their longitudinal expansion, we find that the rate of topological transitions is initially strongly enhanced relative to the thermal sphaleron transition rate and decays with time during the thermalization process. Qualitative features of the time dependence of this nonequilibrium transition rate can be understood when expressed in terms of the magnetic screening length, which wemore » also extract nonperturbatively. Furthermore, a detailed investigation of auto-correlation functions of the Chern-Simons number (N CS) reveals non-Markovian features of the evolution distinct from previous simulations of non-Abelian plasmas in thermal equilibrium.« less

An Approach to Develop 3d Geo-Dbms Topological Operators by Re-Using Existing 2d Operators

NASA Astrophysics Data System (ADS)

Xu, D.; Zlatanova, S.

2013-09-01

Database systems are continuously extending their capabilities to store, process and analyse 3D data. Topological relationships which describe the interaction of objects in space is one of the important spatial issues. However, spatial operators for 3D objects are still insufficient. In this paper we present the development of a new 3D topological function to distinguish intersections of 3D planar polygons. The development uses existing 2D functions in the DBMS and two geometric transformations (rotation and projection). This function is tested for a real dataset to detect overlapping 3D city objects. The paper presents the algorithms and analyses the challenges. Suggestions for improvements of the current algorithm as well as possible extensions to handle more 3D topological cases are discussed at the end.

Topological effects on the mechanical properties of polymer knots

NASA Astrophysics Data System (ADS)

Zhao, Yani; Ferrari, Franco

2017-11-01

The mechanical properties of knotted polymer rings under stretching in a bad or good solvent are investigated by applying a force F to a point of the knot while keeping another point fixed. The Monte Carlo sampling of the polymer conformations is performed on a simple cubic lattice using the Wang-Landau algorithm. The specific energy, specific heat capacity, gyration radius and the force-elongation curves are computed for several knot topologies with lengths up to 120 lattice units. The common features of the mechanical and thermal behavior of stretched short polymer rings forming knots of a given topological type are analyzed as well as the differences arising due to topology and size effects. It is found that these systems admit three different phases depending on the values of the tensile force F and the temperature T. The transitions from one phase to the other are well characterized by the peaks of the specific heat capacity and by the data of the gyration radius and specific energy. At very low temperatures the force-elongation curves show that the stretching of a knot is a stepwise process, which becomes smooth at higher temperatures. Criteria for distinguishing topological and size effects are provided. It turns out from our study that the behavior of short polymer rings is strongly influenced by topological effects. In particular, the swelling and the swelling rate of knots are severely limited by the topological constraints. Several other properties that are affected by topology, like the decay of the specific energy at high tensile forces, are discussed. The fading out of the influences of topological origin with increasing knot lengths has been verified. Some anomalies detected in the plots of the specific heat capacity of very short and complex knots have been explained by the limitations in the number of accessible energy states due to the topological constraints.

Structure-topology-property correlations of sodium phosphosilicate glasses.

PubMed

Hermansen, Christian; Guo, Xiaoju; Youngman, Randall E; Mauro, John C; Smedskjaer, Morten M; Yue, Yuanzheng

2015-08-14

In this work, we investigate the correlations among structure, topology, and properties in a series of sodium phosphosilicate glasses with [SiO2]/[SiO2 + P2O5] ranging from 0 to 1. The network structure is characterized by (29)Si and (31)P magic-angle spinning nuclear magnetic resonance and Raman spectroscopy. The results show the formation of six-fold coordinated silicon species in phosphorous-rich glasses. Based on the structural data, we propose a formation mechanism of the six-fold coordinated silicon, which is used to develop a quantitative structural model for predicting the speciation of the network forming units as a function of chemical composition. The structural model is then used to establish a temperature-dependent constraint description of phosphosilicate glass topology that enables prediction of glass transition temperature, liquid fragility, and indentation hardness. The topological constraint model provides insight into structural origin of the mixed network former effect in phosphosilicate glasses.

Photo-responsive surface topology in chiral nematic media

NASA Astrophysics Data System (ADS)

Liu, Danqing; Bastiaansen, Cees W. M.; Toonder, Jaap. M. J.; Broer, Dirk J.

2012-03-01

We report on the design and fabrication of 'smart surfaces' that exhibit dynamic changes in their surface topology in response to exposure to light. The principle is based on anisotropic geometric changes of a liquid crystal network upon a change of the molecular order parameter. The photomechanical property of the coating is induced by incorporating an azobenzene moiety into the liquid crystal network. The responsive surface topology consists of regions with two different types of molecular order: planar chiral-nematic areas and homeotropic. Under flood exposure with 365 nm light the surfaces deform from flat to one with a surface relief. The height of the relief structures is of the order of 1 um corresponding to strain difference of around 20%. Furthermore, we demonstrate surface reliefs can form either convex or concave structures upon exposure to UV light corresponding to the decrease or increase molecular order parameter, respectively, related to the isomeric state of the azobenzene crosslinker. The reversible deformation to the initial flat state occurs rapidly after removing the light source.

Anomalous quantum diffusion and the topological metal

NASA Astrophysics Data System (ADS)

Tian, Chushun

2012-09-01

Electron wave scattering off disorders provides a key to many fascinating transport phenomena recently observed in topological insulators. Here, we present a nonperturbative diagrammatic theory of this subject. Surprisingly, quantum superdiffusion is found on the surface of three-dimensional strong topological insulators regardless of disorder strength (but not vanishing), where the diffusion coefficient grows in time logarithmically. Such a transport anomaly serves as a main characteristic of the novel quantum metal, the so-called “topological metal,” and indicates that it is a hybridization of Ohmic and perfect metals. It washes out the Anderson transition occurring in two-dimensional normal metals with disordered spin-orbit coupling, and leads to a logarithmic divergence of the conductance in the sample size instead. Therefore, the present work provides an analytical proof of the transport anomaly discovered numerically [Nomura, Koshino, and Ryu, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.146806 99, 146806 (2007); Bardarson , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.106801 99, 106801 (2007)].

Extending Topological Approaches to Microseismic-Derived 3D Fracture Networks

NASA Astrophysics Data System (ADS)

Urbancic, T.; Bosman, K.; Baig, A.; Ardakani, E. P.

2017-12-01

Fracture topology is important for determining the fluid-flow characteristics of a fracture network. In most unconventional petroleum applications, flow through subsurface fracture networks is the primary source of production, as matrix permeability is often in the nanodarcy range. Typical models of reservoir discrete fracture networks (DFNs) are constructed using fracture orientation and average spacing, without consideration of how the connectivity of the fracture network aids the percolation of hydrocarbons back to the wellbore. Topological approaches to DFN characterization have been developed and extensively used in analysis of outcrop data and aerial photography. Such study of the surface expression of fracture networks is straight-forward, and the physical form of the observed fractures is directly reflected in the parameters used to describe the topology. However, this analysis largely ignores the three-dimensional nature of natural fracture networks, which is difficult to define accurately in geological studies. SMTI analysis of microseismic event distributions can produce DFNs, where each event is represented by a penny-shaped crack with radius and orientation determined from the frequency content of the waveforms and assessment of the slip instability of the potential fracture planes, respectively. Analysis of the geometric relationships between a set of fractures can provide details of intersections between fractures, and thus the topological characteristics of the fracture network. Extension of existing 2D topology approaches to 3D fracture networks is non-trivial. In the 2D case, a fracture intersection is a single point (node), and branches connect adjacent nodes along fractures. For the 3D case, intersection "nodes" become lines, and connecting nodes to find branches becomes more complicated. There are several parameters defined in 2D topology to quantify the connectivity of the fracture network. Equivalent quantities must be defined and calibrated

Classification of topological insulators and superconductors in three spatial dimensions