Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera.

PubMed

Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

2018-03-23

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting-henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera

NASA Astrophysics Data System (ADS)

Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

2018-03-01

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting—henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordström black hole background

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-04-01

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordström black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.

Large-Eddy Simulation Analysis of Unsteady Separation Over a Pitching Airfoil at High Reynolds Number

DTIC Science & Technology

2013-12-24

channel flow using explicit filtering and dynamic mixed models, Physics of Fluids, (08 2012): 0. doi : 10.1063/1.4745007 Satbir Singh, Donghyun You...08 2013): 0. doi : 10.1016/j.ijheatfluidflow.2013.02.008 TOTAL: 2 Received Paper TOTAL: Number of Papers published in non peer-reviewed journals...coordinate xi Cartesian coordinates y Wall-normal coordinate z Cross-stream coordinate Greek Symbols α Angle of attack δ Dirac delta function; boundary

Dirac fermions in an antiferromagnetic semimetal

DOE PAGES

Tang, Peizhe; Zhou, Quan; Xu, Gang; ...

2016-08-08

Analogues of the elementary particles have been extensively searched for in condensed-matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low-energy excitations in materials now known as Dirac semimetals. All of the currently known Dirac semimetals are non-magnetic with both time-reversal symmetry and inversion symmetry. Here in this paper, we show that Dirac fermions can exist in one type of antiferromagnetic system, where both and are broken but their combination is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyse the robustness of the Dirac points under symmetry protections andmore » demonstrate its distinctive bulk dispersions, as well as the corresponding surface states, by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism.« less

Three-Dimensional Models of Topological Insulators: Engineering of Dirac Cones and Robustness of the Spin Texture

NASA Astrophysics Data System (ADS)

Soriano, David; Ortmann, Frank; Roche, Stephan

2012-12-01

We design three-dimensional models of topological insulator thin films, showing a tunability of the odd number of Dirac cones driven by the atomic-scale geometry at the boundaries. A single Dirac cone at the Γ-point can be obtained as well as full suppression of quantum tunneling between Dirac states at geometrically differentiated surfaces. The spin texture of surface states changes from a spin-momentum-locking symmetry to a surface spin randomization upon the introduction of bulk disorder. These findings illustrate the richness of the Dirac physics emerging in thin films of topological insulators and may prove utile for engineering Dirac cones and for quantifying bulk disorder in materials with ultraclean surfaces.

Aspects of Quantum Theory

NASA Astrophysics Data System (ADS)

Salam, Abdus; Wigner, E. P.

2010-03-01

Preface; List of contributors; Bibliography of P. A. M. Dirac; 1. Dirac in Cambridge R. J. Eden and J. C. Polkinghorne; 2. Travels with Dirac in the Rockies J. H. Van Vleck; 3. 'The golden age of theoretical physics': P. A. M. Dirac's scientific work from 1924 to 1933 Jagdish Mehra; 4. Foundation of quantum field theory Res Jost; 5. The early history of the theory of electron: 1897-1947 A. Pais; 6. The Dirac equation A. S. Wightman; 7. Fermi-Dirac statistics Rudolph Peierls; 8. Indefinite metric in state space W. Heisenberg; 9. On bras and kets J. M. Jauch; 10. The Poisson bracket C. Lanczos; 11. La 'fonction' et les noyaux L. Schwartz; 12. On the Dirac magnetic poles Edoardo Amadli and Nicola Cabibbo; 13. The fundamental constants and their time variation Freeman J. Dyson; 14. On the time-energy uncertainty relation Eugene P. Wigner; 15. The path-integral quantisation of gravity Abdus Salam and J. Strathdee; Index; Plates.

Gate-dependent Pseudospin Mixing in Graphene/boron Nitride Moire Superlattices

DTIC Science & Technology

2014-08-31

LETTERS PUBLISHED ONLINE: 31 AUGUST 2014 | DOI : 10.1038/NPHYS3075 Gate-dependent pseudospin mixing in graphene/boron nitride moiré superlattices... Dirac –Weyl spinors with a two-component pseudospin1–12. The unique pseudospin structure of Dirac electrons leads to emerging phenomena such as the...massless Dirac cone2, anomalous quantum Hall eect2,3, and Klein tunnelling4,5 in graphene. The capability to manipulate electron pseudospin is highly

[P.A.M. Dirac and antimatter applied to medicine].

PubMed

Kulenović, Fahrudin; Vobornik, Slavenka; Dalagija, Faruk

2003-01-01

Regarding to the hundredth anniversary of P. Dirac birth, it was made review on life and work of this genius in the history of physics and science generally. His ingenious scientific work, that significantly marked contemporary time, was presented in the simplest way with aim to approach more number of readers. Special accent was put on application of Dirac's ideas about antiparticles in medical practice.

Measurement-induced-nonlocality for Dirac particles in Garfinkle-Horowitz-Strominger dilation space-time

NASA Astrophysics Data System (ADS)

He, Juan; Xu, Shuai; Ye, Liu

2016-05-01

We investigate the quantum correlation via measurement-induced-nonlocality (MIN) for Dirac particles in Garfinkle-Horowitz-Strominger (GHS) dilation space-time. It is shown that the physical accessible quantum correlation decreases as the dilation parameter increases monotonically. Unlike the case of scalar fields, the physical accessible correlation is not zero when the Hawking temperature is infinite owing to the Pauli exclusion principle and the differences between Fermi-Dirac and Bose-Einstein statistics. Meanwhile, the boundary of MIN related to Bell-violation is derived, which indicates that MIN is more general than quantum nonlocality captured by the violation of Bell-inequality. As a by-product, a tenable quantitative relation about MIN redistribution is obtained whatever the dilation parameter is. In addition, it is worth emphasizing that the underlying reason why the physical accessible correlation and mutual information decrease is that they are redistributed to the physical inaccessible regions.

Fermi field and Dirac oscillator in a Som-Raychaudhuri space-time

NASA Astrophysics Data System (ADS)

de Montigny, Marc; Zare, Soroush; Hassanabadi, Hassan

2018-05-01

We investigate the relativistic dynamics of a Dirac field in the Som-Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som-Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov-Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som-Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.

Quantum oscillations and coherent interlayer transport in a new topological Dirac semimetal candidate YbMnSb2

NASA Astrophysics Data System (ADS)

Wang, Yi-Yan; Xu, Sheng; Sun, Lin-Lin; Xia, Tian-Long

2018-02-01

Dirac semimetals, which host Dirac fermions and represent a new state of quantum matter, have been studied intensively in condensed-matter physics. The exploration of new materials with topological states is important in both physics and materials science. We report the synthesis and the transport properties of high-quality single crystals of YbMnSb2. YbMnSb2 is a new compound with metallic behavior. Quantum oscillations, including Shubnikov-de Haas (SdH) oscillation and de Haas-van Alphen-type oscillation, have been observed at low temperature and high magnetic field. Small effective masses and nontrivial Berry phase are extracted from the analyses of quantum oscillations, which provide the transport evidence for the possible existence of Dirac fermions in YbMnSb2. The measurements of angular-dependent interlayer magnetoresistance indicate that the interlayer transport is coherent. The Fermi surface of YbMnSb2 possesses a quasi-two-dimensional characteristic as determined by the angular dependence of SdH oscillation frequency. These findings suggest that YbMnSb2 is a new candidate of topological Dirac semimetals.

Atomic and Excitonic Stability in Dirac Materials: A White Dwarf Perspective

NASA Astrophysics Data System (ADS)

Velizhanin, Kirill

2014-03-01

Dirac materials - systems where the low-energy spectrum of electronic excitations can be understood via solving the Dirac equation - draw a great amount of attention of the scientific community lately due to their enormous application potential and interesting basic physics. Examples of such materials include carbon nanotubes, graphene and, more recently, single-layer transition metal dichalcogenides. One surprising application of Dirac materials is their use as a platform to simulate various atomic and high-energy physics ``on a chip.'' For example, graphene has been recently used to ``mimic'' an atomic collapse of superheavy atoms [Y. Wang et al, Science, 340, 734, 2013]. In this talk I will discuss an unexpected similarity between atomic and excitonic collapse in Dirac materials and the limit of stability of such exotic astrophysical objects as degenerate stars (e.g., white dwarfs, neutron stars). Various aspects of this similarity, e.g., an application of the concept of the Chandrasekhar limit to the exciton stability in transition metal dichalcogenides, will be discussed. This work was performed under the NNSA of the U.S. DOE at LANL under Contract No. DE-AC52-06NA25396.

A new Dirac cone material: a graphene-like Be3C2 monolayer.

PubMed

Wang, Bing; Yuan, Shijun; Li, Yunhai; Shi, Li; Wang, Jinlan

2017-05-04

Two-dimensional (2D) materials with Dirac cones exhibit rich physics and many intriguing properties, but the search for new 2D Dirac materials is still a current hotspot. Using the global particle-swarm optimization method and density functional theory, we predict a new stable graphene-like 2D Dirac material: a Be 3 C 2 monolayer with a hexagonal honeycomb structure. The Dirac point occurs exactly at the Fermi level and arises from the merging of the hybridized p z bands of Be and C atoms. Most interestingly, this monolayer exhibits a high Fermi velocity in the same order of graphene. Moreover, the Dirac cone is very robust and retains even included spin-orbit coupling or external strain. These outstanding properties render the Be 3 C 2 monolayer a promising 2D material for special electronics applications.

Space of states in operator BFV-formalism

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

Batalin, I.A.; Tyutin, I.V.

1993-05-15

The dynamically adequate Fock realization of the extended space of asymptotic states is given within the framework of the operator BFV-formalism and of the Dirac quantization scheme as well. Physical subspace is picked out and established to be naturally isomorphic to the Dirac space of states. The formal mechanism (unitary [var epsilon]-limit), by means of which the operator BFV-dynamics reduces to the Dirac one, is studied. 10 refs.

Adjunctation and Scalar Product in the Dirac Equation - II

NASA Astrophysics Data System (ADS)

Dima, M.

2017-02-01

Part-I Dima (Int. J. Theor. Phys. 55, 949, 2016) of this paper showed in a representation independent way that γ 0 is the Bergmann-Pauli adjunctator of the Dirac { γ μ } set. The distiction was made between similarity (MATH) transformations and PHYS transformations - related to the (covariant) transformations of physical quantities. Covariance is due solely to the gauging of scalar products between systems of reference and not to the particular action of γ 0 on Lorentz boosts - a matter that in the past led inadvertently to the definition of a second scalar product (the Dirac-bar product). Part-II shows how two scalar products lead to contradictions and eliminates this un-natural duality in favour of the canonical scalar product and its gauge between systems of reference. What constitutes a proper observable is analysed and for instance spin is revealed not to embody one (except as projection on the boost direction - helicity). A thorough investigation into finding a proper-observable current for the theory shows that the Dirac equation does not possess one in operator form. A number of problems with the Dirac current operator are revealed - its Klein-Gordon counterpart being significantly more physical. The alternative suggested is finding a current for the Dirac theory in scalar form j^{μ } = < ρ rangle _{_{ψ }}v^{μ }_{ψ }.

Observation of a two-dimensional Fermi surface and Dirac dispersion in YbMnSb2

NASA Astrophysics Data System (ADS)

Kealhofer, Robert; Jang, Sooyoung; Griffin, Sinéad M.; John, Caolan; Benavides, Katherine A.; Doyle, Spencer; Helm, T.; Moll, Philip J. W.; Neaton, Jeffrey B.; Chan, Julia Y.; Denlinger, J. D.; Analytis, James G.

2018-01-01

We present the crystal structure, electronic structure, and transport properties of the material YbMnSb2, a candidate system for the investigation of Dirac physics in the presence of magnetic order. Our measurements reveal that this system is a low-carrier-density semimetal with a two-dimensional Fermi surface arising from a Dirac dispersion, consistent with the predictions of density-functional-theory calculations of the antiferromagnetic system. The low temperature resistivity is very large, suggesting that scattering in this system is highly efficient at dissipating momentum despite its Dirac-like nature.

Digital quantum simulation of Dirac equation with a trapped ion

NASA Astrophysics Data System (ADS)

Shen, Yangchao; Zhang, Xiang; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jingning; Kim, Kihwan; Department Of Physical Chemistry Collaboration

2014-05-01

Recently there has been growing interest in simulating relativistic effects in controllable physical system. We digitally simulate the Dirac equation in 3 +1 dimensions with a single trapped ion. We map four internal levels of 171Yb+ ion to the Dirac bispinor. The time evolution of the Dirac equation is implemented by trotter expansion. In the 3 +1 dimension, we can observe a helicoidal motion of a free Dirac particle which reduces to Zitterbewegung in 1 +1 dimension. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts.

Magnetotransport in Layered Dirac Fermion System Coupled with Magnetic Moments

NASA Astrophysics Data System (ADS)

Iwasaki, Yoshiki; Morinari, Takao

2018-03-01

We theoretically investigate the magnetotransport of Dirac fermions coupled with localized moments to understand the physical properties of the Dirac material EuMnBi2. Using an interlayer hopping form, which simplifies the complicated interaction between the layers of Dirac fermions and the layers of magnetic moments in EuMnBi2, the theory reproduces most of the features observed in this system. The hysteresis observed in EuMnBi2 can be caused by the valley splitting that is induced by the spin-orbit coupling and the external magnetic field with the molecular field created by localized moments. Our theory suggests that the magnetotransport in EuMnBi2 is due to the interplay among Dirac fermions, localized moments, and spin-orbit coupling.

Dirac Fermions in an Antiferromagnetic Semimetal

NASA Astrophysics Data System (ADS)

Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng; Shou-Cheng Zhang's Group Team, Prof.

Analogues of the elementary particles have been extensively searched for in condensed matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low energy excitations in materials now known as Dirac semimetals. All the currently known Dirac semimetals are nonmagnetic with both time-reversal symmetry  and inversion symmetry "". Here we show that Dirac fermions can exist in one type of antiferromagnetic systems, where both  and "" are broken but their combination "" is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyze the robustness of the Dirac points under symmetry protections, and demonstrate its distinctive bulk dispersions as well as the corresponding surface states by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism. We acknowledge the DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515, NSF under Grant No.DMR-1305677 and FAME, one of six centers of STARnet.

Three Dimensional Photonic Dirac Points in Metamaterials

NASA Astrophysics Data System (ADS)

Guo, Qinghua; Yang, Biao; Xia, Lingbo; Gao, Wenlong; Liu, Hongchao; Chen, Jing; Xiang, Yuanjiang; Zhang, Shuang

2017-11-01

Topological semimetals, representing a new topological phase that lacks a full band gap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a lesser extent metamaterials. Photonic crystal realizations of Dirac degeneracies are protected by various space symmetries, where Bloch modes span the spin and orbital subspaces. Here, we theoretically show that Dirac points can also be realized in effective media through the intrinsic degrees of freedom in electromagnetism under electromagnetic duality. A pair of spin-polarized Fermi-arc-like surface states is observed at the interface between air and the Dirac metamaterials. Furthermore, eigenreflection fields show the decoupling process from a Dirac point to two Weyl points. We also find the topological correlation between a Dirac point and vortex or vector beams in classical photonics. The experimental feasibility of our scheme is demonstrated by designing a realistic metamaterial structure. The theoretical proposal of the photonic Dirac point lays the foundation for unveiling the connection between intrinsic physics and global topology in electromagnetism.

Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5

PubMed Central

Liu, Yanwen; Yuan, Xiang; Zhang, Cheng; Jin, Zhao; Narayan, Awadhesh; Luo, Chen; Chen, Zhigang; Yang, Lei; Zou, Jin; Wu, Xing; Sanvito, Stefano; Xia, Zhengcai; Li, Liang; Wang, Zhong; Xiu, Faxian

2016-01-01

Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-field transport measurements of the Dirac semimetal candidate ZrTe5. Owing to the large g factor in ZrTe5, the Zeeman splitting can be observed at magnetic field as low as 3 T. Most prominently, high pulsed magnetic field up to 60 T drives the system into the ultra-quantum limit, where we observe abrupt changes in the magnetoresistance, indicating field-induced phase transitions. This is interpreted as an interaction-induced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in high-energy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters. PMID:27515493

First Principles Study of Band Structure and Band Gap Engineering in Graphene for Device Applications

DTIC Science & Technology

2015-03-20

In the bandstructure of graphene which is dominated by Dirac description, valence and conduction bands cross the Fermi level at a single point (K...of energy bands and appearance of Dirac cones near the ‘K’ point and Fermi level the electrons behave like massless Dirac fermions. For applications...results. Introduction Graphene, the super carbon , is now accepted as wonder material with new physics and it has caused major

Dirac cones in artificial structures of 3d transitional-metals doped Mg-Al spinels

NASA Astrophysics Data System (ADS)

Lu, Yuan; Feng, Min; Shao, Bin; Zuo, Xu

2014-05-01

Motivated by recent theoretical predications for Dirac cone in two-dimensional (2D) triangular lattice [H. Ishizuka, Phys. Rev. Lett. 109, 237207 (2012)], first-principles studies are performed to predict Dirac cones in artificial structures of 3d transitional-metals (TM = Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) doped Mg-Al spinels. In investigated artificial structures, TM dopants substitute specific positions of the B sub-lattice in Mg-Al spinel, and form a quasi-2D triangular lattice in the a-b plane. Calculated results illustrate the existence of the spin-polarized Dirac cones formed in d-wave bands at (around) the K-point in the momentum space. The study provides a promising route for engineering Dirac physics in condensed matters.

Unification of Fundamental Forces

NASA Astrophysics Data System (ADS)

Salam, Abdus; Taylor, Foreword by John C.

2005-10-01

Foreword John C. Taylor; 1. Unification of fundamental forces Abdus Salam; 2. History unfolding: an introduction to the two 1968 lectures by W. Heisenberg and P. A. M. Dirac Abdus Salam; 3. Theory, criticism, and a philosophy Werner Heisenberg; 4. Methods in theoretical physics Paul Adrian Maurice Dirac.

Floquet-Engineered Valleytronics in Dirac Systems.

PubMed

Kundu, Arijit; Fertig, H A; Seradjeh, Babak

2016-01-08

Valley degrees of freedom offer a potential resource for quantum information processing if they can be effectively controlled. We discuss an optical approach to this problem in which intense light breaks electronic symmetries of a two-dimensional Dirac material. The resulting quasienergy structures may then differ for different valleys, so that the Floquet physics of the system can be exploited to produce highly polarized valley currents. This physics can be utilized to realize a valley valve whose behavior is determined optically. We propose a concrete way to achieve such valleytronics in graphene as well as in a simple model of an inversion-symmetry broken Dirac material. We study the effect numerically and demonstrate its robustness against moderate disorder and small deviations in optical parameters.

LHCbDIRAC as Apache Mesos microservices

NASA Astrophysics Data System (ADS)

Haen, Christophe; Couturier, Benjamin

2017-10-01

The LHCb experiment relies on LHCbDIRAC, an extension of DIRAC, to drive its offline computing. This middleware provides a development framework and a complete set of components for building distributed computing systems. These components are currently installed and run on virtual machines (VM) or bare metal hardware. Due to the increased workload, high availability is becoming more and more important for the LHCbDIRAC services, and the current installation model is showing its limitations. Apache Mesos is a cluster manager which aims at abstracting heterogeneous physical resources on which various tasks can be distributed thanks to so called “frameworks” The Marathon framework is suitable for long running tasks such as the DIRAC services, while the Chronos framework meets the needs of cron-like tasks like the DIRAC agents. A combination of the service discovery tool Consul together with HAProxy allows to expose the running containers to the outside world while hiding their dynamic placements. Such an architecture brings a greater flexibility in the deployment of LHCbDirac services, allowing for easier deployment maintenance and scaling of services on demand (e..g LHCbDirac relies on 138 services and 116 agents). Higher reliability is also easier, as clustering is part of the toolset, which allows constraints on the location of the services. This paper describes the investigations carried out to package the LHCbDIRAC and DIRAC components into Docker containers and orchestrate them using the previously described set of tools.

A Route to Dirac Liquid Theory: A Fermi Liquid Description for Dirac Materials

NASA Astrophysics Data System (ADS)

Gochan, Matthew; Bedell, Kevin

Since the pioneering work developed by L.V. Landau sixty years ago, Fermi Liquid Theory has seen great success in describing interacting Fermi systems. While much interest has been generated over the study of non-Fermi Liquid systems, Fermi Liquid theory serves as a formidable model for many systems and offers a rich amount of of results and insight. The recent classification of Dirac Materials, and the lack of a unifying theoretical framework for them, has motivated our study. Dirac materials are a versatile class of materials in which an abundance of unique physical phenomena can be observed. Such materials are found in all dimensions, with the shared property that their low-energy fermionic excitations behave as massless Dirac fermions and are therefore governed by the Dirac equation. The most popular Dirac material, graphene, is the focus of this work. We present our Fermi Liquid description of Graphene. We find many interesting results, specifically in the transport and dynamics of the system. Additionally, we expand on previous work regarding the Virial Theorem and its impact on the Fermi Liquid parameters in graphene. Finally, we remark on viscoelasticity of Dirac Materials and other unusual results that are consequences of AdS-CFT.

From Rational Numbers to Dirac's Bra and Ket: Symbolic Representation of Physical Laws

NASA Astrophysics Data System (ADS)

D'Agostino, Salvo

2002-05-01

Beginning at least in the nineteenth century, symbols used by physicists in their equations interacted with their physical concepts. In the 1850s, Wilhelm Eduard Weber introduced a more rational order into symbolization by adopting an absolute system of units, and thus expressing electrodynamic laws in the form of algebraic equations instead of proportionality relationships, the formerly accepted representation of physical laws. In the 1860s, James Clerk Maxwell made a further advance by using dimensional quantities, and more complex symbolic forms such as gradient, convergence, rotor, and the like, in his electromagnetic and kinetic theories. In the twentieth century, Werner Heisenberg, Max Born, Erwin Schrödinger, and others introduced new symbols for complex numbers, operators, and matrices, thus passing from the representation of metrical properties of physical systems to higher-level mathematical objects. This process was enhanced in modern theoretical physics through the introduction of matrices, creation and destruction operators, Paul A. M. Dirac's q and c numbers, and so on. In the 1930s, Dirac radicalized this transformation of symbols, being aware of the profound modification in the method and scope of the mathematical-physical relationship it entailed.

Nonlinear Dirac cones

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Dirac materials

NASA Astrophysics Data System (ADS)

Wehling, T. O.; Black-Schaffer, A. M.; Balatsky, A. V.

2014-01-01

A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian. This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials''. In order to establish this class of materials, we illustrate how Dirac fermions emerge in multiple entirely different condensed matter systems and we discuss how Dirac fermions have been identified experimentally using electron spectroscopy techniques (angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy). As a consequence of their common low-energy excitations, this diverse set of materials shares a significant number of universal properties in the low-energy (infrared) limit. We review these common properties including nodal points in the excitation spectrum, density of states, specific heat, transport, thermodynamic properties, impurity resonances, and magnetic field responses, as well as discuss many-body interaction effects. We further review how the emergence of Dirac excitations is controlled by specific symmetries of the material, such as time-reversal, gauge, and spin-orbit symmetries, and how by breaking these symmetries a finite Dirac mass is generated. We give examples of how the interaction of Dirac fermions with their distinct real material background leads to rich novel physics with common fingerprints such as the suppression of back scattering and impurity-induced resonant states.

A beautiful sea: P. A. M. Dirac's epistemology and ontology of the vacuum.

PubMed

Wright, Aaron Sidney

2016-07-01

This paper charts P.A.M. Dirac's development of his theory of the electron, and its radical picture of empty space as an almost-full plenum. Dirac's Quantum Electrodynamics famously accomplished more than the unification of special relativity and quantum mechanics. It also accounted for the 'duplexity phenomena' of spectral line splitting that we now attribute to electron spin. But the extra mathematical terms that allowed for spin were not alone, and this paper charts Dirac's struggle to ignore or account for them as a sea of strange, negative-energy, particles with positive 'holes'. This work was not done in solitude, but rather in exchanges with Dirac's correspondence network. This social context for Dirac's work contests his image as a lone genius, and documents a community wrestling with the ontological consequences of their work. Unification, consistency, causality, and community are common factors in explanations in the history of physics. This paper argues on the basis of materials in Dirac's archive that --- in addition --- mathematical beauty was an epistemological factor in the development of the electron and hole theory. In fact, if we believe that Dirac's beautiful mathematics captures something of the world, then there is both an epistemology and an ontology of mathematical beauty.

Drive the Dirac electrons into Cooper pairs in SrxBi2Se3.

PubMed

Du, Guan; Shao, Jifeng; Yang, Xiong; Du, Zengyi; Fang, Delong; Wang, Jinghui; Ran, Kejing; Wen, Jinsheng; Zhang, Changjin; Yang, Huan; Zhang, Yuheng; Wen, Hai-Hu

2017-02-15

Topological superconductors are a very interesting and frontier topic in condensed matter physics. Despite the tremendous efforts in exploring topological superconductivity, its presence is however still under heavy debate. The Dirac electrons have been proven to exist on the surface of a topological insulator. It remains unclear whether and how the Dirac electrons fall into Cooper pairing in an intrinsic superconductor with the topological surface states. Here we show the systematic study of scanning tunnelling microscope/spectroscopy on the possible topological superconductor Sr x Bi 2 Se 3 . We first demonstrate that only the intercalated Sr atoms can induce superconductivity. Then we show the full superconducting gaps without any in-gap density of states as expected theoretically for a bulk topological superconductor. Finally, we find that the surface Dirac electrons will simultaneously condense into the superconducting state within the superconducting gap. This vividly demonstrates how the surface Dirac electrons are driven into Cooper pairs.

What does the value of the Dirac CP-violating phase teach us?

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

Farzan, Yasaman

2008-02-21

The 3x3 neutrino mixing matrix accommodates a Dirac CP-violating phase which can in principle show up in the neutrino oscillation patterns. Measuring this phase is going to be one of the main challenges of neutrino physics. Moreover, from the theoretical side it is not clear what a certain value of this phase would indicate. The aim of this talk is to search for possible principles, symmetries and phenomenological relations that can lead to particular values of the Dirac CP-violating phase, {delta}.

Electronic states with nontrivial topology in Dirac materials

NASA Astrophysics Data System (ADS)

Turkevich, R. V.; Perov, A. A.; Protogenov, A. P.; Chulkov, E. V.

2017-08-01

The theoretical studies of phase states with a linear dispersion of the spectrum of low-energy electron excitations have been reviewed. Some main properties and methods of experimental study of these states in socalled Dirac materials have been discussed in detail. The results of modern studies of symmetry-protected electronic states with nontrivial topology have been reported. Combination of approaches based on geometry with homotopic topology methods and results of condensed matter physics makes it possible to clarify new features of topological insulators, as well as Dirac and Weyl semimetals.

Applications of Dirac's Delta Function in Statistics

ERIC Educational Resources Information Center

Khuri, Andre

2004-01-01

The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…

DIRAC3 - the new generation of the LHCb grid software

NASA Astrophysics Data System (ADS)

Tsaregorodtsev, A.; Brook, N.; Casajus Ramo, A.; Charpentier, Ph; Closier, J.; Cowan, G.; Graciani Diaz, R.; Lanciotti, E.; Mathe, Z.; Nandakumar, R.; Paterson, S.; Romanovsky, V.; Santinelli, R.; Sapunov, M.; Smith, A. C.; Seco Miguelez, M.; Zhelezov, A.

2010-04-01

DIRAC, the LHCb community Grid solution, was considerably reengineered in order to meet all the requirements for processing the data coming from the LHCb experiment. It is covering all the tasks starting with raw data transportation from the experiment area to the grid storage, data processing up to the final user analysis. The reengineered DIRAC3 version of the system includes a fully grid security compliant framework for building service oriented distributed systems; complete Pilot Job framework for creating efficient workload management systems; several subsystems to manage high level operations like data production and distribution management. The user interfaces of the DIRAC3 system providing rich command line and scripting tools are complemented by a full-featured Web portal providing users with a secure access to all the details of the system status and ongoing activities. We will present an overview of the DIRAC3 architecture, new innovative features and the achieved performance. Extending DIRAC3 to manage computing resources beyond the WLCG grid will be discussed. Experience with using DIRAC3 by other user communities than LHCb and in other application domains than High Energy Physics will be shown to demonstrate the general-purpose nature of the system.

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

Lu, Yuan; Zuo, Xu, E-mail: xzuo@nankai.edu.cn; Feng, Min

Motivated by recent theoretical predications for Dirac cone in two-dimensional (2D) triangular lattice [H. Ishizuka, Phys. Rev. Lett. 109, 237207 (2012)], first-principles studies are performed to predict Dirac cones in artificial structures of 3d transitional-metals (TM = Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) doped Mg-Al spinels. In investigated artificial structures, TM dopants substitute specific positions of the B sub-lattice in Mg-Al spinel, and form a quasi-2D triangular lattice in the a-b plane. Calculated results illustrate the existence of the spin-polarized Dirac cones formed in d-wave bands at (around) the K-point in the momentum space. The study provides a promisingmore » route for engineering Dirac physics in condensed matters.« less

Zero-bias photocurrent in ferromagnetic topological insulator.

PubMed

Ogawa, N; Yoshimi, R; Yasuda, K; Tsukazaki, A; Kawasaki, M; Tokura, Y

2016-07-20

Magnetic interactions in topological insulators cause essential modifications in the originally mass-less surface states. They offer a mass gap at the Dirac point and/or largely deform the energy dispersion, providing a new path towards exotic physics and applications to realize dissipation-less electronics. The nonequilibrium electron dynamics at these modified Dirac states unveil additional functions, such as highly efficient photon to spin-current conversion. Here we demonstrate the generation of large zero-bias photocurrent in magnetic topological insulator thin films on mid-infrared photoexcitation, pointing to the controllable band asymmetry in the momentum space. The photocurrent spectra with a maximal response to the intra-Dirac-band excitations can be a sensitive measure for the correlation between Dirac electrons and magnetic moments.

Status of the DIRAC Project

NASA Astrophysics Data System (ADS)

Casajus, A.; Ciba, K.; Fernandez, V.; Graciani, R.; Hamar, V.; Mendez, V.; Poss, S.; Sapunov, M.; Stagni, F.; Tsaregorodtsev, A.; Ubeda, M.

2012-12-01

The DIRAC Project was initiated to provide a data processing system for the LHCb Experiment at CERN. It provides all the necessary functionality and performance to satisfy the current and projected future requirements of the LHCb Computing Model. A considerable restructuring of the DIRAC software was undertaken in order to turn it into a general purpose framework for building distributed computing systems that can be used by various user communities in High Energy Physics and other scientific application domains. The CLIC and ILC-SID detector projects started to use DIRAC for their data production system. The Belle Collaboration at KEK, Japan, has adopted the Computing Model based on the DIRAC system for its second phase starting in 2015. The CTA Collaboration uses DIRAC for the data analysis tasks. A large number of other experiments are starting to use DIRAC or are evaluating this solution for their data processing tasks. DIRAC services are included as part of the production infrastructure of the GISELA Latin America grid. Similar services are provided for the users of the France-Grilles and IBERGrid National Grid Initiatives in France and Spain respectively. The new communities using DIRAC started to provide important contributions to its functionality. Among recent additions can be mentioned the support of the Amazon EC2 computing resources as well as other Cloud management systems; a versatile File Replica Catalog with File Metadata capabilities; support for running MPI jobs in the pilot based Workload Management System. Integration with existing application Web Portals, like WS-PGRADE, is demonstrated. In this paper we will describe the current status of the DIRAC Project, recent developments of its framework and functionality as well as the status of the rapidly evolving community of the DIRAC users.

Clifford Algebra Implying Three Fermion Generations Revisited

NASA Astrophysics Data System (ADS)

Krolikowski, Wojciech

2002-09-01

The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure √ {p2} → {Γ }(N)p works, leading to a sequence N = 1,2,3, ... of Dirac-type equations, where four Dirac-type matrices {Γ }(N)μ are embedded into a Clifford algebra via a Jacobi definition introducing four ``centre-of-mass'' and (N-1)× four ``relative'' Dirac-type matrices. These define one ``centre-of-mass'' and (N-1) ``relative'' Dirac bispinor indices. Secundo, the ``centre-of-mass'' Dirac bispinor index is coupled to the Standard Model gauge fields, while (N-1) ``relative'' Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to ``relative'' Dirac indices. This allows only for three Dirac-type equations with N = 1,3,5 in the case of N odd, and two with N = 2,4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3x3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is mτ = 1776.80 MeV, when the input of experimental me and mμ is used.

Quantum transport of two-species Dirac fermions in dual-gated three-dimensional topological insulators

DOE PAGES

Xu, Yang; Miotkowski, Ireneusz; Chen, Yong P.

2016-05-04

Topological insulators are a novel class of quantum matter with a gapped insulating bulk, yet gapless spin-helical Dirac fermion conducting surface states. Here, we report local and non-local electrical and magneto transport measurements in dual-gated BiSbTeSe 2 thin film topological insulator devices, with conduction dominated by the spatially separated top and bottom surfaces, each hosting a single species of Dirac fermions with independent gate control over the carrier type and density. We observe many intriguing quantum transport phenomena in such a fully tunable two-species topological Dirac gas, including a zero-magnetic-field minimum conductivity close to twice the conductance quantum at themore » double Dirac point, a series of ambipolar two-component half-integer Dirac quantum Hall states and an electron-hole total filling factor zero state (with a zero-Hall plateau), exhibiting dissipationless (chiral) and dissipative (non-chiral) edge conduction, respectively. As a result, such a system paves the way to explore rich physics, ranging from topological magnetoelectric effects to exciton condensation.« less

Understanding Quaternions and the Dirac Belt Trick

ERIC Educational Resources Information Center

Staley, Mark

2010-01-01

The Dirac belt trick is often employed in physics classrooms to show that a 2n rotation is not topologically equivalent to the absence of rotation whereas a 4n rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors…

Novel Principles and the Charge-Symmetric Design of Dirac's Quantum Mechanics: I. Enhanced Eriksen's Theorem and the Universal Charge-Index Formalism for Dirac's Equation in (Strong) External Static Fields

NASA Astrophysics Data System (ADS)

Kononets, Yu. V.

2016-12-01

The presented enhanced version of Eriksen's theorem defines an universal transform of the Foldy-Wouthuysen type and in any external static electromagnetic field (ESEMF) reveals a discrete symmetry of Dirac's equation (DE), responsible for existence of a highly influential conserved quantum number—the charge index distinguishing two branches of DE spectrum. It launches the charge-index formalism (CIF) obeying the charge-index conservation law (CICL). Via its unique ability to manipulate each spectrum branch independently, the CIF creates a perfect charge-symmetric architecture of Dirac's quantum mechanics (DQM), which resolves all the riddles of the standard DE theory (SDET). Besides the abstract CIF algebra, the paper discusses: (1) the novel accurate charge-symmetric definition of the electric-current density; (2) DE in the true-particle representation, where electrons and positrons coexist on equal footing; (3) flawless "natural" scheme of second quantization; and (4) new physical grounds for the Fermi-Dirac statistics. As a fundamental quantum law, the CICL originates from the kinetic-energy sign conservation and leads to a novel single-particle physics in strong-field situations. Prohibiting Klein's tunneling (KT) in Klein's zone via the CICL, the precise CIF algebra defines a new class of weakly singular DE solutions, strictly confined in the coordinate space and experiencing the total reflection from the potential barrier.

Observation of three-component fermions in the topological semimetal molybdenum phosphide.

PubMed

Lv, B Q; Feng, Z-L; Xu, Q-N; Gao, X; Ma, J-Z; Kong, L-Y; Richard, P; Huang, Y-B; Strocov, V N; Fang, C; Weng, H-M; Shi, Y-G; Qian, T; Ding, H

2017-06-29

In quantum field theory, Lorentz invariance leads to three types of fermion-Dirac, Weyl and Majorana. Although the existence of Weyl and Majorana fermions as elementary particles in high-energy physics is debated, all three types of fermion have been proposed to exist as low-energy, long-wavelength quasiparticle excitations in condensed-matter systems. The existence of Dirac and Weyl fermions in condensed-matter systems has been confirmed experimentally, and that of Majorana fermions is supported by various experiments. However, in condensed-matter systems, fermions in crystals are constrained by the symmetries of the 230 crystal space groups rather than by Lorentz invariance, giving rise to the possibility of finding other types of fermionic excitation that have no counterparts in high-energy physics. Here we use angle-resolved photoemission spectroscopy to demonstrate the existence of a triply degenerate point in the electronic structure of crystalline molybdenum phosphide. Quasiparticle excitations near a triply degenerate point are three-component fermions, beyond the conventional Dirac-Weyl-Majorana classification, which attributes Dirac and Weyl fermions to four- and two-fold degenerate points, respectively. We also observe pairs of Weyl points in the bulk electronic structure of the crystal that coexist with the three-component fermions. This material thus represents a platform for studying the interplay between different types of fermions. Our experimental discovery opens up a way of exploring the new physics of unconventional fermions in condensed-matter systems.

Observation of three-component fermions in the topological semimetal molybdenum phosphide

NASA Astrophysics Data System (ADS)

Lv, B. Q.; Feng, Z.-L.; Xu, Q.-N.; Gao, X.; Ma, J.-Z.; Kong, L.-Y.; Richard, P.; Huang, Y.-B.; Strocov, V. N.; Fang, C.; Weng, H.-M.; Shi, Y.-G.; Qian, T.; Ding, H.

2017-06-01

In quantum field theory, Lorentz invariance leads to three types of fermion—Dirac, Weyl and Majorana. Although the existence of Weyl and Majorana fermions as elementary particles in high-energy physics is debated, all three types of fermion have been proposed to exist as low-energy, long-wavelength quasiparticle excitations in condensed-matter systems. The existence of Dirac and Weyl fermions in condensed-matter systems has been confirmed experimentally, and that of Majorana fermions is supported by various experiments. However, in condensed-matter systems, fermions in crystals are constrained by the symmetries of the 230 crystal space groups rather than by Lorentz invariance, giving rise to the possibility of finding other types of fermionic excitation that have no counterparts in high-energy physics. Here we use angle-resolved photoemission spectroscopy to demonstrate the existence of a triply degenerate point in the electronic structure of crystalline molybdenum phosphide. Quasiparticle excitations near a triply degenerate point are three-component fermions, beyond the conventional Dirac-Weyl-Majorana classification, which attributes Dirac and Weyl fermions to four- and two-fold degenerate points, respectively. We also observe pairs of Weyl points in the bulk electronic structure of the crystal that coexist with the three-component fermions. This material thus represents a platform for studying the interplay between different types of fermions. Our experimental discovery opens up a way of exploring the new physics of unconventional fermions in condensed-matter systems.

Density functional theory for d- and f-electron materials and compounds

DOE PAGES

Mattson, Ann E.; Wills, John M.

2016-02-12

Here, the fundamental requirements for a computationally tractable Density Functional Theory-based method for relativistic f- and (nonrelativistic) d-electron materials and compounds are presented. The need for basing the Kohn–Sham equations on the Dirac equation is discussed. The full Dirac scheme needs exchange-correlation functionals in terms of four-currents, but ordinary functionals, using charge density and spin-magnetization, can be used in an approximate Dirac treatment. The construction of a functional that includes the additional confinement physics needed for these materials is illustrated using the subsystem-functional scheme. If future studies show that a full Dirac, four-current based, exchange-correlation functional is needed, the subsystemmore » functional scheme is one of the few schemes that can still be used for constructing functional approximations.« less

Twelve inequivalent Dirac cones in two-dimensional ZrB2

NASA Astrophysics Data System (ADS)

Lopez-Bezanilla, Alejandro

2018-01-01

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB2 is presented. Two-dimensional ZrB2 is a mechanically stable d - and p -orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of spin-orbit coupling, is able to remove selectively the Dirac cones. A rational explanation in terms of d - and p -orbital mixing is provided to elucidate the origin of the infrequent Dirac cones in a flat structure. The versatility of transition-metal d orbitals combined with the honeycomb lattice provided by the B atoms yields particular features in a two-dimensional material.

An Introduction to Geometric Algebra with some Preliminary Thoughts on the Geometric Meaning of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Horn, Martin Erik

2014-10-01

It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics.

Twelve inequivalent Dirac cones in two-dimensional ZrB 2

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

Lopez-Bezanilla, Alejandro

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB 2 is presented. Two-dimensional ZrB 2 is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of spin-orbit coupling, is ablemore » to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent Dirac cones in a flat structure. In conclusion, the versatility of transition-metal d orbitals combined with the honeycomb lattice provided by the B atoms yields particular features in a two-dimensional material.« less

Chiral Tricritical Point: A New Universality Class in Dirac Systems

NASA Astrophysics Data System (ADS)

Yin, Shuai; Jian, Shao-Kai; Yao, Hong

2018-05-01

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.

Distribution law of the Dirac eigenmodes in QCD

NASA Astrophysics Data System (ADS)

Catillo, Marco; Glozman, Leonid Ya.

2018-04-01

The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks-Casher relation. At the same time, the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT) with the Gaussian Unitary Ensemble (GUE). Then, it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related SU(2)CS and SU(2NF) symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within NF = 2 dynamical simulations. We find that both the distributions of the near-zero and higher-lying modes are perfectly described by GUE of RMT. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is linked to the confining chromo-electric field.

Strain-Mediated Modification of Phagraphene Dirac Cones

DOE PAGES

Lopez-Bezanilla, Alejandro

2016-07-07

We present a first-principles study on the electronic and dynamical properties of phagraphene [Nano Lett., 2015, 15 (9), pp 6182]. This carbon allotrope exhibits a square unit cell, Dirac cones, and robustness against uniaxial deformation. By analyzing the contribution of each carbon atom orbital in the formation of the electronic states, we conclude that only the pz orbitals of eight out of the twenty atoms in the square unit cell are responsible of the formation of the nano-structure Dirac cones. Spatial symmetry breaking of the underlying honeycomb-like network upon shear stress application leads to a band gap opening. The analysismore » of the phonon spectra demonstrates that the dynamical stability of phagraphene is guaranteed for small distortion angles. Phagraphene is identified here as the first all-C graphitic monolayer with Dirac cones modifiable by a small and realistic physical deformation. The analysis and conclusions of this study can be applied to other monolayered materials exhibiting Dirac cones in square lattices.« less

Drive the Dirac electrons into Cooper pairs in SrxBi2Se3

PubMed Central

Du, Guan; Shao, Jifeng; Yang, Xiong; Du, Zengyi; Fang, Delong; Wang, Jinghui; Ran, Kejing; Wen, Jinsheng; Zhang, Changjin; Yang, Huan; Zhang, Yuheng; Wen, Hai-Hu

2017-01-01

Topological superconductors are a very interesting and frontier topic in condensed matter physics. Despite the tremendous efforts in exploring topological superconductivity, its presence is however still under heavy debate. The Dirac electrons have been proven to exist on the surface of a topological insulator. It remains unclear whether and how the Dirac electrons fall into Cooper pairing in an intrinsic superconductor with the topological surface states. Here we show the systematic study of scanning tunnelling microscope/spectroscopy on the possible topological superconductor SrxBi2Se3. We first demonstrate that only the intercalated Sr atoms can induce superconductivity. Then we show the full superconducting gaps without any in-gap density of states as expected theoretically for a bulk topological superconductor. Finally, we find that the surface Dirac electrons will simultaneously condense into the superconducting state within the superconducting gap. This vividly demonstrates how the surface Dirac electrons are driven into Cooper pairs. PMID:28198378

Twelve inequivalent Dirac cones in two-dimensional ZrB 2

DOE PAGES

Lopez-Bezanilla, Alejandro

2018-01-29

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB 2 is presented. Two-dimensional ZrB 2 is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of spin-orbit coupling, is ablemore » to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent Dirac cones in a flat structure. In conclusion, the versatility of transition-metal d orbitals combined with the honeycomb lattice provided by the B atoms yields particular features in a two-dimensional material.« less

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

Bisio, Alessandro; D’Ariano, Giacomo Mauro; Tosini, Alessandro, E-mail: alessandro.tosini@unipv.it

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound withmore » experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of a hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics. - Highlights: • The free Dirac field in one space dimension as a quantum cellular automaton. • Large scale limit of the automaton and the emergence of the Dirac equation. • Dispersive differential equation for the evolution of smooth states on the automaton. • Optimal discrimination between the automaton evolution and the Dirac equation.« less

Dirac-, Rashba-, and Weyl-type spin-orbit couplings: Toward experimental realization in ultracold atoms

NASA Astrophysics Data System (ADS)

Wang, Bao-Zong; Lu, Yue-Hui; Sun, Wei; Chen, Shuai; Deng, Youjin; Liu, Xiong-Jun

2018-01-01

We propose a hierarchy set of minimal optical Raman lattice schemes to pave the way for experimental realization of high-dimensional spin-orbit (SO) couplings for ultracold atoms, including two-dimensional (2D) Dirac type, 2D Rashba type, and three-dimensional (3D) Weyl type. The proposed Dirac-type SO coupling exhibits precisely controllable high symmetry, for which a large topological phase region is predicted. The generation of 2D Rashba and 3D Weyl types requires that two sources of laser beams have distinct frequencies of factor 2 difference. Surprisingly, we find that 133Cs atoms provide an ideal candidate for the realization. A common and essential feature is of high controllability and absent of any fine-tuning in the realization, and the resulting SO coupled ultracold atoms have a long lifetime. In particular, a long-lived topological Bose gas of 2D Dirac SO coupling has been proved in the follow-up experiment. These schemes essentially improve over the current experimental accessibility and controllability, and open a realistic way to explore novel high-dimensional SO physics, particularly quantum many-body physics and quantum far-from-equilibrium dynamics with novel topology for ultracold atoms.

Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

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

Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx; Elizaga Navascués, Beatriz, E-mail: beatriz.elizaga@iem.cfmac.csic.es; Martín-Benito, Mercedes, E-mail: m.martin@hef.ru.nl

We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under themore » symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.« less

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

DOE PAGES

Zeljkovic, Ilija; Okada, Yoshinori; Serbyn, Maksym; ...

2015-02-16

The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb 1-xSn xSe for a widemore » range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons—a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Lastly, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.« less

Inversion symmetry breaking induced triply degenerate points in orderly arranged PtSeTe family materials

NASA Astrophysics Data System (ADS)

Xiao, R. C.; Cheung, C. H.; Gong, P. L.; Lu, W. J.; Si, J. G.; Sun, Y. P.

2018-06-01

k paths exactly with symmetry allow to find triply degenerate points (TDPs) in band structures. The paths that host the type-II Dirac points in PtSe2 family materials also have the spatial symmetry. However, due to Kramers degeneracy (the systems have both inversion symmetry and time reversal symmetry), the crossing points in them are Dirac ones. In this work, based on symmetry analysis, first-principles calculations, and method, we predict that PtSe2 family materials should undergo topological transitions if the inversion symmetry is broken, i.e. the Dirac fermions in PtSe2 family materials split into TDPs in PtSeTe family materials (PtSSe, PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from the case in high-energy physics that breaking inversion symmetry I leads to the splitting of Dirac fermion into Weyl fermions. We also address a possible method to achieve the orderly arranged in PtSeTe family materials in experiments. Our study provides a real example that Dirac points transform into TDPs, and is helpful to investigate the topological transition between Dirac fermions and TDP fermions.

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.

Giant anisotropic magnetoresistance and planar Hall effect in the Dirac semimetal Cd3As2

NASA Astrophysics Data System (ADS)

Li, Hui; Wang, Huan-Wen; He, Hongtao; Wang, Jiannong; Shen, Shun-Qing

2018-05-01

Anisotropic magnetoresistance is the change tendency of resistance of a material on the mutual orientation of the electric current and the external magnetic field. Here, we report experimental observations in the Dirac semimetal Cd3As2 of giant anisotropic magnetoresistance and its transverse version, called the planar Hall effect. The relative anisotropic magnetoresistance is negative and up to -68% at 2 K and 10 T. The high anisotropy and the minus sign in this isotropic and nonmagnetic material are attributed to a field-dependent current along the magnetic field, which may be induced by the Berry curvature of the band structure. This observation not only reveals unusual physical phenomena in Weyl and Dirac semimetals, but also finds additional transport signatures of Weyl and Dirac fermions other than negative magnetoresistance.

Connecting Dirac and Majorana neutrino mass matrices in the minimal left-right symmetric model.

PubMed

Nemevšek, Miha; Senjanović, Goran; Tello, Vladimir

2013-04-12

Probing the origin of neutrino mass by disentangling the seesaw mechanism is one of the central issues of particle physics. We address it in the minimal left-right symmetric model and show how the knowledge of light and heavy neutrino masses and mixings suffices to determine their Dirac Yukawa couplings. This in turn allows one to make predictions for a number of high and low energy phenomena, such as decays of heavy neutrinos, neutrinoless double beta decay, electric dipole moments of charged leptons, and neutrino transition moments. We also discuss a way of reconstructing the neutrino Dirac Yukawa couplings at colliders such as the LHC.

A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles

NASA Astrophysics Data System (ADS)

Finster, Felix

2011-08-01

In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is introduced, which describes the physical system by a collection of Dirac states, including the states of the Dirac sea. Formulating the interaction by an action principle for the fermionic projector, we obtain a consistent description of interacting quantum fields which reproduces the results of perturbative quantum field theory. We find a new mechanism for the generation of boson masses and obtain small corrections to the field equations which violate causality.

Superpersistent Currents in Dirac Fermion Systems

DTIC Science & Technology

2017-03-06

development of quantum mechanics,, but also to quantum information processing and computing . Exploiting various physical systems to realize two-level...Here, using the QSD method, we calculated the dynamical trajectories of the system in the quantum regime. Our computations extending to the long time...currents in 2D Dirac material systems and pertinent phenomena in the emerging field of relativistic quantum nonlinear dynamics and chaos. Systematic

Topological transport in Dirac nodal-line semimetals

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Few layer epitaxial germanene: a novel two-dimensional Dirac material

NASA Astrophysics Data System (ADS)

Dávila, María Eugenia; Le Lay, Guy

2016-02-01

Monolayer germanene, a novel graphene-like germanium allotrope akin to silicene has been recently grown on metallic substrates. Lying directly on the metal surfaces the reconstructed atom-thin sheets are prone to lose the massless Dirac fermion character and unique associated physical properties of free standing germanene. Here, we show that few layer germanene, which we create by dry epitaxy on a gold template, possesses Dirac cones thanks to a reduced interaction. This finding established on synchrotron-radiation-based photoemission, scanning tunneling microscopy imaging and surface electron diffraction places few layer germanene among the rare two-dimensional Dirac materials. Since germanium is currently used in the mainstream Si-based electronics, perspectives of using germanene for scaling down beyond the 5 nm node appear very promising. Other fascinating properties seem at hand, typically the robust quantum spin Hall effect for applications in spintronics and the engineering of Floquet Majorana fermions by light for quantum computing.

Few layer epitaxial germanene: a novel two-dimensional Dirac material.

PubMed

Dávila, María Eugenia; Le Lay, Guy

2016-02-10

Monolayer germanene, a novel graphene-like germanium allotrope akin to silicene has been recently grown on metallic substrates. Lying directly on the metal surfaces the reconstructed atom-thin sheets are prone to lose the massless Dirac fermion character and unique associated physical properties of free standing germanene. Here, we show that few layer germanene, which we create by dry epitaxy on a gold template, possesses Dirac cones thanks to a reduced interaction. This finding established on synchrotron-radiation-based photoemission, scanning tunneling microscopy imaging and surface electron diffraction places few layer germanene among the rare two-dimensional Dirac materials. Since germanium is currently used in the mainstream Si-based electronics, perspectives of using germanene for scaling down beyond the 5 nm node appear very promising. Other fascinating properties seem at hand, typically the robust quantum spin Hall effect for applications in spintronics and the engineering of Floquet Majorana fermions by light for quantum computing.

Few layer epitaxial germanene: a novel two-dimensional Dirac material

PubMed Central

Dávila, María Eugenia; Le Lay, Guy

2016-01-01

Monolayer germanene, a novel graphene-like germanium allotrope akin to silicene has been recently grown on metallic substrates. Lying directly on the metal surfaces the reconstructed atom-thin sheets are prone to lose the massless Dirac fermion character and unique associated physical properties of free standing germanene. Here, we show that few layer germanene, which we create by dry epitaxy on a gold template, possesses Dirac cones thanks to a reduced interaction. This finding established on synchrotron-radiation-based photoemission, scanning tunneling microscopy imaging and surface electron diffraction places few layer germanene among the rare two-dimensional Dirac materials. Since germanium is currently used in the mainstream Si-based electronics, perspectives of using germanene for scaling down beyond the 5 nm node appear very promising. Other fascinating properties seem at hand, typically the robust quantum spin Hall effect for applications in spintronics and the engineering of Floquet Majorana fermions by light for quantum computing. PMID:26860590

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

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

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua; Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua; Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shownmore » that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.« less

Superconductivity in doped Dirac semimetals

NASA Astrophysics Data System (ADS)

Hashimoto, Tatsuki; Kobayashi, Shingo; Tanaka, Yukio; Sato, Masatoshi

2016-07-01

We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a 4 ×4 matrix and six types of k -independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and d vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the interorbital attraction is dominant, an unconventional superconducting state with point nodes appears. To verify the experimental signature of possible superconducting states, we calculate the temperature dependence of bulk physical properties such as electronic specific heat and spin susceptibility and surface state. In the unconventional superconducting phase, either dispersive or flat Andreev bound states appear between point nodes, which leads to double peaks or a single peak in the surface density of states, respectively. As a result, possible superconducting states can be distinguished by combining bulk and surface measurements.

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

NASA Astrophysics Data System (ADS)

Classen, Laura; Herbut, Igor F.; Janssen, Lukas; Scherer, Michael M.

2016-03-01

We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order ɛ expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2 ), no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic, and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.

Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions

NASA Astrophysics Data System (ADS)

Lee, Yu-Wen; Lee, Yu-Li

2018-01-01

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group (RG) method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type I) or Fermi lines (type II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work we study the effects of Coulomb interactions, following the spirit of Shankar [Rev. Mod. Phys. 66, 129 (1994), 10.1103/RevModPhys.66.129], by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

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

Kaufmann, Ralph M., E-mail: rkaufman@math.purdue.edu; Khlebnikov, Sergei, E-mail: skhleb@physics.purdue.edu; Wehefritz-Kaufmann, Birgit, E-mail: ebkaufma@math.purdue.edu

2012-11-15

Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A{sub n} type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A{sub k} singularity. We then apply these methods in the setting of families of graph Hamiltonians,more » such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties. - Highlights: Black-Right-Pointing-Pointer New method for analytically finding Dirac points. Black-Right-Pointing-Pointer Novel relation of level crossings to singularity theory. Black-Right-Pointing-Pointer More precise version of the von-Neumann-Wigner theorem for arbitrary smooth families of Hamiltonians of fixed size. Black-Right-Pointing-Pointer Analytical proof of the existence of Dirac points for the Gyroid wire network.« less

Electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES)

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

Wu, Yun

The discovery of quantum Hall e ect has motivated the use of topology instead of broken symmetry to classify the states of matter. Quantum spin Hall e ect has been proposed to have a separation of spin currents as an analogue of the charge currents separation in quantum Hall e ect, leading us to the era of topological insulators. Three-dimensional analogue of the Dirac state in graphene has brought us the three-dimensional Dirac states. Materials with three-dimensional Dirac states could potentially be the parent compounds for Weyl semimetals and topological insulators when time-reversal or space inversion symmetry is broken. Inmore » addition to the single Dirac point linking the two dispersion cones in the Dirac/Weyl semimetals, Dirac points can form a line in the momentum space, resulting in a topological node line semimetal. These fascinating novel topological quantum materials could provide us platforms for studying the relativistic physics in condensed matter systems and potentially lead to design of new electronic devices that run faster and consume less power than traditional, silicon based transistors. In this thesis, we present the electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES).« less

Nonsymmorphic cubic Dirac point and crossed nodal rings across the ferroelectric phase transition in LiOsO3

NASA Astrophysics Data System (ADS)

Yu, Wing Chi; Zhou, Xiaoting; Chuang, Feng-Chuan; Yang, Shengyuan A.; Lin, Hsin; Bansil, Arun

2018-05-01

Crystalline symmetries can generate exotic band-crossing features, which can lead to unconventional fermionic excitations with interesting physical properties. We show how a cubic Dirac point—a fourfold-degenerate band-crossing point with cubic dispersion in a plane and a linear dispersion in the third direction—can be stabilized through the presence of a nonsymmorphic glide mirror symmetry in the space group of the crystal. Notably, the cubic Dirac point in our case appears on a threefold axis, even though it has been believed previously that such a point can only appear on a sixfold axis. We show that a cubic Dirac point involving a threefold axis can be realized close to the Fermi level in the nonferroelectric phase of LiOsO3. Upon lowering temperature, LiOsO3 has been shown experimentally to undergo a structural phase transition from the nonferroelectric phase to the ferroelectric phase with spontaneously broken inversion symmetry. Remarkably, we find that the broken symmetry transforms the cubic Dirac point into three mutually crossed nodal rings. There also exist several linear Dirac points in the low-energy band structure of LiOsO3, each of which is transformed into a single nodal ring across the phase transition.

Knots in physics

NASA Astrophysics Data System (ADS)

Cho, Y. M.; Oh, Seung Hun; Zhang, Pengming

2018-03-01

After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological objects in various areas in physics. In particular, we discuss how the knots appear in Maxwell’s theory, Skyrme theory, and multicomponent condensed matter physics.

Casimir force phase transitions in the graphene family

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

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

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. We found that the expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. Here, we discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. Particularly, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences onmore » characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.« less

Casimir force phase transitions in the graphene family

DOE PAGES

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

2017-03-15

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. We found that the expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. Here, we discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. Particularly, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences onmore » characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.« less

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

Hydrodynamic & Transport Properties of Dirac Materials in the Quantum Limit

NASA Astrophysics Data System (ADS)

Gochan, Matthew; Bedell, Kevin

Dirac materials are a versatile class of materials in which an abundance of unique physical phenomena can be observed. Such materials are found in all dimensions, with the shared property that their low-energy fermionic excitations behave as massless Dirac fermions and are therefore governed by the Dirac equation. The most popular Dirac material, its two dimensional version in graphene, is the focus of this work. We seek a deeper understanding of the interactions in the quantum limit within graphene. Specifically, we derive hydrodynamic and transport properties, such as the conductivity, viscosity, and spin diffusion, in the low temperature regime where electron-electron scattering is dominant. To conclude, we look at the so-called universal lower bound conjectured by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for the ratio of shear viscosity to entropy density ratio. The lower bound, given by η / s >= ℏ / (4 πkB) , is supposedly obeyed by all quantum fluids. This leads us to ask whether or not graphene can be considered a quantum fluid and perhaps a ''nearly perfect fluid''(NPF) if this is the case, is it possible to find a violation of this bound at low temperatures.

Relativistic space-charge-limited transport in Dirac semiconductor

NASA Astrophysics Data System (ADS)

Ang, Yee Sin; Zubair, M.; Ang, L. K.; Lavoie, Philippe

The theory of space-charge-limited (SCL) current was first formulated by Mott and Gurney more than 70 years ago based on the semiclassical transport of quasi-free electron in dielectric solids. Its validity for recently fabricated 2D materials, which can host different classes of exotic quasiparticles, remains questionable. Recently, SCL transport measurements in 2D Dirac semiconductor, such as MoS2 and hBN monolayers, revealed anomalous current-voltage scaling of J V 1 . 7 which cannot be satisfactorily explained by conventional theories. In this work, we propose a theory of space-charge-limited transport that takes into account the relativistic quasiparticle dynamics in 2D Dirac semiconductor based on semiclassical Boltzmann transport equation. Our relativistic SCL model reveals an unconventional scaling relation of J Vα with 3 / 2 < α < 2 in the trap-free (or trap-filled) regime, which is in stark contrast to the Mott-Gurney relation of α = 2 and the Mark-Helfrich relation of α > 2 . The α < 2 scaling is a unique manifestation of the massive Dirac quasiparticles and is supported by the experimental data of MoS2. The relativistic SCL model proposed here shall provide a physical basis for the modelling of Dirac-material-based devices

Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

NASA Astrophysics Data System (ADS)

Li, Shuai; Wang, Chen; Zheng, Shi-Han; Wang, Rui-Qiang; Li, Jun; Yang, Mou

2018-04-01

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.

Nontrivial Berry phase in magnetic BaMnSb2 semimetal

PubMed Central

Huang, Silu; Shelton, W. A.; Plummer, E. W.; Jin, Rongying

2017-01-01

The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either time-reversal or inversion symmetry breaking to lift degeneracy at Dirac points. Here we demonstrate experimentally that canted antiferromagnetic BaMnSb2 is a 3D Weyl semimetal with a 2D electronic structure. The Shubnikov–de Hass oscillations of the magnetoresistance give nearly zero effective mass with high mobility and the nontrivial Berry phase. The ordered magnetic arrangement (ferromagnetic ordering in the ab plane and antiferromagnetic ordering along the c axis below 286 K) breaks the time-reversal symmetry, thus offering us an ideal platform to study magnetic Weyl fermions in a centrosymmetric material. PMID:28539436

Dynamical centrosymmetry breaking — A novel mechanism for second harmonic generation in graphene

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

Carvalho, David N.; Marini, Andrea; Biancalana, Fabio, E-mail: f.biancalana@hw.ac.uk

2017-03-15

We discover an unusual phenomenon that occurs when a graphene monolayer is illuminated by a short and intense pulse at normal incidence. Due to the pulse-induced oscillations of the Dirac cones, a dynamical breaking of the layer’s centrosymmetry takes place, leading to the generation of second harmonic waves. We prove that this result can only be found by using the full Dirac equation and show that the widely used semiconductor Bloch equations fail to reproduce this and some other important physics of graphene. Our results open new windows in the understanding of nonlinear light-matter interactions in a wide variety ofmore » new 2D materials with a gapped or ungapped Dirac-like dispersion.« less

Particlelike solutions of the Einstein-Dirac equations

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-05-01

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

Probing quantum entanglement in the Schwarzschild space-time beyond the single-mode approximation

NASA Astrophysics Data System (ADS)

He, Juan; Ding, Zhi-Yong; Ye, Liu

2018-05-01

In this paper, we deduce the vacuum structure for Dirac fields in the background of Schwarzschild space-time beyond the single-mode approximation and discuss the performance of quantum entanglement between particle and antiparticle modes of a Dirac field with Hawking effect. It is shown that Hawking radiation does not always destroy the physically accessible entanglement, and entanglement amplification may happen in some cases. This striking result is different from that of the single-mode approximation, which holds that the Hawking radiation can only destroy entanglement. Lastly, we analyze the physically accessible entanglement relation outside the event horizon and demonstrate that the monogamy inequality is constantly established regardless of the choice of given parameters.

Coexistence of type-II Dirac point and weak topological phase in Pt 3 Sn

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

Kim, Minsung; Wang, Cai -Zhuang; Ho, Kai -Ming

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show “relativistic” linear band crossings. Here, we report an unusual topological state of Pt 3Sn, where the two topological features appear simultaneously. Based on first-principles calculations, we show that Pt 3Sn is a three-dimensional weak topological semimetal with topologically nontrivial band inversion between the valence and conduction bands, where the band structure also possesses type-II Dirac points at the boundary of two electron pockets. The formation of the Dirac points can be understood in terms of the representationsmore » of relevant symmetry groups and the compatibility relations. The topological surface states appear in accordance with the nontrivial bulk band topology. As a result, the unique coexistence of the two distinct topological features in Pt 3Sn enlarges the material scope in topological physics, and is potentially useful for spintronics.« less

Coexistence of type-II Dirac point and weak topological phase in Pt 3 Sn

DOE PAGES

Kim, Minsung; Wang, Cai -Zhuang; Ho, Kai -Ming

2017-11-06

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show “relativistic” linear band crossings. Here, we report an unusual topological state of Pt 3Sn, where the two topological features appear simultaneously. Based on first-principles calculations, we show that Pt 3Sn is a three-dimensional weak topological semimetal with topologically nontrivial band inversion between the valence and conduction bands, where the band structure also possesses type-II Dirac points at the boundary of two electron pockets. The formation of the Dirac points can be understood in terms of the representationsmore » of relevant symmetry groups and the compatibility relations. The topological surface states appear in accordance with the nontrivial bulk band topology. As a result, the unique coexistence of the two distinct topological features in Pt 3Sn enlarges the material scope in topological physics, and is potentially useful for spintronics.« less

A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

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

Lienert, Matthias, E-mail: lienert@math.lmu.de

2015-04-15

The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to amore » relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.« less

The impact of the Fermi-Dirac distribution on charge injection at metal/organic interfaces.

PubMed

Wang, Z B; Helander, M G; Greiner, M T; Lu, Z H

2010-05-07

The Fermi level has historically been assumed to be the only energy-level from which carriers are injected at metal/semiconductor interfaces. In traditional semiconductor device physics, this approximation is reasonable as the thermal distribution of delocalized states in the semiconductor tends to dominate device characteristics. However, in the case of organic semiconductors the weak intermolecular interactions results in highly localized electronic states, such that the thermal distribution of carriers in the metal may also influence device characteristics. In this work we demonstrate that the Fermi-Dirac distribution of carriers in the metal has a much more significant impact on charge injection at metal/organic interfaces than has previously been assumed. An injection model which includes the effect of the Fermi-Dirac electron distribution was proposed. This model has been tested against experimental data and was found to provide a better physical description of charge injection. This finding indicates that the thermal distribution of electronic states in the metal should, in general, be considered in the study of metal/organic interfaces.

Goldstone Gauginos.

PubMed

Alves, Daniele S M; Galloway, Jamison; McCullough, Matthew; Weiner, Neal

2015-10-16

Models of supersymmetry with Dirac gauginos provide an attractive scenario for physics beyond the standard model. The "supersoft" radiative corrections and suppressed supersymmetry production at colliders provide for more natural theories and an understanding of why no new states have been seen. Unfortunately, these models are handicapped by a tachyon which is naturally present in existing models of Dirac gauginos. We argue that this tachyon is absent, with the phenomenological successes of the model preserved, if the right-handed gaugino is a (pseudo-)Goldstone field of a spontaneously broken anomalous flavor symmetry.

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

NASA Astrophysics Data System (ADS)

Oganesov, Armen; Vahala, George; Vahala, Linda; Soe, Min

2018-04-01

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.

Chain of Dirac spectrum loops of nodes in crossed magnetic and electric fields

NASA Astrophysics Data System (ADS)

Gavrilenko, V. I.; Perov, A. A.; Protogenov, A. P.; Turkevich, R. V.; Chulkov, E. V.

2018-03-01

New semimetal systems along with Dirac and Weyl semimetals contain compounds, in which the energy of electron excitations vanishes not at nodes but on lines. A higher dimension of the degeneracy space changes many physical properties. We consider a chain of loops consisting of Dirac spectrum nodes in nonsymmorphic crystalline compounds placed in external mutually perpendicular magnetic and electric fields. An exact solution for the spectrum is obtained under the assumption of particle-hole symmetry. An analysis of this spectrum shows the existence of a line of critical values of the magnetic and electric fields, at which a quantum phase transition to a gapless state occurs. The use of the obtained spectrum allows also predicting a number of new oscillation and resonance effects in the field of magneto-optical phenomena.

Exotic Lifshitz transitions in topological materials

NASA Astrophysics Data System (ADS)

Volovik, G. E.

2018-01-01

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

Two-dimensional Dirac fermions in thin films of C d3A s2

NASA Astrophysics Data System (ADS)

Galletti, Luca; Schumann, Timo; Shoron, Omor F.; Goyal, Manik; Kealhofer, David A.; Kim, Honggyu; Stemmer, Susanne

2018-03-01

Two-dimensional states in confined thin films of the three-dimensional Dirac semimetal C d3A s2 are probed by transport and capacitance measurements under applied magnetic and electric fields. The results establish the two-dimensional Dirac electronic spectrum of these states. We observe signatures of p -type conduction in the two-dimensional states as the Fermi level is tuned across their charge neutrality point and the presence of a zero-energy Landau level, all of which indicate topologically nontrivial states. The resistance at the charge neutrality point is approximately h /e2 and increases rapidly under the application of a magnetic field. The results open many possibilities for gate-tunable topological devices and for the exploration of novel physics in the zero-energy Landau level.

Shortcuts to adiabaticity. Suppression of pair production in driven Dirac dynamics

DOE PAGES

Deffner, Sebastian

2015-12-21

By achieving effectively adiabatic dynamics in finite time, we have found that it is our ubiquitous goal in virtually all areas of modern physics. So-called shortcuts to adiabaticity refer to a set of methods and techniques that allow us to produce in a short time the same final state that would result from an adiabatic, infinitely slow process. In this paper we generalize one of these methods—the fast-forward technique—to driven Dirac dynamics. We find that our main result shortcuts to adiabaticity for the (1+1)-dimensional Dirac equation are facilitated by a combination of both scalar and pseudoscalar potentials. Our findings aremore » illustrated for two analytically solvable examples, namely charged particles driven in spatially homogeneous and linear vector fields.« less

Optical spectroscopy study of the three-dimensional Dirac semimetal ZrTe 5

DOE PAGES

Chen, R. Y.; Gu, G. D.; Zhang, S. J.; ...

2015-08-05

Three-dimensional (3D) topological Dirac materials have been under intensive study recently. The layered compound ZrTe 5 has been suggested to be one such material as a result of transport and angle-resolved photoemission spectroscopy experiments. Here, we perform infrared reflectivity measurements to investigate the underlying physics of this material. The derived optical conductivity increases linearly with frequency below normal interband transitions, which provides optical spectroscopic proof of a 3D Dirac semimetal. In addition, the plasma edge shifts dramatically to lower energy upon temperature cooling, which might be due to the shrinking of the lattice parameters. Additionally, an extremely sharp peak showsmore » up in the frequency-dependent optical conductivity, indicating the presence of a Van Hove singularity in the joint density of state.« less

Field equations from Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür

2018-02-01

From the Killing spinor equation and the equations satisfied by their bilinears, we deduce some well-known bosonic and fermionic field equations of mathematical physics. Aside from the trivially satisfied Dirac equation, these relativistic wave equations in curved spacetimes, respectively, are Klein-Gordon, Maxwell, Proca, Duffin-Kemmer-Petiau, Kähler, twistor, and Rarita-Schwinger equations. This result shows that, besides being special kinds of Dirac fermions, Killing fermions can be regarded as physically fundamental. For the Maxwell case, the problem of motion is analysed in a reverse manner with respect to the studies of Einstein-Groemer-Infeld-Hoffmann and Jean Marie Souriau. In the analysis of the gravitino field, a generalised 3-ψ rule is found which is termed the vanishing trace constraint.

Nonequilibrium Fractional Hall Response After a Topological Quench

NASA Astrophysics Data System (ADS)

Unal, Nur; Mueller, Erich; Oktel, M. O.

When a system is suddenly driven between two topologically different phases, aspects of the original topology survive the quench, but most physical observables (edge currents, Hall conductivity) appear to be non-universal. I will present the non-equilibrium Hall response of a Chern insulator following a quench where the mass term of a single Dirac cone changes sign. In the limit where the physics is dominated by a single Dirac cone, we theoretically find that the Hall conductivity universally changes by two-thirds of the quantum of conductivity. I will analyze this universal behavior by considering the Haldane model, and discuss experimental aspects for its observation in cold atoms. This work is supported by TUBITAK, NSFPHY-1508300, ARO-MURI W9111NF-14-1-0003.

(Never) Mind your p's and q's: Von Neumann versus Jordan on the foundations of quantum theory

NASA Astrophysics Data System (ADS)

Duncan, A.; Janssen, M.

2013-03-01

In 1927, in two papers entitled "On a new foundation [Neue Begründung] of quantum mechanics," Pascual Jordan presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. Jordan and Paul Dirac arrived at essentially the same theory independently of one another at around the same time. Later in 1927, partly in response to Jordan and Dirac and avoiding the mathematical difficulties facing their approach, John von Neumann developed the modern Hilbert space formalism of quantum mechanics. We focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan and Dirac were the first to state those rules in full generality. Von Neumann rephrased them and, in a paper published a few months later, sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.

Dirac electrons in quantum rings

NASA Astrophysics Data System (ADS)

Gioia, L.; Zülicke, U.; Governale, M.; Winkler, R.

2018-05-01

We consider quantum rings realized in materials where the dynamics of charge carriers mimics that of two-dimensional (2D) Dirac electrons. A general theoretical description of the ring-subband structure is developed that applies to a range of currently available 2D systems, including graphene, transition-metal dichalcogenides, and narrow-gap semiconductor quantum wells. We employ the scattering-matrix approach to calculate the electronic two-terminal conductance through the ring and investigate how it is affected by Dirac-electron interference. The interplay of pseudospin chirality and hard-wall confinement is found to distinctly affect the geometric phase that is experimentally accessible in mesoscopic-conductance measurements. We derive an effective Hamiltonian for the azimuthal motion of charge carriers in the ring that yields deeper insight into the physical origin of the observed transport effects, including the unique behavior exhibited by the lowest ring subband in the normal and topological (i.e., band-inverted) regimes. Our paper provides a unified approach to characterizing confined Dirac electrons, which can be used to explore the design of valley- and spintronic devices based on quantum interference and the confinement-tunable geometric phase.

Minimally doubled fermions and spontaneous chiral symmetry breaking

NASA Astrophysics Data System (ADS)

Osmanaj (Zeqirllari), Rudina; Hyka (Xhako), Dafina

2018-03-01

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks - Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss - Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

Split Dirac cones in HgTe/CdTe quantum wells due to symmetry-enforced level anticrossing at interfaces

NASA Astrophysics Data System (ADS)

Tarasenko, S. A.; Durnev, M. V.; Nestoklon, M. O.; Ivchenko, E. L.; Luo, Jun-Wei; Zunger, Alex

2015-02-01

HgTe is a band-inverted compound which forms a two-dimensional topological insulator if sandwiched between CdTe barriers for a HgTe layer thickness above the critical value. We describe the fine structure of Dirac states in the HgTe/CdTe quantum wells of critical and close-to-critical thicknesses and show that the necessary creation of interfaces brings in another important physical effect: the opening of a significant anticrossing gap between the tips of the Dirac cones. The level repulsion driven by the natural interface inversion asymmetry of zinc-blende heterostructures considerably modifies the electron states and dispersion but preserves the topological transition at the critical thickness. By combining symmetry analysis, atomistic calculations, and extended k .p theory with interface terms, we obtain a quantitative description of the energy spectrum and extract the interface mixing coefficient. We discuss how the fingerprints of the predicted zero-magnetic-field splitting of the Dirac cones could be detected experimentally by studying magnetotransport phenomena, cyclotron resonance, Raman scattering, and THz radiation absorption.

Multilepton collider signatures of heavy Dirac and Majorana neutrinos

NASA Astrophysics Data System (ADS)

Chen, Chien-Yi; Dev, P. S. Bhupal

2012-05-01

We discuss the possibility of observing multi-lepton signals at the Large Hadron Collider (LHC) from the production and decay of heavy standard model (SM) singlet neutrinos added in extensions of SM to explain the observed light neutrino masses by seesaw mechanism. In particular, we analyze two “smoking gun” signals depending on the Dirac or Majorana nature of the heavy neutrino: (i) for Majorana case, the same-sign di-lepton signal which can be used as a probe of lepton-number violation, and (ii) for Dirac case, the tri-lepton signal which conserves lepton number but may violate lepton flavor. Within a minimal Left-Right symmetric framework in which these additional neutrino states arise naturally, we find that in both cases, the signals can be identified with virtually no background beyond a TeV, and the heavy gauge boson WR can be discovered in this process. This analysis also provides a direct way to probe the nature of seesaw physics involving the SM singlets at TeV-scale, and in particular, to distinguish type-I seesaw with purely Majorana heavy neutrinos from inverse seesaw with pseudo-Dirac counterparts.

The Future of Our Physics

NASA Astrophysics Data System (ADS)

Zichichi, Antonino

The following sections are included: * Physics Problems * The Whole of our Knowledge * The Future * Appendices * Appendix A: Dirac - Antiparticles & Antimatter * Appendix B: Blackett - The discovery of the "Vacuum Polarization" (1932) [the 1st example of radiative effect: pre-the Lamb-shift (1947)] * Appendix C: The New Manhattan Project * References

Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

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

Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

2011-04-15

Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

Paul Weiss and the genesis of canonical quantization

NASA Astrophysics Data System (ADS)

Rickles, Dean; Blum, Alexander

2015-12-01

This paper describes the life and work of a figure who, we argue, was of primary importance during the early years of field quantisation and (albeit more indirectly) quantum gravity. A student of Dirac and Born, he was interned in Canada during the second world war as an enemy alien and after his release never seemed to regain a good foothold in physics, identifying thereafter as a mathematician. He developed a general method of quantizing (linear and non-linear) field theories based on the parameters labelling an arbitrary hypersurface. This method (the `parameter formalism' often attributed to Dirac), though later discarded, was employed (and viewed at the time as an extremely important tool) by the leading figures associated with canonical quantum gravity: Dirac, Pirani and Schild, Bergmann, DeWitt, and others. We argue that he deserves wider recognition for this and other innovations.

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.

Reduced Order Podolsky Model

NASA Astrophysics Data System (ADS)

Thibes, Ronaldo

2017-02-01

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.

Application of Dirac's Generalized Hamiltonian Dynamics to Atomic and Molecular Systems

NASA Astrophysics Data System (ADS)

Uzer, Turgay

2002-10-01

Incorporating electronic degrees of freedom into classical treatments of atoms and molecules is a challenging problem from both the practical and fundamental points of view. Because it goes to the heart of classical-quantal correspondence, there are now a number of prescriptions which differ by the extent of quantal information that they include. We reach back to Dirac for inspiration, who, half a century ago, designed a so-called Generalized Hamiltonian Dynamics (GHD) with applications to field theory in mind. Physically, the GHD is a purely classical formalism for systems with constraints; it incorporates the constraints into the Hamiltonian. We apply the GHD to atomic and molecular physics by choosing integrals of motion as the constraints. We show that this purely classical formalism allows the derivation of energies of non-radiating states.

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2-xTe3.

PubMed

Lee, Inhee; Kim, Chung Koo; Lee, Jinho; Billinge, Simon J L; Zhong, Ruidan; Schneeloch, John A; Liu, Tiansheng; Valla, Tonica; Tranquada, John M; Gu, Genda; Davis, J C Séamus

2015-02-03

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr0.08(Bi0.1Sb0.9)1.92Te3. Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship [Formula: see text] is confirmed throughout and exhibits an electron-dopant interaction energy J* = 145 meV·nm(2). These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2-xTe3

PubMed Central

Lee, Inhee; Kim, Chung Koo; Lee, Jinho; Billinge, Simon J. L.; Zhong, Ruidan; Schneeloch, John A.; Liu, Tiansheng; Valla, Tonica; Tranquada, John M.; Gu, Genda; Davis, J. C. Séamus

2015-01-01

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a “Dirac-mass gap” in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr0.08(Bi0.1Sb0.9)1.92Te3. Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship Δ(r)∝n(r) is confirmed throughout and exhibits an electron–dopant interaction energy J* = 145 meV·nm2. These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential. PMID:25605947

DIRAC: A new version of computer algebra tools for studying the properties and behavior of hydrogen-like ions

NASA Astrophysics Data System (ADS)

McConnell, Sean; Fritzsche, Stephan; Surzhykov, Andrey

2010-03-01

During recent years, the DIRAC package has proved to be an efficient tool for studying the structural properties and dynamic behavior of hydrogen-like ions. Originally designed as a set of MAPLE procedures, this package provides interactive access to the wave and Green's functions in the non-relativistic and relativistic frameworks and supports analytical evaluation of a large number of radial integrals that are required for the construction of transition amplitudes and interaction cross sections. We provide here a new version of the DIRAC program which is developed within the framework of MATHEMATICA (version 6.0). This new version aims to cater to a wider community of researchers that use the MATHEMATICA platform and to take advantage of the generally faster processing times therein. Moreover, the addition of new procedures, a more convenient and detailed help system, as well as source code revisions to overcome identified shortcomings should ensure expanded use of the new DIRAC program over its predecessor. New version program summaryProgram title: DIRAC Catalogue identifier: ADUQ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 45 073 No. of bytes in distributed program, including test data, etc.: 285 828 Distribution format: tar.gz Programming language: Mathematica 6.0 or higher Computer: All computers with a license for the computer algebra package Mathematica (version 6.0 or higher) Operating system: Mathematica is O/S independent Classification: 2.1 Catalogue identifier of previous version: ADUQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 165 (2005) 139 Does the new version supersede the previous version?: Yes Nature of problem: Since the early days of quantum mechanics, the "hydrogen atom" has served as one of the key models for studying the structure and dynamics of various quantum systems. Its analytic solutions are frequently used in case studies in atomic and molecular physics, quantum optics, plasma physics, or even in the field of quantum information and computation. Fast and reliable access to functions and properties of the hydrogenic systems are frequently required, in both the non-relativistic and relativistic frameworks. Despite all the knowledge about one-electron ions, providing such an access is not a simple task, owing to the rather complicated mathematical structure of the Schrödinger and especially Dirac equations. Moreover, for analyzing experimental results as well as for performing advanced theoretical studies one often needs (apart from the detailed information on atomic wave- and Green's functions) to be able to calculate a number of integrals involving these functions. Although for many types of transition operators these integrals can be evaluated analytically in terms of special mathematical functions, such an evaluation is usually rather involved and prone to mistakes. Solution method: A set of Mathematica procedures is developed which provides both the non-relativistic and relativistic solutions of the "Hydrogen atom model". It facilitates, moreover, the symbolic evaluation of integrals involved in the calculations of cross sections and transition amplitudes. These procedures are based on a large number of relations among special mathematical functions, information about their integral representations, recurrence formulae and series expansions. Based on this knowledge, the DIRAC tools provide a fast and reliable algebraic (and if necessary, numeric) manipulation of functions and properties of one-electron systems, thus helping to obtain further insight into the behavior of quantum physical systems. Reasons for new version: The original version of the DIRAC program was developed as a toolbox of Maple procedures and was submitted to the CPC library in 2004 (cf. Ref. [1]). Since then DIRAC has found its niche in advanced theoretical studies carried out in realm of heavy ion physics. With the help of this program detailed analysis has been performed, in particular, for the various excitation and ionization processes occurring in relativistic ion-atom collisions [2], the polarization of the characteristic X-ray radiation following radiative electron capture [3], the correlation properties of the two-photon emission from few-electron heavy ions [4], the spin entanglement phenomena in atomic photoionization [5] and even for exploring the vibrational excitations of the heavy nuclei [6]. Although these studies have conclusively proven the potential of the program, they have also illuminated routes for its further enhancement. Apart from certain source code revisions, demand has grown for a new version of DIRAC compatible with the Mathematica platform. The version presented here includes a wider ranging and more user friendly interactive help system, a number of new procedures and reprogramming for greater computational efficiency. Summary of revisions: The most important new capabilities of the DIRAC program since the previous version are: The utilization of the Mathematica (version 6.0) platform. The addition of a number of new procedures. Since the complete list of the new (and updated) procedures can be found in the interactive help library of the program, we mention here only the most important ones: DiracGlobal[] - Displays a list of the current global settings which specify the framework, nuclear charge and the units which are to be used by the DIRAC program. DiracRadialOrbitalMomentum[] - Returns a non-relativistic radial orbital in momentum space for both, the bound and free electron states. DiracSlaterRadial[] - Evaluates the radial Slater integral both, with the non-relativistic and relativistic wavefunctions. In the previous version of the program this procedure was restricted to the non-relativistic framework only. DiracGreensIntegralRadial[] - Evaluates the two-dimensional radial integrals with the wave- and Green's functions both in non-relativistic and relativistic frameworks. DiracAngularMatrixElement[] - Calculates the angular matrix elements for various irreducible tensor operators. The elimination of some redundant procedures. In particular, the previous version supported evaluation of the spherical Bessel functions, Wigner 3j symbols, Clebsch-Gordan coefficients and spherical harmonics functions. These tools are now superseded by in-built procedures of Mathematica. The development of a full featured interactive help system which follows the style of the Mathematica Help Pages. Extensive revision of the source code in order to correct a number of bugs and inconsistencies that have been identified during use of the previous version of Dirac. The DIRAC package is distributed as a compressed tar file from which the DIRAC root directory can be (re-)generated. The root directory contains the source code and help libraries, a "Readme" file, Dirac_Installation_Instructions, as well as the notebook DemonstrationNotebook.nb that includes a number of test cases to illustrate the use of the program. These test cases, which concern the theoretical analysis of wavefunctions and the fine-structure of hydrogen-like ions, has already been discussed in detail in Ref. [1] and are provided here in order to underline the continuity between the previous (Maple) and new (Mathematica) versions of the DIRAC program. Unusual features: Even though all basic features of the previous Maple version have been retained in as close to the original form as possible, some small syntax changes became necessary in the new version of DIRAC in order to follow Mathematica standards. First of all, these changes concern naming conventions for DIRAC's procedures. As was discussed in Ref. [1], previously rather long names were employed in which each word was separated by an underscore. For example, when running the Maple version of the program one had to call the procedure Dirac_Slater_radial() in order to evaluate the Slater integral. Such a naming convention however, cannot be used in the Mathematica framework where the underscore character is reserved to represent Blank, a built-in symbol. In the new version of DIRAC we therefore follow the Mathematica convention of delimiting each word in a procedure's name by capitalization. Evaluation of the Slater determinant can be accomplished now simply by entering DiracSlaterRadial[]. Besides procedure names, a new convention is introduced to represent fundamental physical constants. In this version of DIRAC the group of (preset) global variables has changed to resemble their conventional symbols, specifically α, a, e, m, c and ℏ, being the fine structure constant, Bohr radius, electron charge, electron mass, speed of light and the Planck constant respectively. If the numerical evaluator N is wrapped around any of these constants, their numerical values are returned. Running time: Although the program replies promptly upon most requests, the running time also depends on the particular task. For example, computation of (radial) matrix elements involving components of relativistic wavefunctions might require a few seconds of a runtime. A number of test calculations performed regarding this and other tasks clearly indicate that the new version of Dirac requires up to 90% less evaluation time compared to its predecessor. References:A. Surzhykov, P. Koval, S. Fritzsche, Comput. Phys. Comm. 165 (2005) 139. H. Ogawa, et al., Phys. Rev. A 75 (2007) 1. A.V. Maiorova, et al., J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 125003. L. Borowska, A. Surzhykov, Th. Stöhlker, S. Fritzsche, Phys. Rev. A 74 (2006) 062516. T. Radtke, S. Fritzsche, A. Surzhykov, Phys. Rev. A 74 (2006) 032709. A. Pálffy, Z. Harman, A. Surzhykov, U.D. Jentschura, Phys. Rev. A 75 (2007) 012712.

Crystal growth of Dirac semimetal ZrSiS with high magnetoresistance and mobility.

PubMed

Sankar, Raman; Peramaiyan, G; Muthuselvam, I Panneer; Butler, Christopher J; Dimitri, Klauss; Neupane, Madhab; Rao, G Narsinga; Lin, M-T; Chou, F C

2017-01-18

High quality single crystal ZrSiS as a theoretically predicted Dirac semimetal has been grown successfully using a vapor phase transport method. The single crystals of tetragonal structure are easy to cleave into perfect square-shaped pieces due to the van der Waals bonding between the sulfur atoms of the quintuple layers. Physical property measurement results including resistivity, Hall coefficient (R H ), and specific heat are reported. The transport and thermodynamic properties suggest a Fermi liquid behavior with two Fermi pockets at low temperatures. At T = 3 K and magnetic field of Hǁc up to 9 Tesla, large magneto-resistance up to 8500% and 7200% for Iǁ (100) and Iǁ (110) were found. Shubnikov de Haas (SdH) oscillations were identified from the resistivity data, revealing the existence of two Fermi pockets at the Fermi level via the fast Fourier transform (FFT) analysis. The Hall coefficient (R H ) showed hole-dominated carriers with a high mobility of 3.05 × 10 4  cm 2 V -1 s -1 at 3 K. ZrSiS has been confirmed to be a Dirac semimetal by the Dirac cone mapping near the X-point via angle resolved photoemission spectroscopy (ARPES) with a Dirac nodal line near the Fermi level identified using scanning tunneling spectroscopy (STS).

New generation of two-dimensional spintronic systems realized by coupling of Rashba and Dirac fermions

PubMed Central

Eremeev, Sergey V.; Tsirkin, Stepan S.; Nechaev, Ilya A.; Echenique, Pedro M.; Chulkov, Evgueni V.

2015-01-01

Intriguing phenomena and novel physics predicted for two-dimensional (2D) systems formed by electrons in Dirac or Rashba states motivate an active search for new materials or combinations of the already revealed ones. Being very promising ingredients in themselves, interplaying Dirac and Rashba systems can provide a base for next generation of spintronics devices, to a considerable extent, by mixing their striking properties or by improving technically significant characteristics of each other. Here, we demonstrate that in BiTeI@PbSb2Te4 composed of a BiTeI trilayer on top of the topological insulator (TI) PbSb2Te4 weakly- and strongly-coupled Dirac-Rashba hybrid systems are realized. The coupling strength depends on both interface hexagonal stacking and trilayer-stacking order. The weakly-coupled system can serve as a prototype to examine, e.g., plasmonic excitations, frictional drag, spin-polarized transport, and charge-spin separation effect in multilayer helical metals. In the strongly-coupled regime, within ~100 meV energy interval of the bulk TI projected bandgap a helical state substituting for the TI surface state appears. This new state is characterized by a larger momentum, similar velocity, and strong localization within BiTeI. We anticipate that our findings pave the way for designing a new type of spintronics devices based on Rashba-Dirac coupled systems. PMID:26239268

Hidden symmetry in the presence of fluxes

NASA Astrophysics Data System (ADS)

Kubizňák, David; Warnick, Claude M.; Krtouš, Pavel

2011-03-01

We derive the most general first-order symmetry operator for the Dirac equation coupled to arbitrary fluxes. Such an operator is given in terms of an inhomogeneous form ω which is a solution to a coupled system of first-order partial differential equations which we call the generalized conformal Killing-Yano system. Except trivial fluxes, solutions of this system are subject to additional constraints. We discuss various special cases of physical interest. In particular, we demonstrate that in the case of a Dirac operator coupled to the skew symmetric torsion and U(1) field, the system of generalized conformal Killing-Yano equations decouples into the homogeneous conformal Killing-Yano equations with torsion introduced in D. Kubiznak et al. (2009) [8] and the symmetry operator is essentially the one derived in T. Houri et al. (2010) [9]. We also discuss the Dirac field coupled to a scalar potential and in the presence of 5-form and 7-form fluxes.

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

Gyenis, András; Inoue, Hiroyuki; Jeon, Sangjun

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions.Weemployed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. Bymore » mapping the quasiparticle interference (QPI) and emerging Landau levels at high magnetic field in Dirac semimetals Cd 3As 2 and Na 3Bi, we observed extended Dirac-like bulk electronic bands. QPI imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface projected Weyl nodes.« less

Dirac R -matrix calculations for the electron-impact excitation of neutral tungsten providing noninvasive diagnostics for magnetic confinement fusion

NASA Astrophysics Data System (ADS)

Smyth, R. T.; Ballance, C. P.; Ramsbottom, C. A.; Johnson, C. A.; Ennis, D. A.; Loch, S. D.

2018-05-01

Neutral tungsten is the primary candidate as a wall material in the divertor region of the International Thermonuclear Experimental Reactor (ITER). The efficient operation of ITER depends heavily on precise atomic physics calculations for the determination of reliable erosion diagnostics, helping to characterize the influx of tungsten impurities into the core plasma. The following paper presents detailed calculations of the atomic structure of neutral tungsten using the multiconfigurational Dirac-Fock method, drawing comparisons with experimental measurements where available, and includes a critical assessment of existing atomic structure data. We investigate the electron-impact excitation of neutral tungsten using the Dirac R -matrix method, and by employing collisional-radiative models, we benchmark our results with recent Compact Toroidal Hybrid measurements. The resulting comparisons highlight alternative diagnostic lines to the widely used 400.88-nm line.

Dynamical class of a two-dimensional plasmonic Dirac system.

PubMed

Silva, Érica de Mello

2015-10-01

A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.

Theoretical X-ray production cross sections at incident photon energies across Li (i=1-3) absorption edges of Br

NASA Astrophysics Data System (ADS)

Puri, Sanjiv

2015-08-01

The X-ray production (XRP) cross sections, σLk (k = l, η, α, β6, β1, β3, β4, β9,10, γ1,5, γ2,3) have been evaluated at incident photon energies across the Li(i=1-3) absorption edge energies of 35Br using theoretical data sets of different physical parameters, namely, the Li(i=1-3) sub-shell the X-ray emission rates based on the Dirac-Fock (DF) model, the fluorescence and Coster Kronig yields based on the Dirac-Hartree-Slater (DHS) model, and two sets of the photoionisation cross sections based on the relativistic Hartree-Fock-Slater (RHFS) model and the Dirac-Fock (DF) model, in order to highlight the importance of electron exchange effects at photon energies in vicinity of absorption edge energies.

Cosmic time and reduced phase space of general relativity

NASA Astrophysics Data System (ADS)

Ita, Eyo Eyo; Soo, Chopin; Yu, Hoi-Lai

2018-05-01

In an ever-expanding spatially closed universe, the fractional change of the volume is the preeminent intrinsic time interval to describe evolution in general relativity. The expansion of the universe serves as a subsidiary condition which transforms Einstein's theory from a first class to a second class constrained system when the physical degrees of freedom (d.o.f.) are identified with transverse traceless excitations. The super-Hamiltonian constraint is solved by eliminating the trace of the momentum in terms of the other variables, and spatial diffeomorphism symmetry is tackled explicitly by imposing transversality. The theorems of Maskawa-Nishijima appositely relate the reduced phase space to the physical variables in canonical functional integral and Dirac's criterion for second class constraints to nonvanishing Faddeev-Popov determinants in the phase space measures. A reduced physical Hamiltonian for intrinsic time evolution of the two physical d.o.f. emerges. Freed from the first class Dirac algebra, deformation of the Hamiltonian constraint is permitted, and natural extension of the Hamiltonian while maintaining spatial diffeomorphism invariance leads to a theory with Cotton-York term as the ultraviolet completion of Einstein's theory.

Some Consequences of a Time Dependent Speed of Light

NASA Astrophysics Data System (ADS)

Smith, Felix T.

2007-06-01

For reasons connected with both cosmology (the flatness and horizon problems) and atomic physics (n-body Dirac equation, etc.), various proposals have been made to modify general or special relativity(SR) to accommodate a cosmologically decreasing light speed [J. Magueijo, Rep. Prog. Phys. 66, 2025 (2003)]. Two such theories, projective SR [S.N. Manida, gr-qc/9905046; S. S. Stepanov, physics/9909009 and Phys. Rev. D, 62, 023507 (2000)] and symmetric SR [F.T. Smith, Ann. Fond. L. de Broglie, 30, 179 (2005)] adapt special relativity to in different ways to an expanding, hyperbolically curved position space and predict time-dependences of c within reach of measurement but differing by a factor of two. Both theories bring in a new constant λ-1=σ=c^2H0-1. As Magueijo points, out the role of c in physics and cosmology is so profound that many deep changes must follow if is not absolutely invariant in space and time. In particular, symmetric SR brings a new light to the Dirac large-number relationship between the constants of gravitation and atomic physics.

PEOPLE IN PHYSICS: Interview with Peter Higgs

NASA Astrophysics Data System (ADS)

Fancey, Conducted by Norman

1998-01-01

Peter Higgs, FRSE, FRS held until recently a personal chair in theoretical physics at the University of Edinburgh and is now an emeritus professor. Peter is well known for predicting the existence of a new particle, the Higgs boson - as yet unconfirmed. He has been awarded a number of prizes in recognition of his work, most recently the Paul Dirac Medal and Prize for outstanding contributions to theoretical physics from the Institute of Physics and the 1997 High Energy and Particle Physics Prize by the European Physical Society.

Observation of valleylike edge states of sound at a momentum away from the high-symmetry points

NASA Astrophysics Data System (ADS)

Xia, Bai-Zhan; Zheng, Sheng-Jie; Liu, Ting-Ting; Jiao, Jun-Rui; Chen, Ning; Dai, Hong-Qing; Yu, De-Jie; Liu, Jian

2018-04-01

In condensed matter physics, topologically protected edge transportation has drawn extensive attention over recent years. Thus far, the topological valley edge states have been produced near the Dirac cones fixed at the high-symmetry points of the Brillouin zone. In this paper, we demonstrate a unique valleylike phononic crystal (PnC) with the position-varying Dirac cones at the high-symmetry lines of the Brillouin zone boundary. The emergence of such Dirac cones, characterized by the vortex structure in a momentum space, is attributed to the unavoidable band crossing protected by the mirror symmetry. The Dirac cones can be unbuckled and a complete band gap can be induced through breaking the mirror symmetry. Interestingly, by simply rotating the square columns, we realize the valleylike vortex states and the band inversion effect which leads to the valley Hall phase transition. Along the valleylike PnC interfaces separating two distinct acoustic valley Hall phases, the valleylike protected edge transport of sound in domain walls is observed in both the simulations and the experiments. These results are promising for the exploration of alternative topological phenomena in the valleylike PnCs beyond the graphenelike lattice.

From lattice Hamiltonians to tunable band structures by lithographic design

NASA Astrophysics Data System (ADS)

Tadjine, Athmane; Allan, Guy; Delerue, Christophe

2016-08-01

Recently, new materials exhibiting exotic band structures characterized by Dirac cones, nontrivial flat bands, and band crossing points have been proposed on the basis of effective two-dimensional lattice Hamiltonians. Here, we show using atomistic tight-binding calculations that these theoretical predictions could be experimentally realized in the conduction band of superlattices nanolithographed in III-V and II-VI semiconductor ultrathin films. The lithographed patterns consist of periodic lattices of etched cylindrical holes that form potential barriers for the electrons in the quantum well. In the case of honeycomb lattices, the conduction minibands of the resulting artificial graphene host several Dirac cones and nontrivial flat bands. Similar features, but organized in different ways, in energy or in k -space are found in kagome, distorted honeycomb, and Lieb superlattices. Dirac cones extending over tens of meV could be obtained in superlattices with reasonable sizes of the lithographic patterns, for instance in InAs/AlSb heterostructures. Bilayer artificial graphene could be also realized by lithography of a double quantum-well heterostructure. These new materials should be interesting for the experimental exploration of Dirac-based quantum systems, for both fundamental and applied physics.

Dirac electrons in Moiré superlattice: From two to three dimensions

NASA Astrophysics Data System (ADS)

Hu, Chen; Michaud-Rioux, Vincent; Kong, Xianghua; Guo, Hong

2017-11-01

Moiré patterns in van der Waals (vdW) heterostructures bring novel physical effects to the materials. We report theoretical investigations of the Moiré pattern formed by graphene (Gr) on hexagonal boron nitride (h BN). For both the two-dimensional (2D) flat-sheet and the freestanding three-dimensional (3D) wavelike film geometries, the behaviors of Dirac electrons are strongly modulated by the local high-symmetry stacking configurations of the Moiré pattern. In the 2D flat sheet, the secondary Dirac cone (SDC) dispersion emerges due to the stacking-selected localization of SDC wave functions, while the original Dirac cone (ODC) gap is suppressed due to an overall effect of ODC wave functions. In the freestanding 3D wavelike Moiré structure, we predict that a specific local stacking in the Moiré superlattice is promoted at the expense of other local stackings, leading to an electronic structure more similar to that of the perfectly matching flat Gr/h BN than that of the flat-sheet 2D Moiré pattern. To capture the overall picture of the Moiré superlattice, supercells containing 12 322 atoms are simulated by first principles.

Hamiltonian structure of Dubrovin{close_quote}s equation of associativity in 2-d topological field theory

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

Galvao, C.A.; Nutku, Y.

1996-12-01

mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential.

PubMed

Akemann, G; Bloch, J; Shifrin, L; Wettig, T

2008-01-25

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.

Numerical investigation of the flat band Bloch modes in a 2D photonic crystal with Dirac cones

DOE PAGES

Zhang, Peng; Fietz, Chris; Tassin, Philippe; ...

2015-04-14

A numerical method combining complex-k band calculations and absorbing boundary conditions for Bloch waves is presented. We use this method to study photonic crystals with Dirac cones. We demonstrate that the photonic crystal behaves as a zero-index medium when excited at normal incidence, but that the zero-index behavior is lost at oblique incidence due to excitation of modes on the flat band. We also investigate the formation of monomodal and multimodal cavity resonances inside the photonic crystals, and the physical origins of their different line-shape features.

Antibonding ground state of adatom molecules in bulk Dirac semimetals

NASA Astrophysics Data System (ADS)

Marques, Y.; Obispo, A. E.; Ricco, L. S.; de Souza, M.; Shelykh, I. A.; Seridonio, A. C.

2017-07-01

The ground state of the diatomic molecules in nature is inevitably bonding, and its first excited state is antibonding. We demonstrate theoretically that, for a pair of distant adatoms placed buried in three-dimensional-Dirac semimetals, this natural order of the states can be reversed and an antibonding ground state occurs at the lowest energy of the so-called bound states in the continuum. We propose an experimental protocol with the use of a scanning tunneling microscope tip to visualize the topographic map of the local density of states on the surface of the system to reveal the emerging physics.

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr x(Bi 0.1Sb 0.9) 2-xTe 3

DOE PAGES

Lee, Inhee; Kim, Chung Koo; Lee, Jinho; ...

2015-01-20

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a “Dirac-mass gap” in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in themore » ferromagnetic TI Cr₀.₀₈(Bi₀.₁Sb₀.₉)₁.₉₂Te₃. Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship Δ(r)∝n(r) is confirmed throughout and exhibits an electron–dopant interaction energy J* = 145 meV·nm². In addition, these observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.« less

Photon-Electron Interactions in Dirac Quantum Materials

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

Xu, Xiaodong

The objective of this proposal was to explore the fundamental light-matter interactions in a new class of Dirac quantum materials, atomically thin transition metal dichalcogenides (TMDs). Monolayer TMDs are newly discovered two-dimensional semiconductors with direct bandgap. Due to their hexagonal lattice structure, the band edge localizes at corner of Brillouin zone, i.e. “Dirac valleys”. This gives the corresponding electron states a “valley index” (or pseudospin) in addition to the real spin. Remarkably, the valley pseudospins have circularly polarized optical selection rules, providing the first solid state system for dynamic control of the valley degree of freedom. During this award, wemore » have developed a suite of advanced nano-optical spectroscopy tools in the investigation and manipulation of charge, spin, and valley degrees of freedom in monolayer semiconductors. Emerging physical phenomena, such as quantum coherence between valley pseudospins, have been demonstrated for the first time in solids. In addition to monolayers, we have developed a framework in engineering, formulating, and understanding valley pseudospin physics in 2D heterostructures formed by different monolayer semiconductors. We demonstrated long-lived valley-polarized interlayer excitons with valley-dependent many-body interaction effects. These works push the research frontier in understanding the light-matter interactions in atomically-thin quantum materials for protentional transformative energy technologies.« less

Dirac potential in the Doebner-Goldin equation

NASA Astrophysics Data System (ADS)

Jia, Wei; Ma, Yi Rong; Hu, Fang Qi; Zhao, Qing

2018-01-01

We study a dissipative quantum system which is described by the Doebner-Goldin equation (DGE) model. For time-independent states, the new three-dimensional analytical solutions of the DGE are obtained by binding the vertical relation of velocity and the gradient of density in the system, when the form of a central potential such as hard core or harmonic oscillator is suggested. Through the gauge-invariant parameters which characterize the physical nature of the dissipation, we find a novel set of gauge-invariant parameters which show that the Galilean invariance is broken in this system. Moreover, a subfamily of the DGE can be obtained after a gauge transformation, which describes a dissipative quantum system with the conserved Galilean invariance. It is interesting that this dissipative quantum system is completely equivalent to a charge-monopole system, in which the Dirac potential is supplied with the nonlinear terms and two cases of the velocity potential. Especially, the two gauge potentials given by Wu and Yang emerge from solving the DGE as two cases in our approach. The results not only present some new physical comprehension of the dissipative quantum system, but also might shed light on the Dirac monopole potential, in the sense that the partition into south and north hemisphere is avoided in our new solutions.

Project Physics Reader 5, Models of the Atom.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

As a supplement to Project Physics Unit 5, a collection of articles is presented in this reader for student browsing. Nine excerpts are given under the following headings: failure and success, Einstein, Mr. Tompkins and simultaneity, parable of the surveyors, outside and inside the elevator, the teacher and the Bohr theory of atom, Dirac and Born,…

Quantum scar and breakdown of universality in graphene: A theoretical insight

NASA Astrophysics Data System (ADS)

Iyakutti, Kombiah; Rajeswarapalanichamy, Ratnavelu; Surya, Velappa Jayaraman; Kawazoe, Yoshiyuki

2017-12-01

Graphene has brought forward a lot of new physics. One of them is the emergence of massless Dirac fermions in addition to the electrons and these features are new to physics. In this theoretical study, the signatures for quantum scar and the breakdown of universality in graphene are investigated with reference to the presence of these two types of fermions. Taking the graphene quantum dot (QD) potential as the confining potential, the radial part of Dirac equations are solved numerically. Concentrations of the two component eigen-wavefunctions about classical periodic orbits emerge as the signatures for the quantum scar. The sudden variations, in the ratio of the radial wave-functions (large and small components), R(g/f), with mass ratio κ are the signatures for breakdown of universality in graphene. The breakdown of universality occurs for the states k = -1 and k = 1, and the state k = -1 is more susceptible to the breakdown of universality.

Physics of Electronic Materials

NASA Astrophysics Data System (ADS)

Rammer, Jørgen

2017-03-01

1. Quantum mechanics; 2. Quantum tunneling; 3. Standard metal model; 4. Standard conductor model; 5. Electric circuit theory; 6. Quantum wells; 7. Particle in a periodic potential; 8. Bloch currents; 9. Crystalline solids; 10. Semiconductor doping; 11. Transistors; 12. Heterostructures; 13. Mesoscopic physics; 14. Arithmetic, logic and machines; Appendix A. Principles of quantum mechanics; Appendix B. Dirac's delta function; Appendix C. Fourier analysis; Appendix D. Classical mechanics; Appendix E. Wave function properties; Appendix F. Transfer matrix properties; Appendix G. Momentum; Appendix H. Confined particles; Appendix I. Spin and quantum statistics; Appendix J. Statistical mechanics; Appendix K. The Fermi-Dirac distribution; Appendix L. Thermal current fluctuations; Appendix M. Gaussian wave packets; Appendix N. Wave packet dynamics; Appendix O. Screening by symmetry method; Appendix P. Commutation and common eigenfunctions; Appendix Q. Interband coupling; Appendix R. Common crystal structures; Appendix S. Effective mass approximation; Appendix T. Integral doubling formula; Bibliography; Index.

Lifshitz Transitions, Type-II Dirac and Weyl Fermions, Event Horizon and All That

NASA Astrophysics Data System (ADS)

Volovik, G. E.; Zhang, K.

2017-12-01

The type-II Weyl and type-II Dirac points emerge in semimetals and also in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. In this case the horizon with Painlevé-Gullstrand metric serves as the surface of the Lifshitz transition. This relativistic analogy allows us to simulate the black hole horizon and Hawking radiation using the fermionic superfluid with supercritical velocity, and the Dirac and Weyl semimetals with the interface separating the type-I and type-II states. The difference between such type of the artificial event horizon and that which arises in acoustic metric is discussed. At the Lifshitz transition between type-I and type-II fermions the Dirac lines may also emerge, which are supported by the combined action of topology and symmetry. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. Different configurations of the Fermi surfaces, involved in such Lifshitz transition, are discussed. In one case the type-II Weyl point connects the Fermi pockets and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds. For the interacting electrons, the Lifshitz transitions may lead to the formation of the dispersionless (flat) band with zero energy and singular density of states, which opens the route to room-temperature superconductivity. Originally, the idea of the enhancement of T_c due to flat band has been put forward by the nuclear physics community, and this also demonstrates the close connections between different areas of physics.

Symplectic analysis of three-dimensional Abelian topological gravity

NASA Astrophysics Data System (ADS)

Cartas-Fuentevilla, R.; Escalante, Alberto; Herrera-Aguilar, Alfredo

2017-02-01

A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide with each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.

Tuning topological phases in the XMnSb2 system via chemical substitution from first principles

NASA Astrophysics Data System (ADS)

Griffin, Sinead M.; Neaton, Jeffrey B.

New Dirac materials are sought for their interesting fundamental physics and for their potential technological applications. Protected symmetries offer a route to potential zero mass Dirac and Weyl fermions, and can lead unique transport properties and spectroscopic signatures. In this work, we use first-principles calculations to study the XMnSb2 family of materials and show how varying X changes the nature of bulk protected topological features in their electronic structure. We further discuss new design rules for predicting new topological materials suggested by our calculations. SG is supported by the Early Postdoc Mobility Fellowship of the SNF.

Theory of the Decoherence Effect in Finite and Infinite Open Quantum Systems Using the Algebraic Approach

NASA Astrophysics Data System (ADS)

Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert

Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.

Dirac δ -function potential in quasiposition representation of a minimal-length scenario

NASA Astrophysics Data System (ADS)

Gusson, M. F.; Gonçalves, A. Oakes O.; Francisco, R. O.; Furtado, R. G.; Fabris, J. C.; Nogueira, J. A.

2018-03-01

A minimal-length scenario can be considered as an effective description of quantum gravity effects. In quantum mechanics the introduction of a minimal length can be accomplished through a generalization of Heisenberg's uncertainty principle. In this scenario, state eigenvectors of the position operator are no longer physical states and the representation in momentum space or a representation in a quasiposition space must be used. In this work, we solve the Schroedinger equation with a Dirac δ -function potential in quasiposition space. We calculate the bound state energy and the coefficients of reflection and transmission for the scattering states. We show that leading corrections are of order of the minimal length ({ O}(√{β })) and the coefficients of reflection and transmission are no longer the same for the Dirac delta well and barrier as in ordinary quantum mechanics. Furthermore, assuming that the equivalence of the 1s state energy of the hydrogen atom and the bound state energy of the Dirac {{δ }}-function potential in the one-dimensional case is kept in a minimal-length scenario, we also find that the leading correction term for the ground state energy of the hydrogen atom is of the order of the minimal length and Δx_{\\min } ≤ 10^{-25} m.

Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride

DOE PAGES

Wang, Eryin; Lu, Xiaobo; Ding, Shijie; ...

2016-08-22

Graphene/hexagonal boron nitride (h-BN) has emerged as a model van der Waals heterostructure as the superlattice potential, which is induced by lattice mismatch and crystal orientation, gives rise to various novel quantum phenomena, such as the self-similar Hofstadter butterfly states. Although the newly generated second-generation Dirac cones (SDCs) are believed to be crucial for understanding such intriguing phenomena, fundamental knowledge of SDCs, such as locations and dispersion, and the effect of inversion symmetry breaking on the gap opening, still remains highly debated due to the lack of direct experimental results. In this work we report direct experimental results on themore » dispersion of SDCs in 0°-aligned graphene/h-BN heterostructures using angle-resolved photoemission spectroscopy. Our data unambiguously reveal SDCs at the corners of the superlattice Brillouin zone, and at only one of the two superlattice valleys. Moreover, gaps of approximately 100 meV and approximately 160 meV are observed at the SDCs and the original graphene Dirac cone, respectively. Our work highlights the important role of a strong inversion-symmetry-breaking perturbation potential in the physics of graphene/h-BN, and fills critical knowledge gaps in the band structure engineering of Dirac fermions by a superlattice potential.« less

Nanophysics in graphene: neutrino physics in quantum rings and superlattices.

PubMed

Fertig, H A; Brey, Luis

2010-12-13

Electrons in graphene at low energy obey a two-dimensional Dirac equation, closely analogous to that of neutrinos. As a result, quantum mechanical effects when the system is confined or subjected to potentials at the nanoscale may be quite different from what happens in conventional electronic systems. In this article, we review recent progress on two systems where this is indeed the case: quantum rings and graphene electrons in a superlattice potential. In the former case, we demonstrate that the spectrum reveals signatures of 'effective time-reversal symmetry breaking', in which the spectra are most naturally interpreted in terms of effective magnetic flux contained in the ring, even when no real flux is present. A one-dimensional superlattice potential is shown to induce strong band-structure changes, allowing the number of Dirac points at zero energy to be manipulated by the strength and/or period of the potential. The emergence of new Dirac points is shown to be accompanied by strong signatures in the conduction properties of the system.

Quasiparticle interference mapping of ZrSiS

NASA Astrophysics Data System (ADS)

Lodge, Michael; Hosen, Md Mofazzle; Neupane, Madhab; Ishigami, Masa; Chang, Guoqing; Singh, Bahadur; Lin, Hsin; Weber, Bent; Hellerstedt, Jack; Edmonds, Mark; Fuhrer, Michael; Kaczorowski, Dariusz

The emergent class of 3D Dirac semimetals presents intriguing new systems in which to study the rich physics of the robust, topologically-protected quasiparticles hosted within their bulk. For example, in nodal-line Dirac semimetals, the conductance and valence bands meet along a closed loop in momentum space and disperse linearly in the vicinity of the resultant line node. This results in novel scattering phenomena, owing to the unique Fermi surfaces and scattering selection rules of these systems. Here, we have performed scanning tunneling microscopy and spectroscopy of ZrSiS, one such nodal-line Dirac semimetal,at 4.5 K. We have visualized quasiparticle scattering using differential conductance mapping. In conjunction with numerical modeling, we identify at least six allowed scattering vectors in the material, which gives insight into the scattering selection rules of these novel materials. This work is based upon research supported by the National Science Foundation under Grant No. 0955625 (MSL and MI) and Fellowship No. 1614303 (MSL), and by the Australian Research Council under DECRA Fellowship No. DE160101334 (BW).

Imaging electronic states on topological semimetals using scanning tunneling microscopy

DOE PAGES

Gyenis, András; Inoue, Hiroyuki; Jeon, Sangjun; ...

2016-10-18

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions.Weemployed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. Bymore » mapping the quasiparticle interference (QPI) and emerging Landau levels at high magnetic field in Dirac semimetals Cd 3As 2 and Na 3Bi, we observed extended Dirac-like bulk electronic bands. QPI imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface projected Weyl nodes.« less

The enhancement of quantum entanglement under an open Dirac system with the Hawking effect in Schwarzschild space-time

NASA Astrophysics Data System (ADS)

Sun, Wen-Yang; Wang, Dong; Fang, Bao-Long; Shi, Jia-Dong; Ye, Liu

2018-06-01

In this letter, we mainly investigate how to enhance the damaged quantum entanglement under an open Dirac system with the Hawking effect within Schwarzschild space-time. We consider that particle A held by Alice undergoes generalized amplitude damping noise in a flat space-time, and that another particle B by Bob entangled with A is under a Schwarzschild space-time. Subsequently, we put forward a physical scheme to recover the damaged quantum entanglement by prior weak measurement on subsystem A before the interaction with the decoherence noise followed by post-measurement filtering operation. The results indicate that our scheme can effectively recover the damaged quantum entanglement affected by the Hawking effect and the noisy channel. Thus, our work might be beneficial to understand the dynamic behavior of the quantum state and recover the damaged quantum entanglement with open Dirac systems under the Hawking effect in the background of a Schwarzschild black hole.

Hydrogenated borophene as a stable two-dimensional Dirac material with an ultrahigh Fermi velocity.

PubMed

Xu, Li-Chun; Du, Aijun; Kou, Liangzhi

2016-10-05

The recent synthesis of monolayer borophene (triangular boron monolayer) on a substrate has opened the era of boron nanosheets (Science, 2015, 350, 1513), but the structural instability and a need to explore the novel physical properties are still open issues. Here we demonstrated that borophene can be stabilized by full surface hydrogenation (borophane), from first-principles calculations. Most interestingly, our calculations show that borophane has direction-dependent Dirac cones, which are mainly caused by the in-plane p x and p y orbitals of boron atoms. The Dirac fermions possess an ultrahigh Fermi velocity of up to 3.5 × 10 6 m s -1 under the HSE06 level, which is 4 times higher than that of graphene. The Young's moduli are calculated to be 190 and 120 GPa nm along two different directions, which are comparable to those of steel. The ultrahigh Fermi velocity and good mechanical features render borophane ideal for nanoelectronic applications.

Theoretical X-ray production cross sections at incident photon energies across L{sub i} (i=1-3) absorption edges of Br

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

Puri, Sanjiv

The X-ray production (XRP) cross sections, σ{sub Lk} (k = l, η, α, β{sub 6}, β{sub 1}, β{sub 3}, β{sub 4}, β{sub 9,10}, γ{sub 1,5}, γ{sub 2,3}) have been evaluated at incident photon energies across the L{sub i}(i=1-3) absorption edge energies of {sub 35}Br using theoretical data sets of different physical parameters, namely, the L{sub i}(i=1-3) sub-shell the X-ray emission rates based on the Dirac-Fock (DF) model, the fluorescence and Coster Kronig yields based on the Dirac-Hartree-Slater (DHS) model, and two sets of the photoionisation cross sections based on the relativistic Hartree-Fock-Slater (RHFS) model and the Dirac-Fock (DF) model, inmore » order to highlight the importance of electron exchange effects at photon energies in vicinity of absorption edge energies.« less

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.

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

Theoretical Explanations in Mathematical Physics

NASA Astrophysics Data System (ADS)

Rivadulla, Andrés

Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.

CALL FOR PAPERS: Special cluster in Biomedical Optics: honouring Professor Valery Tuchin, Saratov University

NASA Astrophysics Data System (ADS)

Wang, Ruikang K.; Priezzhev, Alexander; Fantini, Sergio

2004-07-01

To honour Professor Valery Tuchin, one of the pioneers in biomedical optics, Journal of Physics D: Applied Physics invites manuscript submissions on topics in biomedical optics, for publication in a Special section in May 2005. Papers may cover a variety of topics related to photon propagation in turbid media, spectroscopy and imaging. This Special cluster will reflect the diversity, breadth and impact of Professor Tuchin's contributions to the field of biomedical optics over the course of his distinguished career. Biomedical optics is a recently emerged discipline providing a broad variety of optical techniques and instruments for diagnostic, therapeutic and basic science applications. Together with contributions from other pioneers in the field, Professor Tuchin's work on fundamental and experimental aspects in tissue optics contributed enormously to the formation of this exciting field. Although general submissions in biomedical optics are invited, the Special cluster Editors especially encourage submissions in areas that are explicitly or implicitly influenced by Professor Tuchin's contributions to the field of biomedical optics. Manuscripts submitted to this Special cluster of Journal of Physics D: Applied Physics will be refereed according to the normal criteria and procedures of the journal, in accordance with the following schedule: Deadline for receipt of contributed papers: 31 November 2004 Deadline for acceptance and completion of refereeing process: 28 February 2005 Publication of special issue: May 2005 Please submit your manuscript electronically to jphysd@iop.org or via the Web site at www.iop.org/Journals. Otherwise, please send a copy of your typescript, a set of original figures and a cover letter to: The Publishing Administrator, Journal of Physics D: Applied Physics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, United Kingdom. Further information on how to submit may be obtained upon request by e-mailing the journal at the above address. Alternatively, visit the homepage of the journal on the World Wide Web (http://www.iop.org/journals/jphysd)

Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals

DOE PAGES

Classen, Laura; Herbut, Igor F.; Scherer, Michael M.

2017-09-20

In this paper, we establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end, we study the quantum phase transition of gapless Dirac fermions coupled to a Z 3 symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekulé transition in honeycomb lattice materials. For this model, the standard Landau-Ginzburg approach suggests a first-order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have tomore » be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions N f. A nonperturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers and we obtain the critical N f, where the nature of the transition changes. Furthermore, it is shown that for large N f the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. Finally, we compute the critical exponents and predict sizable corrections to scaling for N f = 2.« less

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

Migdal's theorem and electron-phonon vertex corrections in Dirac materials

NASA Astrophysics Data System (ADS)

Roy, Bitan; Sau, Jay D.; Das Sarma, S.

2014-04-01

Migdal's theorem plays a central role in the physics of electron-phonon interactions in metals and semiconductors, and has been extensively studied theoretically for parabolic band electronic systems in three-, two-, and one-dimensional systems over the last fifty years. In the current work, we theoretically study the relevance of Migdal's theorem in graphene and Weyl semimetals which are examples of 2D and 3D Dirac materials, respectively, with linear and chiral band dispersion. Our work also applies to 2D and 3D topological insulator systems. In Fermi liquids, the renormalization of the electron-phonon vertex scales as the ratio of sound (vs) to Fermi (vF) velocity, which is typically a small quantity. In two- and three-dimensional quasirelativistic systems, such as undoped graphene and Weyl semimetals, the one loop electron-phonon vertex renormalization, which also scales as η =vs/vF as η →0, is, however, enhanced by an ultraviolet logarithmic divergent correction, arising from the linear, chiral Dirac band dispersion. Such enhancement of the electron-phonon vertex can be significantly softened due to the logarithmic increment of the Fermi velocity, arising from the long range Coulomb interaction, and therefore, the electron-phonon vertex correction does not have a logarithmic divergence at low energy. Otherwise, the Coulomb interaction does not lead to any additional renormalization of the electron-phonon vertex. Therefore, electron-phonon vertex corrections in two- and three-dimensional Dirac fermionic systems scale as vs/vF0, where vF0 is the bare Fermi velocity, and small when vs≪vF0. These results, although explicitly derived for the intrinsic undoped systems, should hold even when the chemical potential is tuned away from the Dirac points.

Magnetic charge and photon mass: Physical string singularities, Dirac condition, and magnetic confinement

NASA Astrophysics Data System (ADS)

Evans, Timothy J.; Singleton, Douglas

2018-04-01

We find exact, simple solutions to the Proca version of Maxwell’s equations with magnetic sources. Several properties of these solutions differ from the usual case of magnetic charge with a massless photon: (i) the string singularities of the usual 3-vector potentials become real singularities in the magnetic fields; (ii) the different 3-vector potentials become gauge inequivalent and physically distinct solutions; (iii) the magnetic field depends on r and 𝜃 and thus is no longer rotationally symmetric; (iv) a combined system of electric and magnetic charge carries a field angular momentum even when the electric and magnetic charges are located at the same place (i.e. for dyons); (v) for these dyons, one recovers the standard Dirac condition despite the photon being massive. We discuss the reason for this. We conclude by proposing that the string singularity in the magnetic field of an isolated magnetic charge suggests a confinement mechanism for magnetic charge, similar to the flux tube confinement of quarks in QCD.

Superconductivity in the antiperovskite Dirac-metal oxide Sr3−xSnO

PubMed Central

Oudah, Mohamed; Ikeda, Atsutoshi; Hausmann, Jan Niklas; Yonezawa, Shingo; Fukumoto, Toshiyuki; Kobayashi, Shingo; Sato, Masatoshi; Maeno, Yoshiteru

2016-01-01

Investigations of perovskite oxides triggered by the discovery of high-temperature and unconventional superconductors have had crucial roles in stimulating and guiding the development of modern condensed-matter physics. Antiperovskite oxides are charge-inverted counterpart materials to perovskite oxides, with unusual negative ionic states of a constituent metal. No superconductivity was reported among the antiperovskite oxides so far. Here we present the first superconducting antiperovskite oxide Sr3−xSnO with the transition temperature of around 5 K. Sr3SnO possesses Dirac points in its electronic structure, and we propose from theoretical analysis a possibility of a topological odd-parity superconductivity analogous to the superfluid 3He-B in moderately hole-doped Sr3−xSnO. We envision that this discovery of a new class of oxide superconductors will lead to a rapid progress in physics and chemistry of antiperovskite oxides consisting of unusual metallic anions. PMID:27941805

Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2017-12-01

The Atiyah-Patodi-Singer (APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a nonlocal boundary condition known as the "APS boundary condition" by hand, which is unlikely to be realized in the materials. In this work, we attempt to reformulate the APS index in a "physicist-friendly" way for a simple setup with U (1 ) or S U (N ) gauge group on a flat four-dimensional Euclidean space. We find that the same index as APS is obtained from the domain-wall fermion Dirac operator with a local boundary condition, which is naturally given by the kink structure in the mass term. As the boundary condition does not depend on the gauge fields, our new definition of the index is easy to compute with the standard Fujikawa method.

Off the Beat. An Appreciation of Werner Heisenberg and Some Talk About How Physics Was in the Good Old Days

ERIC Educational Resources Information Center

Thomsen, Dietrick E.

1976-01-01

Presented is an insight into man's idea about physics and being a physicist in the days when Heisenberg, P. A. M. Dirac, Louis de Broglic and other famous physicists were young men. Heisenberg is compared to Newton, inventing new math as he needed it. Emphasis is placed on the fact that he was not a Nazi sympathizer. (EB)

From lepton protoplasm to the genesis of hadrons

NASA Astrophysics Data System (ADS)

Eliseev, S. M.; Kosmachev, O. S.

2016-01-01

Theory of matter under extreme conditions opens a new stage in particle physics. It is necessary here to combine Dirac's elementary particle physics with Prigogine's dynamics of nonequilibrium systems. In the article we discuss the problem of the hierarchy of complexity. What can be considered as the lowest level of the organization of extreme matter on the basis of which the self-organization of the complex form occur?

a Simpler Solution of the Non-Uniqueness Problem of the Covariant Dirac Theory

NASA Astrophysics Data System (ADS)

Arminjon, Mayeul

2013-05-01

Although the standard generally covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory.

Large single crystal growth, transport property, and spectroscopic characterizations of three-dimensional Dirac semimetal Cd3As2.

PubMed

Sankar, R; Neupane, M; Xu, S-Y; Butler, C J; Zeljkovic, I; Panneer Muthuselvam, I; Huang, F-T; Guo, S-T; Karna, Sunil K; Chu, M-W; Lee, W L; Lin, M-T; Jayavel, R; Madhavan, V; Hasan, M Z; Chou, F C

2015-08-14

The three dimensional (3D) Dirac semimetal is a new quantum state of matter that has attracted much attention recently in physics and material science. Here, we report on the growth of large plate-like single crystals of Cd3As2 in two major orientations by a self-selecting vapor growth (SSVG) method, and the optimum growth conditions have been experimentally determined. The crystalline imperfections and electrical properties of the crystals were examined with transmission electron microscopy (TEM), scanning tunneling microscopy (STM), and transport property measurements. This SSVG method makes it possible to control the as-grown crystal compositions with excess Cd or As leading to mobilities near 5-10(5) cm(2)V(-1)s(-1). Zn-doping can effectively reduce the carrier density to reach the maximum residual resistivity ratio (RRRρ300K/ρ5K) of 7.6. A vacuum-cleaved single crystal has been investigated using angle-resolved photoemission spectroscopy (ARPES) to reveal a single Dirac cone near the center of the surface Brillouin zone with a binding energy of approximately 200 meV.

Asymmetric capture of Dirac dark matter by the Sun

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

Blennow, Mattias; Clementz, Stefan

2015-08-18

Current problems with the solar model may be alleviated if a significant amount of dark matter from the galactic halo is captured in the Sun. We discuss the capture process in the case where the dark matter is a Dirac fermion and the background halo consists of equal amounts of dark matter and anti-dark matter. By considering the case where dark matter and anti-dark matter have different cross sections on solar nuclei as well as the case where the capture process is considered to be a Poisson process, we find that a significant asymmetry between the captured dark particles andmore » anti-particles is possible even for an annihilation cross section in the range expected for thermal relic dark matter. Since the captured number of particles are competitive with asymmetric dark matter models in a large range of parameter space, one may expect solar physics to be altered by the capture of Dirac dark matter. It is thus possible that solutions to the solar composition problem may be searched for in these type of models.« less

Spectral geometry of {kappa}-Minkowski space

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

D'Andrea, Francesco

After recalling Snyder's idea [Phys. Rev. 71, 38 (1947)] of using vector fields over a smooth manifold as 'coordinates on a noncommutative space', we discuss a two-dimensional toy-model whose 'dual' noncommutative coordinates form a Lie algebra: this is the well-known {kappa}-Minkowski space [Phys. Lett. B 334, 348 (1994)]. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of {kappa}-Minkowski as linear operators on an Hilbert space (a major problem in the construction of a physical theory), study its 'spectral properties', and discuss how tomore » obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of Dimitrijevic et al. [Eur. Phys. J. C 31, 129 (2003)] can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.« less

Reviews Book: How to Teach Quantum Physics to Your Dog Equipment: LEGO Renewable Energy Add-on Set 9688 Book: The Rough Guide to the Future Book: Seven Tales of the Pendulum Equipment: Genecon DUE Equipment: Manual Electrostatic Generator Book: Quantify! A Crash Course in Smart Thinking Book: Fads and Fallacies in the Name of Science Book: The Strangest Man Book: The Ultimate Quotable Einstein Web Watch

NASA Astrophysics Data System (ADS)

2011-05-01

WE RECOMMEND How to Teach Quantum Physics to Your Dog The key theories of quantum physics explained using canine behaviour LEGO Renewable Energy Add-on Set 9688 Set builds a hand generator, solar station, wind turbine, hydro turbine, boat pulley, solar vehicle, and much more The Rough Guide to the Future Book explores the insights that science can contribute to predicting the future Seven Tales of the Pendulum This book deals with the significance of the pendulum in science, history and culture Genecon DUE Equipment demonstrates generation of electricity Fads and Fallacies in the Name of Science Book investigates the nature of human gullibility The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius Biography charts the life of Paul Dirac WORTH A LOOK Manual Electrostatic Generator Kit acts as a miniature Van de Graaff Quantify! A Crash Course in Smart Thinking Various topics illustrate the application of basic physical laws The Ultimate Quotable Einstein A compilation of Einstein's famous quotes WEB WATCH Open Source Physics simulations are worth a look

Extremely large magnetoresistance and Kohler's rule in PdSn 4 : A complete study of thermodynamic, transport, and band-structure properties

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

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

The recently discovered material PtSn 4 is known to exhibit extremely large magnetoresistance (XMR) that also manifests Dirac arc nodes on the surface. PdSn 4 is isostructural to PtSn 4 with the same electron count. Here, we report on the physical properties of high-quality single crystals of PdSn 4 including specific heat, temperature- and magnetic-field-dependent resistivity and magnetization, and electronic band-structure properties obtained from angle-resolved photoemission spectroscopy (ARPES). We observe that PdSn 4 has physical properties that are qualitatively similar to those of PtSn 4 , but find also pronounced differences. Importantly, the Dirac arc node surface state of PtSnmore » 4 is gapped out for PdSn 4. By comparing these similar compounds, we address the origin of the extremely large magnetoresistance in PdSn 4 and PtSn 4; based on detailed analysis of the magnetoresistivity ρ ( H , T ) , we conclude that neither the carrier compensation nor the Dirac arc node surface state are the primary reason for the extremely large magnetoresistance. On the other hand, we also find that, surprisingly, Kohler's rule scaling of the magnetoresistance, which describes a self-similarity of the field-induced orbital electronic motion across different length scales and is derived for a simple electronic response of metals to an applied magnetic field is obeyed over the full range of temperatures and field strengths that we explore.« less

New quantum number for the many-electron Dirac-Coulomb Hamiltonian

NASA Astrophysics Data System (ADS)

Komorovsky, Stanislav; Repisky, Michal; Bučinský, Lukáš

2016-11-01

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator K+, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator K , the K+2 has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that K+ is connected to K through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call K+ the generator of the many-electron TR symmetry. By diagonalizing the operator K+2 in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with K+2 has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree-Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

Extremely large magnetoresistance and Kohler's rule in PdSn 4 : A complete study of thermodynamic, transport, and band-structure properties

DOE PAGES

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

2017-10-27

The recently discovered material PtSn 4 is known to exhibit extremely large magnetoresistance (XMR) that also manifests Dirac arc nodes on the surface. PdSn 4 is isostructural to PtSn 4 with the same electron count. Here, we report on the physical properties of high-quality single crystals of PdSn 4 including specific heat, temperature- and magnetic-field-dependent resistivity and magnetization, and electronic band-structure properties obtained from angle-resolved photoemission spectroscopy (ARPES). We observe that PdSn 4 has physical properties that are qualitatively similar to those of PtSn 4 , but find also pronounced differences. Importantly, the Dirac arc node surface state of PtSnmore » 4 is gapped out for PdSn 4. By comparing these similar compounds, we address the origin of the extremely large magnetoresistance in PdSn 4 and PtSn 4; based on detailed analysis of the magnetoresistivity ρ ( H , T ) , we conclude that neither the carrier compensation nor the Dirac arc node surface state are the primary reason for the extremely large magnetoresistance. On the other hand, we also find that, surprisingly, Kohler's rule scaling of the magnetoresistance, which describes a self-similarity of the field-induced orbital electronic motion across different length scales and is derived for a simple electronic response of metals to an applied magnetic field is obeyed over the full range of temperatures and field strengths that we explore.« less

Cubic Dirac fermions in quasi-one-dimensional transition-metal chalcogenide semimetals immune to Peierls distortion

NASA Astrophysics Data System (ADS)

Liu, Qihang; Zunger, Alex

A Cubic Dirac Fermion in condensed-matter physics refers to a band crossing in periodic solids that has 4-fold degeneracy with cubic dispersions in certain directions. Such a crystalline symmetry induced fermion is composed of 6 Weyl fermions where 3 have left-handed and 3 have right-handed chirality, and constitutes one of the ``new fermions'' that have no counterpart in high-energy physics. However, no prediction has yet pointed to a plausible example of a material candidate hosting such a cubically-dispersed Dirac semimetal (CDSM). Here we establish the design principles for CDSM finding that only 2 out of 230 space groups possess the required symmetry elements. Adding the required band occupancy criteria, we conduct a material search using density functional band theory identifying a group of quasi-one-dimensional molybdenum chalcogenide compounds A(MoX)3 (A = Na, K, Rb, In, Tl; X = S, Se, Te) with space group P63/m as ideal CDSM candidates. Studying the stability of the A(MoX)3 family towards a Peierls distortion reveals a few candidates such as Rb(MoTe)3 and Tl(MoTe)3 that are resilliant to Peierls distortion, thus retaining the metallic character. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under Grant No. DE-FG02-13ER46959 to University of Colorado, Boulder.

DIRAC distributed secure framework

NASA Astrophysics Data System (ADS)

Casajus, A.; Graciani, R.; LHCb DIRAC Team

2010-04-01

DIRAC, the LHCb community Grid solution, provides access to a vast amount of computing and storage resources to a large number of users. In DIRAC users are organized in groups with different needs and permissions. In order to ensure that only allowed users can access the resources and to enforce that there are no abuses, security is mandatory. All DIRAC services and clients use secure connections that are authenticated using certificates and grid proxies. Once a client has been authenticated, authorization rules are applied to the requested action based on the presented credentials. These authorization rules and the list of users and groups are centrally managed in the DIRAC Configuration Service. Users submit jobs to DIRAC using their local credentials. From then on, DIRAC has to interact with different Grid services on behalf of this user. DIRAC has a proxy management service where users upload short-lived proxies to be used when DIRAC needs to act on behalf of them. Long duration proxies are uploaded by users to a MyProxy service, and DIRAC retrieves new short delegated proxies when necessary. This contribution discusses the details of the implementation of this security infrastructure in DIRAC.

Final Technical Report

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

Li, Lian

2017-03-08

Our BES supported program integrates molecular beam epitaxy growth with in situ atomic scale imaging using scanning tunneling microscopy/spectroscopy and atomic force microscopy. Aided by density functional theory calculations, we explore enhanced functionalities emerging from the interplay of strain, proximity, and spin-orbit interactions in heterostructures of wide band gap semiconductors, graphene, and Dirac materials, focusing on three thrusts: 1) doping wide bandgap semiconductors and graphene; 2) graphene nanoribbons and graphene-semiconductor heterostructures; and 3) Dirac materials. Our findings and discoveries have led to the publication of one book chapter and twenty-three refereed journal articles, including several in high impact journals suchmore » as Nature Communications, Physical Review Letters, and Nano Letters. Highlights of each thrust are provided in the report.« less

Comment on “Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term” [J. Math. Phys. 51, 023525 (2010)

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

Ghoumaid, A.; Benamira, F.; Guechi, L.

2016-02-15

It is shown that the application of the Nikiforov-Uvarov method by Ikhdair for solving the Dirac equation with the radial Rosen-Morse potential plus the spin-orbit centrifugal term is inadequate because the required conditions are not satisfied. The energy spectra given is incorrect and the wave functions are not physically acceptable. We clarify the problem and prove that the spinor wave functions are expressed in terms of the generalized hypergeometric functions {sub 2}F{sub 1}(a, b, c; z). The energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function.

Electrical manipulation of dynamic magnetic impurity and spin texture of helical Dirac fermions

NASA Astrophysics Data System (ADS)

Wang, Rui-Qiang; Zhong, Min; Zheng, Shi-Han; Yang, Mou; Wang, Guang-Hui

2016-05-01

We have theoretically investigated the spin inelastic scattering of helical electrons off a high-spin nanomagnet absorbed on a topological surface. The nanomagnet is treated as a dynamic quantum spin and driven by the spin transfer torque effect. We proposed a mechanism to electrically manipulate the spin texture of helical Dirac fermions rather than by an external magnetic field. By tuning the bias voltage and the direction of impurity magnetization, we present rich patterns of spin texture, from which important fingerprints exclusively associated with the spin helical feature are obtained. Furthermore, it is found that the nonmagnetic potential can create the resonance state in the spin density with different physics as the previously reported resonance of charge density.

Evidence for the Confinement of Magnetic Monopoles in Quantum Spin Ice.

PubMed

Sarte, Paul Maximo; Aczel, Adam; Ehlers, Georg; Stock, Christopher; Gaulin, Bruce D; Mauws, Cole; Stone, Matthew B; Calder, Stuart; Nagler, Stephen; Hollett, Joshua; Zhou, Haidong; Gardner, Jason S; Attfield, J Paul; Wiebe, Christopher R

2017-09-25

Magnetic monopoles are hypothesised elementary particles connected by Dirac strings that behave like infinitely thin solenoids [Dirac 1931 Proc. Roy. Soc. A 133 60]. Despite decades of searches, free magnetic monopoles and their Dirac strings have eluded experimental detection, although there is substantial evidence for deconfined magnetic monopole quasiparticles in spin ice materials [Castelnovo, Moessner & Sondhi 2008 Nature 326 411]. Here we report the detection of a hierarchy of unequally-spaced magnetic excitations via high resolution inelastic neutron spectroscopic measurements on the quantum spin ice candidate Pr₂Sn₂O₇. These excitations are well-described by a simple model of monopole pairs bound by a linear potential [Coldea et al. Science 327 177] with an effective tension of 0.7(1) K/Angstrom. The success of the linear potential model suggests that these low energy magnetic excitations are direct spectroscopic evidence for the confinement of magnetic monopole quasiparticles in the quantum spin ice candidate Pr₂Sn₂O₇. © 2017 IOP Publishing Ltd.

Status and perspectives of neutrino physics at present and future experiments

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

Pagliarone, Carmine Elvezio, E-mail: pagliarone@unicas.it, E-mail: carmine.pagliarone@lngs.infn.it; Laboratori Nazionali del Gran Sasso

2016-03-25

Neutrino Physics and Dark Matter searches play a crucial role in nowadays Particle and Astroparticle Physics. The present review paper will describe general properties of neutrinos and neutrino mass phenomenology (Dirac and Majorana masses). Space will be dedicated to the experimental attempts to answer the question of the neutrino mass hierarchy. We will give, then, a short review of the results of part of the experiments that have been running so far. We will also shortly summarize future experiments that plan to explore this very wide scientific area.

Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

NASA Astrophysics Data System (ADS)

Surzhykov, Andrey; Koval, Peter; Fritzsche, Stephan

2005-01-01

Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the DIRAC program which has been developed originally for studying the properties and dynamical behavior of the (hydrogen-like) ions. In the present version, a set of MAPLE procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the DIRAC program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. Program summaryTitle of program:DIRAC Catalogue number: ADUQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the program is designed and has been tested: All computers with a license of the computer algebra package MAPLE [1] Program language used: Maple 8 and 9 No. of lines in distributed program, including test data, etc.:2186 No. of bytes in distributed program, including test data, etc.: 162 591 Distribution format: tar gzip file CPC Program Library subprograms required: None Nature of the physical problem: Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure of the hydrogen-like ions, however, the underlying 'mathematics' is not always that easy to deal with. Apart from the well-known level structure of these ions as obtained from either the Schrödinger or Dirac equation, namely, a great deal of other properties are often needed. These properties are related to the interaction of bound electron(s) with external particles and fields and, hence, require to evaluate transition amplitudes, including wavefunctions and (transition) operators of quite different complexity. Although various special functions, such as the Laguerre polynomials, spherical harmonics, Whittaker functions, or the hypergeometric functions of various kinds can be used in most cases in order to express these amplitudes in a concise form, their derivation is time consuming and prone for making errors. In addition to their complexity, moreover, there exist a large number of mathematical relations among these functions which are difficult to remember in detail and which have often hampered quantitative studies in the past. Method of solution: A set of MAPLE procedures is developed which provides both the nonrelativistic and relativistic (analytical) solutions of the 'hydrogen atom model' and which facilitates the symbolic evaluation of various transition amplitudes. Restrictions onto the complexity of the problem: Over the past decades, a large number of representations have been worked out for the hydrogenic wave and Green's functions, using different variables and coordinates [2]. From these, the position-space representation in spherical coordinates is certainly of most practical interest and has been used as the basis of the present implementation. No attempt has been made by us so far to provide the wave and Green's functions also in momentum space, for which the relativistic momentum functions would have to be constructed numerically. Although the DIRAC program supports both symbolic and numerical computations, the latter one are based on MAPLE's standard software floating-point algorithms and on the (attempted) precision as defined by the global Digits variable. Although the default number, Digits = 10, appears sufficient for many computations, it often leads to a rather dramatic loss in the accuracy of the relativistic wave functions and integrals, mainly owing to MAPLE's imprecise internal evaluation of the corresponding special functions. Therefore, in order to avoid such computational difficulties, the Digits variable is set to 20 whenever the DIRAC program is (re-)loaded. Unusual features of the program: The DIRAC program has been designed for interactive work which, apart from the standard solutions and integrals of the hydrogen atom, also support the use of (approximate) semirelativistic wave functions for both, the bound- and continuum-states of the electron. To provide a fast and accurate access to a number of radial integrals which arise frequently in applications, the analytical expressions for these integrals have been implemented for the one-particle operators r, e, d/dr, j(kr) as well as for the (so-called) two-particle Slater integrals which are needed to describe the Coulomb repulsion among the electrons. Further procedures of the DIRAC program concern, for instance, the conversion of the physical results between different unit systems or for different sets of quantum numbers. A brief description of all procedures as available in the present version of the DIRAC program is given in the user manual Dirac-commands.pdf which is distributed together with the code. Typical running time: Although the program replies promptly on most requests, the running time also depends on the particular task. References: [1] Maple is a registered trademark of Waterloo Maple Inc. [2] H.A. Bethe and E.E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms, Springer, Berlin, 1957. [3] J. Eichler and W. Meyerhof, Relativistic Atomic Collisions, Academic Press, New York, 1995.

Magnon Dirac materials

NASA Astrophysics Data System (ADS)

Fransson, J.; Black-Schaffer, A. M.; Balatsky, A. V.

2016-08-01

We demonstrate how a Dirac-like magnon spectrum is generated for localized magnetic moments forming a two-dimensional honeycomb lattice. The Dirac crossing point is proven to be robust against magnon-magnon interactions, as these only shift the spectrum. Local defects induce impurity resonances near the Dirac point, as well as magnon Friedel oscillations. The energy of the Dirac point is controlled by the exchange coupling, and thus a two-dimensional array of magnetic dots is an experimentally feasible realization of Dirac magnons with tunable dispersion.

Paul Dirac

NASA Astrophysics Data System (ADS)

Pais, Abraham; Jacob, Maurice; Olive, David I.; Atiyah, Michael F.

2005-09-01

Preface Peter Goddard; Dirac memorial address Stephen Hawking; 1. Paul Dirac: aspects of his life and work Abraham Pais; 2. Antimatter Maurice Jacob; 3. The monopole David Olive; 4. The Dirac equation and geometry Michael F. Atiyah.

Paul Dirac

NASA Astrophysics Data System (ADS)

Pais, Abraham; Jacob, Maurice; Olive, David I.; Atiyah, Michael F.

1998-02-01

Preface Peter Goddard; Dirac memorial address Stephen Hawking; 1. Paul Dirac: aspects of his life and work Abraham Pais; 2. Antimatter Maurice Jacob; 3. The monopole David Olive; 4. The Dirac equation and geometry Michael F. Atiyah.

Photoconductivity in Dirac materials

NASA Astrophysics Data System (ADS)

Shao, J. M.; Yang, G. W.

2015-11-01

Two-dimensional (2D) Dirac materials including graphene and the surface of a three-dimensional (3D) topological insulator, and 3D Dirac materials including 3D Dirac semimetal and Weyl semimetal have attracted great attention due to their linear Dirac nodes and exotic properties. Here, we use the Fermi's golden rule and Boltzmann equation within the relaxation time approximation to study and compare the photoconductivity of Dirac materials under different far- or mid-infrared irradiation. Theoretical results show that the photoconductivity exhibits the anisotropic property under the polarized irradiation, but the anisotropic strength is different between 2D and 3D Dirac materials. The photoconductivity depends strongly on the relaxation time for different scattering mechanism, just like the dark conductivity.

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

PubMed

Owerre, Solomon; Nsofini, Joachim

2017-09-20

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

A Short Biography of Paul A. M. Dirac and Historical Development of Dirac Delta Function

ERIC Educational Resources Information Center

Debnath, Lokenath

2013-01-01

This paper deals with a short biography of Paul Dirac, his first celebrated work on quantum mechanics, his first formal systematic use of the Dirac delta function and his famous work on quantum electrodynamics and quantum statistics. Included are his first discovery of the Dirac relativistic wave equation, existence of positron and the intrinsic…

Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

NASA Astrophysics Data System (ADS)

Banerjee, S.; Fransson, J.; Black-Schaffer, A. M.; Ågren, H.; Balatsky, A. V.

2016-04-01

We examine the low-energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in a honeycomb lattice structure. Using the example of graphene, we present evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K' points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an intergrain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with fermionic Dirac materials. The Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of bosonic Dirac materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.

Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators

PubMed Central

Miao, Lin; Wang, Z. F.; Ming, Wenmei; Yao, Meng-Yu; Wang, Meixiao; Yang, Fang; Song, Y. R.; Zhu, Fengfeng; Fedorov, Alexei V.; Sun, Z.; Gao, C. L.; Liu, Canhua; Xue, Qi-Kun; Liu, Chao-Xing; Liu, Feng; Qian, Dong; Jia, Jin-Feng

2013-01-01

Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi2Te3 substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi2Te3 film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi2Se3, where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi2Se3 are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states. PMID:23382185

Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators.

PubMed

Miao, Lin; Wang, Z F; Ming, Wenmei; Yao, Meng-Yu; Wang, Meixiao; Yang, Fang; Song, Y R; Zhu, Fengfeng; Fedorov, Alexei V; Sun, Z; Gao, C L; Liu, Canhua; Xue, Qi-Kun; Liu, Chao-Xing; Liu, Feng; Qian, Dong; Jia, Jin-Feng

2013-02-19

Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi(2)Te(3) substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi(2)Te(3) film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi(2)Se(3), where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi(2)Se(3) are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.

CALL FOR PAPERS: Special cluster issue on `Experimental studies of zonal flow and turbulence'

NASA Astrophysics Data System (ADS)

Itoh, S.-I.

2005-07-01

Plasma Physics and Controlled Fusion (PPCF) invites submissions on the topic of `Experimental studies of zonal flow and turbulence', for consideration for a special topical cluster of articles to be published early in 2006. The topical cluster will be published in an issue of PPCF, combined with regular articles. The Guest Editor for the special cluster will be S-I Itoh, Kyushu University, Japan. There has been remarkable progress in the area of structure formation by turbulence. One of the highlights has been the physics of zonal flow and drift wave turbulence in toroidal plasmas. Extensive theoretical as well as computational studies have revealed the various mechanisms in turbulence and zonal flows. At the same time, experimental research on the zonal flow, geodesic acoustic modes and generation of global electric field by turbulence has evolved rapidly. Fast growth in reports of experimental results has stimulated further efforts to develop increased knowledge and systematic understanding. Each paper considered for the special cluster should describe the present research status and new scientific knowledge/results from the authors on experimental studies of zonal flow, geodesic acoustic modes and generation of electric field by turbulence (including studies of Reynolds-Maxwell stresses, etc). Manuscripts submitted to this special cluster in Plasma Physics and Controlled Fusion will be refereed according to the normal criteria and procedures of the journal. The Guest Editor guides the progress of the cluster from the initial open call, through the standard refereeing process, to publication. To be considered for inclusion in the special cluster, articles must be submitted by 2 September 2005 and must clearly state `for inclusion in the Turbulent Plasma Cluster'. Articles submitted after this deadline may not be included in the cluster issue but may be published in a later issue of the journal. Please submit your manuscript electronically via our web site at www.iop.org/journals/ppcf or by e-mail to mailto:ppcf@iop.org. Electronic submissions are encouraged but if you wish to submit a hard copy of your article then please send your typescript, a set of original figures and a covering letter to: The Publishing Administrator Plasma Physics and Controlled Fusion Institute of Physics Publishing Dirac House Temple Back Bristol BS1 6BE UK Further information on how to submit may be obtained on request by e-mailing the journal at the above address. Alternatively, visit the homepage of the journal (www.iop.org/journals/ppcf).

Relativistic quantum Darwinism in Dirac fermion and graphene systems

NASA Astrophysics Data System (ADS)

Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis

2012-02-01

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.

Nexus fermions in topological symmorphic crystalline metals

DOE PAGES

Chang, Guoqing; Xu, Su-Yang; Huang, Shin-Ming; ...

2017-05-10

Topological metals and semimetals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in transport and spectroscopic experiments. It has been well-established that the known TMs can be classified by the dimensionality of the topologically protected band degeneracies. While Weyl and Dirac semimetals feature zero-dimensional points, the band crossing of nodal-line semimetals forms a one-dimensional closed loop. In this paper, we identify a TM that goes beyond the above paradigms. It shows an exotic configuration of degeneracies without a well-defined dimensionality. Specifically, itmore » consists of 0D nexus with triple-degeneracy that interconnects 1D lines with double-degeneracy. We show that, because of the novel form of band crossing, the new TM cannot be described by the established results that characterize the topology of the Dirac and Weyl nodes. Moreover, triply-degenerate nodes realize emergent fermionic quasiparticles not present in relativistic quantum field theory. We present materials candidates. Thus, our results open the door for realizing new topological phenomena and fermions including transport anomalies and spectroscopic responses in metallic crystals with nontrivial topology beyond the Weyl/Dirac paradigm.« less

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.

PubMed

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards

NASA Astrophysics Data System (ADS)

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)2I3

PubMed Central

Kobayashi, Akito; Katayama, Shinya; Suzumura, Yoshikazu

2009-01-01

The quasi-two-dimensional molecular conductor α-(BEDT-TTF)2I3 exhibits anomalous transport phenomena where the temperature dependence of resistivity is weak but the ratio of the Hall coefficient at 10 K to that at room temperature is of the order of 104. These puzzling phenomena were solved by predicting massless Dirac fermions, whose motions are described using the tilted Weyl equation with anisotropic velocity. α-(BEDT-TTF)2I3 is a unique material among several materials with Dirac fermions, i.e. graphene, bismuth, and quantum wells such as HgTe, from the view-points of both the structure and electronic states described as follows. α-(BEDT-TTF)2I3 has the layered structure with highly two-dimensional massless Dirac fermions. The anisotropic velocity and incommensurate momenta of the contact points, ±k0, originate from the inequivalency of the BEDT-TTF sites in the unit cell, where ±k0 moves in the first Brillouin zone with increasing pressure. The massless Dirac fermions exist in the presence of the charge disproportionation and are robust against the increase in pressure. The electron densities on those inequivalent BEDT-TTF sites exhibit anomalous momentum distributions, reflecting the angular dependences of the wave functions around the contact points. Those unique electronic properties affect the spatial oscillations of the electron densities in the vicinity of an impurity. A marked behavior of the Hall coefficient, where the sign of the Hall coefficient reverses sharply but continuously at low temperatures around 5 K, is investigated by treating the interband effects of the magnetic field exactly. It is shown that such behavior is possible by assuming the existence of the extremely small amount of electron doping. The enhancement of the orbital diamagnetism is also expected. The results of the present research shed light on a new aspect of Dirac fermion physics, i.e. the emergence of unique electronic properties owing to the structure of the material. PMID:27877282

How device-independent approaches change the meaning of physical theory

NASA Astrophysics Data System (ADS)

Grinbaum, Alexei

2017-05-01

Dirac sought an interpretation of mathematical formalism in terms of physical entities and Einstein insisted that physics should describe ;the real states of the real systems;. While Bell inequalities put into question the reality of states, modern device-independent approaches do away with the idea of entities: physical theory may contain no physical systems. Focusing on the correlations between operationally defined inputs and outputs, device-independent methods promote a view more distant from the conventional one than Einstein's 'principle theories' were from 'constructive theories'. On the examples of indefinite causal orders and almost quantum correlations, we ask a puzzling question: if physical theory is not about systems, then what is it about? Device-independent models suggest that physical theory can be 'about' languages.

Semi-Metallic Be5C2 Monolayer Global Minimum with Quasi-Planar Pentacoordinate Carbons and Negative Poissons Ratio (Open Access Publisher’s Version)

DTIC Science & Technology

2016-05-03

ARTICLE Received 25 Nov 2015 | Accepted 1 Apr 2016 | Published 3 May 2016 Semi-metallic Be5C2 monolayer global minimum with quasi -planar...forming a quasi -planar pentacoordinate carbon moiety. Be5C2 monolayer appears to have good stability as revealed by its moderate cohesive energy...some promise to be realized experimentally . Be5C2 monolayer is a gapless semiconductor with a Dirac-like point in the band structure and also has an

Full utilization of semi-Dirac cones in photonics

NASA Astrophysics Data System (ADS)

Yasa, Utku G.; Turduev, Mirbek; Giden, Ibrahim H.; Kurt, Hamza

2018-05-01

In this study, realization and applications of anisotropic zero-refractive-index materials are proposed by exposing the unit cells of photonic crystals that exhibit Dirac-like cone dispersion to rotational symmetry reduction. Accidental degeneracy of two Bloch modes in the Brillouin zone center of two-dimensional C2-symmetric photonic crystals gives rise to the semi-Dirac cone dispersion. The proposed C2-symmetric photonic crystals behave as epsilon-and-mu-near-zero materials (ɛeff≈ 0 , μeff≈ 0 ) along one propagation direction, but behave as epsilon-near-zero material (ɛeff≈ 0 , μeff≠ 0 ) for the perpendicular direction at semi-Dirac frequency. By extracting the effective medium parameters of the proposed C4- and C2-symmetric periodic media that exhibit Dirac-like and semi-Dirac cone dispersions, intrinsic differences between isotropic and anisotropic materials are investigated. Furthermore, advantages of utilizing semi-Dirac cone materials instead of Dirac-like cone materials in photonic applications are demonstrated in both frequency and time domains. By using anisotropic transmission behavior of the semi-Dirac materials, photonic application concepts such as beam deflectors, beam splitters, and light focusing are proposed. Furthermore, to the best of our knowledge, semi-Dirac cone dispersion is also experimentally demonstrated for the first time by including negative, zero, and positive refraction states of the given material.

Dirac structures in vakonomic mechanics

NASA Astrophysics Data System (ADS)

Jiménez, Fernando; Yoshimura, Hiroaki

2015-08-01

In this paper, we explore dynamics of the nonholonomic system called vakonomic mechanics in the context of Lagrange-Dirac dynamical systems using a Dirac structure and its associated Hamilton-Pontryagin variational principle. We first show the link between vakonomic mechanics and nonholonomic mechanics from the viewpoints of Dirac structures as well as Lagrangian submanifolds. Namely, we clarify that Lagrangian submanifold theory cannot represent nonholonomic mechanics properly, but vakonomic mechanics instead. Second, in order to represent vakonomic mechanics, we employ the space TQ ×V∗, where a vakonomic Lagrangian is defined from a given Lagrangian (possibly degenerate) subject to nonholonomic constraints. Then, we show how implicit vakonomic Euler-Lagrange equations can be formulated by the Hamilton-Pontryagin variational principle for the vakonomic Lagrangian on the extended Pontryagin bundle (TQ ⊕T∗ Q) ×V∗. Associated with this variational principle, we establish a Dirac structure on (TQ ⊕T∗ Q) ×V∗ in order to define an intrinsic vakonomic Lagrange-Dirac system. Furthermore, we also establish another construction for the vakonomic Lagrange-Dirac system using a Dirac structure on T∗ Q ×V∗, where we introduce a vakonomic Dirac differential. Finally, we illustrate our theory of vakonomic Lagrange-Dirac systems by some examples such as the vakonomic skate and the vertical rolling coin.

Realization of non-symmorphic Dirac cones in PbFCl materials

NASA Astrophysics Data System (ADS)

Schoop, Leslie

While most 3D Dirac semimetals require two bands with different orbital character to be protected, there is also the possibility to find 3D Dirac semimetals that are guaranteed to exist in certain space groups. Those are resulting from the non-symmoprhic symmetry of the space group, which forces the bands to degenerate at high symmetry points in the Brillouin zone. Non-symmorphic space groups can force three- four, six and eight fold degeneracies which led to the proposal to find 3D Dirac Semimetals as well as new quasiparticles in such space groups. Problematic for realizing this types of Dirac materials is that they require and odd band filling in order to have the Fermi level located at or also near by the band crossing points. Therefore, although the first prediction for using non-symmoprhic symmetry to create a Dirac material was made in 2012, it took almost four years for an experimental verification of this type of Dirac crossing. In this talk I will introduce the material ZrSiS that has, besides other Dirac features, a Dirac cone protected by non-symmorphic symmetry at about 0.5 eV below the Fermi level and was the first material where this type of Dirac cone was imaged with ARPES. I will then proceed to discuss ways to shift this crossing to the Fermi edge and finally show an experimental verification of a fourfold Dirac crossing, protected by non-symmorphic symmetry, at the Fermi energy.

Spectrum of the Wilson Dirac operator at finite lattice spacings

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

Akemann, G.; Damgaard, P. H.; Splittorff, K.

2011-04-15

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral random matrix theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac operator. The low-energymore » constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator.« less

Chiral Magnetic Effect in Condensed Matters

NASA Astrophysics Data System (ADS)

Li, Qiang

The chiral magnetic effect is the generation of electrical current induced by chirality imbalance in the presence of magnetic field. It is a macroscopic manifestation of the quantum chiral anomaly in systems possessing charged chiral fermions. In quark-gluon plasma containing nearly massless quarks, the chirality imbalance is sourced by the topological transitions. In condensed matter systems, the chiral quasiparticles emerge in the 3D Dirac and Weyl semimetals having a linear dispersion relation. Recently, the chiral magnetic effect was discovered in a 3D Dirac semimetal - zirconium pentatelluride, ZrTe5, in which a large negative magnetoresistance is observed when magnetic field is parallel with the current. It is now reported in more than a dozen Dirac and Weyl semimetals. Broadly speaking, the chiral magnetic effect can exist in a variety of condensed matters. In some cases, a material may be transformed into a Weyl semimetal by magnetic field, exhibiting the chiral magnetic effect. In other cases, the chiral magnetic current may be generated in magnetic Dirac semimetals without external magnetic field, or in asymmetric Weyl semimetals without electric field where only a magnetic field and the source of chiral quasipartiles would be necessary. In the limit of conserved quasiparticle chirality, charge transport by the chiral magnetic current is non-dissipative. The powerful notion of chirality, originally discovered in high-energy and nuclear physics, holds promise in new ways of transmitting and processing information and energy. At the same time, chiral materials have opened a fascinating possibility to study the quantum dynamics of relativistic field theory in condensed matter experiments.

Precise identification of Dirac-like point through a finite photonic crystal square matrix

PubMed Central

Dong, Guoyan; Zhou, Ji; Yang, Xiulun; Meng, Xiangfeng

2016-01-01

The phenomena of the minimum transmittance spectrum or the maximum reflection spectrum located around the Dirac frequency have been observed to demonstrate the 1/L scaling law near the Dirac-like point through the finite ribbon structure. However, so far there is no effective way to identify the Dirac-like point accurately. In this work we provide an effective measurement method to identify the Dirac-like point accurately through a finite photonic crystal square matrix. Based on the Dirac-like dispersion achieved by the accidental degeneracy at the centre of the Brillouin zone of dielectric photonic crystal, both the simulated and experimental results demonstrate that the transmittance spectra through a finite photonic crystal square matrix not only provide the clear evidence for the existence of Dirac-like point but also can be used to identify the precise location of Dirac-like point by the characteristics of sharp cusps embedded in the extremum spectra surrounding the conical singularity. PMID:27857145

Dirac node arcs in PtSn 4

DOE PAGES

Wu, Yun; Wang, Lin -Lin; Mun, Eundeok; ...

2016-04-04

In topological quantum materials 1,2,3 the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals 4,5,6,7,8. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space 2,3. Here we report the discovery of a novel topological structure—Dirac node arcs—in the ultrahigh magnetoresistive material PtSn 4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arcmore » structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. Here, we propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.« less

Tuning the Fermi velocity in Dirac materials with an electric field.

PubMed

Díaz-Fernández, A; Chico, Leonor; González, J W; Domínguez-Adame, F

2017-08-14

Dirac materials are characterized by energy-momentum relations that resemble those of relativistic massless particles. Commonly denominated Dirac cones, these dispersion relations are considered to be their essential feature. These materials comprise quite diverse examples, such as graphene and topological insulators. Band-engineering techniques should aim to a full control of the parameter that characterizes the Dirac cones: the Fermi velocity. We propose a general mechanism that enables the fine-tuning of the Fermi velocity in Dirac materials in a readily accessible way for experiments. By embedding the sample in a uniform electric field, the Fermi velocity is substantially modified. We first prove this result analytically, for the surface states of a topological insulator/semiconductor interface, and postulate its universality in other Dirac materials. Then we check its correctness in carbon-based Dirac materials, namely graphene nanoribbons and nanotubes, thus showing the validity of our hypothesis in different Dirac systems by means of continuum, tight-binding and ab-initio calculations.

Topological Anderson insulator phase in a Dirac-semimetal thin film

NASA Astrophysics Data System (ADS)

Chen, Rui; Xu, Dong-Hui; Zhou, Bin

2017-06-01

The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three-dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that the quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either a normal insulator or quantum spin Hall insulator, depending on the thin-film thickness. We present the study of disorder effects in a thin film of Dirac semimetals. It is found that moderate Anderson disorder strength can drive a topological phase transition from a normal band insulator to a topological Anderson insulator in a Dirac-semimetal thin film. The numerical calculation based on the model parameters of Dirac semimetal Na3Bi shows that in the topological Anderson insulator phase, a quantized conductance plateau occurs in the bulk gap of the band insulator, and the distributions of local currents further confirm that the quantized conductance plateau arises from the helical edge states induced by disorder. Finally, an effective medium theory based on the Born approximation fits the numerical data.

Strong topological metal material with multiple Dirac cones

DOE PAGES

Ji, Huiwen; Valla, T.; Pletikosic, I.; ...

2016-01-25

We report a new, cleavable, strong topological metal, Zr 2Te 2P, which has the same tetradymite-type crystal structure as the topological insulator Bi 2Te 2Se. Instead of being a semiconductor, however, Zr 2Te 2P is metallic with a pseudogap between 0.2 and 0.7 eV above the Fermi energy (E F). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone with a largely linear dispersion over a 2 eV energy range. A third surface TRS-protected Dirac cone is predicted, andmore » observed using angle-resolved photoemission spectroscopy, making Z r2Te 2P the first system, to our knowledge, to realize TRS-protected Dirac cones at M¯ points. The high anisotropy of this Dirac cone is similar to the one in the hypothetical Dirac semimetal BiO 2. As a result, we propose that if E F can be tuned into the pseudogap where the Dirac dispersions exist, it may be possible to observe ultrahigh carrier mobility and large magnetoresistance in this material.« less

Non-Abelian statistics of vortices with non-Abelian Dirac fermions.

PubMed

Yasui, Shigehiro; Hirono, Yuji; Itakura, Kazunori; Nitta, Muneto

2013-05-01

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.

Double Dirac point semimetal in 2D material: Ta2Se3

NASA Astrophysics Data System (ADS)

Ma, Yandong; Jing, Yu; Heine, Thomas

2017-06-01

Here, we report by first-principles calculations one new stable 2D Dirac material, Ta2Se3 monolayer. For this system, stable layered bulk phase exists, and exfoliation should be possible. Ta2Se3 monolayer is demonstrated to support two Dirac points close to the Fermi level, achieving the exotic 2D double Dirac semimetal. And like 2D single Dirac and 2D node-line semimetals, spin-orbit coupling could introduce an insulating state in this new class of 2D Dirac semimetals. Moreover, the Dirac feature in this system is layer-dependent and a metal-to-insulator transition is identified in Ta2Se3 when reducing the layer-thickness from bilayer to monolayer. These findings are of fundamental interests and of great importance for nanoscale device applications.

Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires

NASA Astrophysics Data System (ADS)

Zhang, Rui-Xing; Liu, Chao-Xing

2018-04-01

One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to realize such Majorana physics. By inserting magnetic flux, a DSM nanowire is driven into a 1D crystalline-symmetry-protected semimetallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. We also explore several experimental consequences of Majorana signals.

Quantum phase transitions in the noncommutative Dirac oscillator

NASA Astrophysics Data System (ADS)

Panella, O.; Roy, P.

2014-10-01

We study the (2 + 1)-dimensional Dirac oscillator in a homogeneous magnetic field in the noncommutative plane. It is shown that the effect of noncommutativity is twofold: (i) momentum noncommuting coordinates simply shift the critical value (Bcr) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); (ii) noncommutativity in the space coordinates induces a new critical value of the magnetic field, Bcr*, where there is a second quantum phase transition (right-left): this critical point disappears in the commutative limit. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetization of the system. Possible applications to the physics of silicene and graphene are briefly discussed.

Many-body interactions in quasi-freestanding graphene

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

Siegel, David; Park, Cheol-Hwan; Hwang, Choongyu

2011-06-03

The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities tomore » marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.« less

Effect of wave function on the proton induced L XRP cross sections for 62Sm and 74W

NASA Astrophysics Data System (ADS)

Shehla, Kaur, Rajnish; Kumar, Anil; Puri, Sanjiv

2015-08-01

The Lk(k= 1, α, β, γ) X-ray production cross sections have been calculated for 74W and 62Sm at different incident proton energies ranging 1-5 MeV using theoretical data sets of different physical parameters, namely, the Li(i=1-3) sub-shell X-ray emission rates based on the Dirac-Fork (DF) model, the fluorescence and Coster Kronig yields based on the Dirac- Hartree-Slater (DHS) model and two sets the proton ionization cross sections based on the DHS model and the ECPSSR in order to assess the influence of the wave function on the XRP cross sections. The calculated cross sections have been compared with the measured cross sections reported in the recent compilation to check the reliability of the calculated values.

Anisotropic Weyl fermions from the quasiparticle excitation spectrum of a 3D Fulde-Ferrell superfluid.

PubMed

Xu, Yong; Chu, Rui-Lin; Zhang, Chuanwei

2014-04-04

Weyl fermions, first proposed for describing massless chiral Dirac fermions in particle physics, have not been observed yet in experiments. Recently, much effort has been devoted to explore Weyl fermions around band touching points of single-particle energy dispersions in certain solid state materials (named Weyl semimetals), similar as graphene for Dirac fermions. Here we show that such Weyl semimetals also exist in the quasiparticle excitation spectrum of a three-dimensional spin-orbit-coupled Fulde-Ferrell superfluid. By varying Zeeman fields, the properties of Weyl fermions, such as their creation and annihilation, number and position, as well as anisotropic linear dispersions around band touching points, can be tuned. We study the manifestation of anisotropic Weyl fermions in sound speeds of Fulde-Ferrell fermionic superfluids, which are detectable in experiments.

CALL FOR PAPERS: Optical implementation of quantum computers

NASA Astrophysics Data System (ADS)

Rarity, John; Weinfurter, Harald

2004-09-01

A topical issue of Journal of Optics B: Quantum and Semiclassical Optics will be devoted to recent advances in optical implementation of quantum computers. The topics to be covered will include, but are not limited to: bullet Linear optics quantum gates bullet Progress towards nonlinear optics quantum gates bullet Interface between optical qubits and atomic/solid state qubits bullet Novel architectures bullet Single-photon sources and detectors bullet Photonic quantum networks bullet Few-qubit applications The DEADLINE for submission of contributions is 15 January 2005 to allow the topical issue to be published in about October 2005. All contributions will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Submissions should preferably be in either standard LaTeX form or Microsoft Word. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. There are no page charges for publication. The corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should preferably be submitted electronically at www.iop.org/journals/authors/jopb or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions (enclosing the electronic code) to: Dr Claire Bedrock (Publisher), Journal of Optics B: Quantum and Semiclassical Optics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. All contributions should be accompanied by a readme file or covering letter, quoting `JOPB Topical Issue - Optical implementation of quantum computers', giving the postal and e-mail addresses for correspondence. Any subsequent change of address should be notified to the publishing office. We look forward to receiving your contribution to this topical issue.

A novel quantum-mechanical interpretation of the Dirac equation

NASA Astrophysics Data System (ADS)

K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

2016-04-01

A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

Bosonic Dirac materials in two dimensions

NASA Astrophysics Data System (ADS)

Banerjee, Saikat; Fransson, Jonas; Black-Schaffer, Annica; Ågren, Hans; Balatsky, Alexander

We examine the low energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Two different types of collective phase oscillations are obtained, which are analogous to the massive Leggett and massless Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. It is shown that the spectra of these collective bosonic modes cross each other at the K and K' points in the Brillouin zone and form a Dirac node. Dirac node dispersion of bosonic excitations is representative of Bosonic Dirac Materials (BDM). We show that the Dirac node is preserved in presence of an inter-grain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with Fermionic Dirac materials.

Tilted Dirac Cone Effect on Interlayer Magnetoresistance in α-(BEDT-TTF)2I3

NASA Astrophysics Data System (ADS)

Tajima, Naoya; Morinari, Takao

2018-04-01

We report the effect of Dirac cone tilting on interlayer magnetoresistance in α-(BEDT-TTF)2I3, which is a Dirac semimetal under pressure. Fitting of the experimental data by the theoretical formula suggests that the system is close to a type-II Dirac semimetal.

All-Metallic Vertical Transistors Based on Stacked Dirac Materials

NASA Astrophysics Data System (ADS)

Wang, Yangyang; Ni, Zeyuan; Liu, Qihang; Quhe, Ruge; Zheng, Jiaxin; Ye, Meng; Yu, Dapeng; Shi, Junjie; Yang, Jinbo; Li, Ju; Lu, Jing; Collaborative Innovation Center of Quantum Matter, Beijing Collaboration

2015-03-01

All metallic transistor can be fabricated from pristine semimetallic Dirac materials (such as graphene, silicene, and germanene), but the on/off current ratio is very low. In a vertical heterostructure composed by two Dirac materials, the Dirac cones of the two materials survive the weak interlayer van der Waals interaction based on density functional theory method, and electron transport from the Dirac cone of one material to the one of the other material is therefore forbidden without assistance of phonon because of momentum mismatch. First-principles quantum transport simulations of the all-metallic vertical Dirac material heterostructure devices confirm the existence of a transport gap of over 0.4 eV, accompanied by a switching ratio of over 104. Such a striking behavior is robust against the relative rotation between the two Dirac materials and can be extended to twisted bilayer graphene. Therefore, all-metallic junction can be a semiconductor and novel avenue is opened up for Dirac material vertical structures in high-performance devices without opening their band gaps. A visiting student in MIT now.

Dirac cones in isogonal hexagonal metallic structures

NASA Astrophysics Data System (ADS)

Wang, Kang

2018-03-01

A honeycomb hexagonal metallic lattice is equivalent to a triangular atomic one and cannot create Dirac cones in its electromagnetic wave spectrum. We study in this work the low-frequency electromagnetic band structures in isogonal hexagonal metallic lattices that are directly related to the honeycomb one and show that such structures can create Dirac cones. The band formation can be described by a tight-binding model that allows investigating, in terms of correlations between local resonance modes, the condition for the Dirac cones and the consequence of the third structure tile sustaining an extra resonance mode in the unit cell that induces band shifts and thus nonlinear deformation of the Dirac cones following the wave vectors departing from the Dirac points. We show further that, under structure deformation, the deformations of the Dirac cones result from two different correlation mechanisms, both reinforced by the lattice's metallic nature, which directly affects the resonance mode correlations. The isogonal structures provide new degrees of freedom for tuning the Dirac cones, allowing adjustment of the cone shape by modulating the structure tiles at the local scale without modifying the lattice periodicity and symmetry.

Nonequilibrium transport in the pseudospin-1 Dirac-Weyl system

NASA Astrophysics Data System (ADS)

Wang, Cheng-Zhen; Xu, Hong-Ya; Huang, Liang; Lai, Ying-Cheng

2017-09-01

Recently, solid state materials hosting pseudospin-1 quasiparticles have attracted a great deal of attention. In these materials, the energy band contains a pair of Dirac cones and a flatband through the connecting point of the cones. As the "caging" of carriers with a zero group velocity, the flatband itself has zero conductivity. However, in a nonequilibrium situation where a constant electric field is suddenly switched on, the flatband can enhance the resulting current in both the linear and nonlinear response regimes through distinct physical mechanisms. Using the (2 +1 )-dimensional pseudospin-1 Dirac-Weyl system as a concrete setting, we demonstrate that, in the weak field regime, the interband current is about twice larger than that for pseudospin-1/2 system due to the interplay between the flatband and the negative band, with the scaling behavior determined by the Kubo formula. In the strong field regime, the intraband current is √{2 } times larger than that in the pseudospin-1/2 system, due to the additional contribution from particles residing in the flatband. In this case, the current and field follow the scaling law associated with Landau-Zener tunneling. These results provide a better understanding of the role of the flatband in nonequilibrium transport and are experimentally testable using electronic or photonic systems.

Effect of Eu magnetism on the electronic properties of the candidate Dirac material EuMnBi2

NASA Astrophysics Data System (ADS)

May, Andrew F.; McGuire, Michael A.; Sales, Brian C.

2014-08-01

The crystal structure and physical properties of the layered material EuMnBi2 have been characterized by measurements on single crystals. EuMnBi2 is isostructural with the Dirac material SrMnBi2 based on single-crystal x-ray diffraction, crystallizing in the I4/mmm space group (No. 139). Magnetic susceptibility measurements suggest antiferromagnetic (AFM) ordering of moments on divalent Eu ions near TN=22 K. For low fields, the ordered Eu moments are aligned along the c axis, and a spin flop is observed near 5.4 T at 5 K. The moment is not saturated in an applied field of 13 T at 5 K, which is uncommon for compounds containing Eu2+. The magnetic behavior suggests an anisotropy enhancement via interaction between Eu and the Mn moments that appear to be ordered antiferromagnetically below ≈310 K. A large increase in the magnetoresistance is observed across the spin flop, with absolute magnetoresistance reaching ≈650% at 5 K and 12 T. Hall effect measurements reveal a decrease in the carrier density below TN, which implies a manipulation of the Fermi surface by magnetism on the sites surrounding the Bi square nets that lead to Dirac cones in this family of materials.

Generalized Equations and Their Solutions in the (S, 0) ⊕ (0, S) Representations of the Lorentz Group

NASA Astrophysics Data System (ADS)

Dvoeglazov, V. V.

2017-05-01

We present three explicit examples of generalizations in relativistic quantum mechanics. First of all, we discuss the generalized spin-1/2 equations for neutrinos. They have been obtained by means of the Gersten-Sakurai method for derivations of arbitrary-spin relativistic equations. Possible physical consequences are discussed. Next, it is easy to check that both Dirac algebraic equation {Det}(\\hat{p}-m)=0 and {Det}(\\hat{p}+m)=0 for u- and v- 4-spinors have solutions with {p}0=+/- {E}p=+/- \\sqrt{{p}2+{m}2}. The same is true for higher-spin equations. Meanwhile, every book considers the equality p0 = Ep for both u- and v- spinors of the (1/2, 0) ⊕ (0, 1/2)) representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both S = 1/2 and higher spin particles. The third example is: we postulate the non-commutativity of 4-momenta, and we derive the mass splitting in the Dirac equation. Some applications are discussed.

Polar phase of superfluid 3He: Dirac lines in the parameter and momentum spaces

NASA Astrophysics Data System (ADS)

Volovik, G. E.

2018-03-01

The time reversal symmetric polar phase of the spin-triplet superfluid 3He has two types of Dirac nodal lines. In addition to the Dirac loop in the spectrum of the fermionic Bogoliubov quasiparticles in the momentum space (p x , p y , p z ), the spectrum of bosons (magnons) has Dirac loop in the 3D space of parameters-the components of magnetic field (H x , H y , H z ). The bosonic Dirac system lives on the border between the type-I and type-II.

Photoinduced Chern insulating states in semi-Dirac materials

NASA Astrophysics Data System (ADS)

Saha, Kush

2016-08-01

Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D systems in the presence of an electromagnetic field. We show that a Chern insulating state emerges in a semi-Dirac system with two gapless Dirac nodes in the presence of light. In particular, we show that the intensity of a circularly polarized light can be used as a knob to generate topological states with nonzero Chern number. In addition, for fixed intensity and frequency of the light, a semi-Dirac system with two gapped Dirac nodes with trivial band topology can reveal the topological transition as a function of polarization of the light.

Convergence from divergence

NASA Astrophysics Data System (ADS)

Costin, Ovidiu; Dunne, Gerald V.

2018-01-01

We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being convergent, these new series allow rigorous extrapolation from an asymptotic region with a large parameter, to the opposite region where the parameter is small. We illustrate the method with various physical examples, and discuss how these convergent series relate to standard methods such as Borel summation, and also how they incorporate the physical Stokes phenomenon. We comment on the relation of these results to Dyson’s physical argument for the divergence of perturbation theory. This approach also leads naturally to a wide class of relations between bosonic and fermionic partition functions, and Klein-Gordon and Dirac determinants.

The Trieste Lecture of John Stewart Bell

NASA Astrophysics Data System (ADS)

Bassi, Angelo; Carlo Ghirardi, Gian

2007-03-01

Delivered at Trieste on the occasion of the 25th Anniversary of the International Centre for Theoretical Physics, 2 November 1989 The video of this lecture is available here. Please see the PDF for the transcript of the lecture. General remarks by Angelo Bassi and GianCarlo Ghirardi During the autumn of 1989 the International Centre for Theoretical Physics, Trieste, celebrated the 25th anniversary of its creation. Among the many prestigious speakers, who delivered extremely interesting lectures on that occasion, was the late John Stewart Bell. All lectures have been recorded on tape. We succeeded in getting a copy of John's lecture. In the lecture, many of the arguments that John had lucidly stressed in his writings appear once more, but there are also extremely interesting new remarks which, to our knowledge, have not been presented elsewhere. In particular he decided, as pointed out by the very choice of the title of his lecture, to call attention to the fact that the theory presents two types of difficulties, which Dirac classified as first and second class. The former are those connected with the so-called macro-objectification problem, the latter with the divergences characterizing relativistic quantum field theories. Bell describes the precise position of Dirac on these problems and he stresses appropriately how, contrary to Dirac's hopes, the steps which have led to a partial overcoming of the second class difficulties have not helped in any way whatsoever to overcome those of the first class. He then proceeds to analyse the origin and development of the Dynamical Reduction Program and draws attention to the problems that still affect it, in particular that of a consistent relativistic generalization. When the two meetings Are there quantum jumps? and On the present status of Quantum Mechanics were organized in Trieste and Losinj (Croatia), on 5 10 September 2005, it occurred to us that this lecture, which has never been published, might represent an extremely interesting historical record for all the participants who certainly shared with us a great admiration for this outstanding scientist and deep thinker. Accordingly, with the permission of the Abdus Salam International Centre for Theoretical Physics, and with thanks to the financial support of the Consorzio per la Fisica of the Trieste University, we have produced from the original record a DVD which has been given to all participants although, unfortunately, the video tape of the event was not particularly good. Taking into account that the participants to the meetings represented only a very small subset of those scientists who might be interested in hearing what John Bell said in probably his last lecture, we considered that it would be useful for the scientific community interested in foundational problems to publish the text of this lecture in order to make it accessible to everybody. The lecture was preceded by a presentation by the Chairman, Alain Aspect, which we have also included. Due to the aforementioned low quality of the recording it has not been easy to pass from the tape to the text we are presenting below, and we have to thank, for her precious collaboration, Dr Julia Filingeri who did most of the work, as well as Mrs Anne Gatti from ICTP, Professors Detlef Düurr and Sheldon Goldstein, and the staff of IOP Publishing who contributed in an essential way in deciphering some particularly difficult passages. Obviously, we take full responsibility for any possible inappropriate rendering of the original talk. We thank the Abdus Salam International Centre for Theoretical Physics for authorizing IOP Publishing to publish this important document. Some final remarks are in order. Firstly, we have put in square brackets parenthetical remarks that John made while reading sentences from his transparencies. We have also indicated by parenthetical ellipsis (...) very short parts of the speech (usually one word) which we have not been able to decipher. We have included a picture (figure 1) shown by him, taking it from the tape image which is of rather poor quality (we apologize for this) and three figures taken from his transparencies. Moreover, to help the reader in grasping the various points John Stewart Bell brilliantly raised in his talk we have divided the paper into six sections whose titles have been chosen by us to summarize the most crucial points of his argument. Presentation by the Chairman, Alain Aspect It is a great pleasure and an honour to introduce Professor Bell. When looking to my old papers I discovered that this 25th anniversary of the ICTP also coincides with the famous paper in which appeared, for the first time, inequalities that are now known as Bell's inequalities so it's a very good opportunity to have a talk by John Bell here. Many of us have been strongly influenced by this work of John Bell because he has shown us that quantum mechanics is much more difficult to understand that we thought it was. I am sure that today he will again raise some questions which are very embarrassing but that we have definitely to face.

Investigating and improving student understanding of the expectation values of observables in quantum mechanics

NASA Astrophysics Data System (ADS)

Marshman, Emily; Singh, Chandralekha

2017-07-01

The expectation value of an observable is an important concept in quantum mechanics since measurement outcomes are, in general, probabilistic and we only have information about the probability distribution of measurement outcomes in a given quantum state of a system. However, we find that upper-level undergraduate and PhD students in physics have both conceptual and procedural difficulties when determining the expectation value of a physical observable in a given quantum state in terms of the eigenstates and eigenvalues of the corresponding operator, especially when using Dirac notation. Here we first describe the difficulties that these students have with determining the expectation value of an observable in Dirac notation. We then discuss how the difficulties found via student responses to written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the expectation value. The QuILT strives to help students integrate conceptual understanding and procedural skills to develop a coherent understanding of the expectation value. We discuss the effectiveness of the QuILT in helping students learn this concept from in-class evaluations.

Type-II Weyl semimetals.

PubMed

Soluyanov, Alexey A; Gresch, Dominik; Wang, Zhijun; Wu, QuanSheng; Troyer, Matthias; Dai, Xi; Bernevig, B Andrei

2015-11-26

Fermions--elementary particles such as electrons--are classified as Dirac, Majorana or Weyl. Majorana and Weyl fermions had not been observed experimentally until the recent discovery of condensed matter systems such as topological superconductors and semimetals, in which they arise as low-energy excitations. Here we propose the existence of a previously overlooked type of Weyl fermion that emerges at the boundary between electron and hole pockets in a new phase of matter. This particle was missed by Weyl because it breaks the stringent Lorentz symmetry in high-energy physics. Lorentz invariance, however, is not present in condensed matter physics, and by generalizing the Dirac equation, we find the new type of Weyl fermion. In particular, whereas Weyl semimetals--materials hosting Weyl fermions--were previously thought to have standard Weyl points with a point-like Fermi surface (which we refer to as type-I), we discover a type-II Weyl point, which is still a protected crossing, but appears at the contact of electron and hole pockets in type-II Weyl semimetals. We predict that WTe2 is an example of a topological semimetal hosting the new particle as a low-energy excitation around such a type-II Weyl point. The existence of type-II Weyl points in WTe2 means that many of its physical properties are very different to those of standard Weyl semimetals with point-like Fermi surfaces.

Chiral magnetic effect in condensed matter systems

NASA Astrophysics Data System (ADS)

Li, Qiang; Kharzeev, Dmitri E.

2016-12-01

The chiral magnetic effect (CME) is the generation of electrical current induced by chirality imbalance in the presence of magnetic field. It is a macroscopic manifestation of the quantum chiral anomaly [S. L. Adler. Axial-vector vertex in spinor electrodynamics. Physical Review, 177, 2426 (1969), J. S. Bell and R. Jackiw. A PCAC puzzle: π 0 γγin the σ-model. Il Nuovo Cimento A, 60, 47-61 (1969)] in systems possessing charged chiral fermions. In quark-gluon plasma containing nearly massless quarks, the chirality imbalance is sourced by the topological transitions. In condensed matter systems, the chiral quasiparticles emerge in gapless semiconductors with two energy bands having pointlike degeneracies opening the path to the study of chiral anomaly [H. B. Nielsen and M. Ninomiya. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Physics Letters B, 130, 389-396 (1983)]. Recently, these novel materials - so-called Dirac and Weyl semimetals have been discovered experimentally, are suitable for the investigation of the CME in condensed matter experiments. Here we report on the first experimental observation of the CME in a 3D Dirac semimetal ZrTe5 [Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosić, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu, and T. Valla. Chiral magnetic effect in ZrTe5. Nature Physics (2016) doi:10.1038/nphys3648].

Strong Anisotropy of Dirac Cones in SrMnBi2 and CaMnBi2 Revealed by Angle-Resolved Photoemission Spectroscopy

PubMed Central

Feng, Ya; Wang, Zhijun; Chen, Chaoyu; Shi, Youguo; Xie, Zhuojin; Yi, Hemian; Liang, Aiji; He, Shaolong; He, Junfeng; Peng, Yingying; Liu, Xu; Liu, Yan; Zhao, Lin; Liu, Guodong; Dong, Xiaoli; Zhang, Jun; Chen, Chuangtian; Xu, Zuyan; Dai, Xi; Fang, Zhong; Zhou, X. J.

2014-01-01

The Dirac materials, such as graphene and three-dimensional topological insulators, have attracted much attention because they exhibit novel quantum phenomena with their low energy electrons governed by the relativistic Dirac equations. One particular interest is to generate Dirac cone anisotropy so that the electrons can propagate differently from one direction to the other, creating an additional tunability for new properties and applications. While various theoretical approaches have been proposed to make the isotropic Dirac cones of graphene into anisotropic ones, it has not yet been met with success. There are also some theoretical predictions and/or experimental indications of anisotropic Dirac cone in novel topological insulators and AMnBi2 (A = Sr and Ca) but more experimental investigations are needed. Here we report systematic high resolution angle-resolved photoemission measurements that have provided direct evidence on the existence of strongly anisotropic Dirac cones in SrMnBi2 and CaMnBi2. Distinct behaviors of the Dirac cones between SrMnBi2 and CaMnBi2 are also observed. These results have provided important information on the strong anisotropy of the Dirac cones in AMnBi2 system that can be governed by the spin-orbital coupling and the local environment surrounding the Bi square net. PMID:24947490

Excitonic gap formation in pumped Dirac materials

NASA Astrophysics Data System (ADS)

Triola, Christopher; Pertsova, Anna; Markiewicz, Robert S.; Balatsky, Alexander V.

2017-05-01

Recent pump-probe experiments demonstrate the possibility that Dirac materials may be driven into transient excited states describable by two chemical potentials, one for the electrons and one for the holes. Given the Dirac nature of the spectrum, such an inverted population allows the optical tunability of the density of states of the electrons and holes, effectively offering control of the strength of the Coulomb interaction. Here we discuss the feasibility of realizing transient excitonic instabilities in optically pumped Dirac materials. We demonstrate, theoretically, the reduction of the critical coupling leading to the formation of a transient condensate of electron-hole pairs and identify signatures of this state. Furthermore, we provide guidelines for experiments by both identifying the regimes in which such exotic many-body states are more likely to be observed and estimating the magnitude of the excitonic gap for a few important examples of existing Dirac materials. We find a set of material parameters for which our theory predicts large gaps and high critical temperatures and which could be realized in future Dirac materials. We also comment on transient excitonic instabilities in three-dimensional Dirac and Weyl semimetals. This study provides an example of a transient collective instability in driven Dirac materials.

Bosonic Dirac Materials in 2 dimensions

NASA Astrophysics Data System (ADS)

Banerjee, Saikat; Black-Schaffer, A. M.; Fransson, J.; Agren, H.; Balatsky, A. V.

We examine the low energy effective theory of phase oscillations in a two dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Two different types of collective phase oscillations are obtained, which are analogous to the massive Leggett and massless Bogoliubov-Anderson-Gorkov modes for two-band superconductor. It is explicitly shown that the spectra of these collective Bosonic modes cross each other at K and K' points in the Brillouin zone and form a Dirac node. This Dirac node behavior in Bosonic excitations represent the case of Bosonic Dirac Materials (BDM). Dirac node is preserved in presence of an inter-grain interaction despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sub lattice symmetry by choosing different on-site potentials for the two sub lattices leads to a gap opening near the Dirac node, in analogy with Fermionic Dirac material. Supported by US DOE E304, ERC DM 321031, KAW, VR2012-3447.

Self-Assembled Si(111) Surface States: 2D Dirac Material for THz Plasmonics.

PubMed

Wang, Z F; Liu, Feng

2015-07-10

Graphene, the first discovered 2D Dirac material, has had a profound impact on science and technology. In the last decade, we have witnessed huge advances in graphene related fundamental and applied research. Here, based on first-principles calculations, we propose a new 2D Dirac band on the Si(111) surface with 1/3 monolayer halogen coverage. The sp(3) dangling bonds form a honeycomb superstructure on the Si(111) surface that results in an anisotropic Dirac band with a group velocity (∼10(6)  m/s) comparable to that in graphene. Most remarkably, the Si-based surface Dirac band can be used to excite a tunable THz plasmon through electron-hole doping. Our results demonstrate a new way to design Dirac states on a traditional semiconductor surface, so as to make them directly compatible with Si technology. We envision this new type of Dirac material to be generalized to other semiconductor surfaces with broad applications.

Self-Assembled Si(111) Surface States: 2D Dirac Material for THz Plasmonics

NASA Astrophysics Data System (ADS)

Wang, Z. F.; Liu, Feng

2015-07-01

Graphene, the first discovered 2D Dirac material, has had a profound impact on science and technology. In the last decade, we have witnessed huge advances in graphene related fundamental and applied research. Here, based on first-principles calculations, we propose a new 2D Dirac band on the Si(111) surface with 1 /3 monolayer halogen coverage. The s p3 dangling bonds form a honeycomb superstructure on the Si(111) surface that results in an anisotropic Dirac band with a group velocity (˜106 m /s ) comparable to that in graphene. Most remarkably, the Si-based surface Dirac band can be used to excite a tunable THz plasmon through electron-hole doping. Our results demonstrate a new way to design Dirac states on a traditional semiconductor surface, so as to make them directly compatible with Si technology. We envision this new type of Dirac material to be generalized to other semiconductor surfaces with broad applications.

Faà di Bruno's formula and the distributions of random partitions in population genetics and physics.

PubMed

Hoppe, Fred M

2008-06-01

We show that the formula of Faà di Bruno for the derivative of a composite function gives, in special cases, the sampling distributions in population genetics that are due to Ewens and to Pitman. The composite function is the same in each case. Other sampling distributions also arise in this way, such as those arising from Dirichlet, multivariate hypergeometric, and multinomial models, special cases of which correspond to Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann distributions in physics. Connections are made to compound sampling models.

Berry phase jumps and giant nonreciprocity in Dirac quantum dots

NASA Astrophysics Data System (ADS)

Rodriguez-Nieva, Joaquin F.; Levitov, Leonid S.

2016-12-01

We predict that a strong nonreciprocity in the resonance spectra of Dirac quantum dots can be induced by the Berry phase. The nonreciprocity arises in relatively weak magnetic fields and is manifest in anomalously large field-induced splittings of quantum dot resonances which are degenerate at B =0 due to time-reversal symmetry. This exotic behavior, which is governed by field-induced jumps in the Berry phase of confined electronic states, is unique to quantum dots in Dirac materials and is absent in conventional quantum dots. The effect is strong for gapless Dirac particles and can overwhelm the B -induced orbital and Zeeman splittings. A finite Dirac mass suppresses the effect. The nonreciprocity, predicted for generic two-dimensional Dirac materials, is accessible through Faraday and Kerr optical rotation measurements and scanning tunneling spectroscopy.

Simultaneous Magnetic and Charge Doping of Topological Insulators with Carbon

NASA Astrophysics Data System (ADS)

Shen, Lei; Zeng, Minggang; Lu, Yunhao; Yang, Ming; Feng, Yuan Ping

2013-12-01

A two-step doping process, magnetic followed by charge or vice versa, is required to produce massive topological surface states (TSS) in topological insulators for many physics and device applications. Here, we demonstrate simultaneous magnetic and hole doping achieved with a single dopant, carbon, in Bi2Se3 by first-principles calculations. Carbon substitution for Se (CSe) results in an opening of a sizable surface Dirac gap (up to 82 meV), while the Fermi level remains inside the bulk gap and close to the Dirac point at moderate doping concentrations. The strong localization of 2p states of CSe favors spontaneous spin polarization via a p-p interaction and formation of ordered magnetic moments mediated by surface states. Meanwhile, holes are introduced into the system by CSe. This dual function of carbon doping suggests a simple way to realize insulating massive TSS.

Heptagraphene: Tunable dirac cones in a graphitic structure

DOE PAGES

Lopez-Bezanilla, Alejandro; Martin, Ivar; Littlewood, Peter B.

2016-09-13

Here, we predict the existence and dynamical stability of heptagraphene, a new graphitic structure formed of rings of 10 carbon atoms bridged by carbene groups yielding seven-membered rings. Despite the rectangular unit cell, the band structure is topologically equivalent to that of strongly distorted graphene. Density-functional-theory calculations demonstrate that heptagraphene has Dirac cones on symmetry lines that are robust against biaxial strain but which open a gap under shear. At high deformation values bond reconstructions lead to different electronic band arrangements in dynamically stable configurations. Within a tight-binding framework this richness of the electronic behavior is identified as a directmore » consequence of the symmetry breaking within the cell which, unlike other graphitic structures, leads to band gap opening. A combined approach of chemical and physical modification of graphene unit cell unfurls the opportunity to design carbon-based systems in which one aims to tune an electronic band gap.« less

On the synchrotron radiation reaction in external magnetic field

NASA Astrophysics Data System (ADS)

Tursunov, Arman; Kološ, Martin

2017-12-01

We study the dynamics of point electric charges undergoing radiation reaction force due to synchrotron radiation in the presence of external uniform magnetic field. The radiation reaction force cannot be neglected in many physical situations and its presence modifies the equations of motion significantly. The exact form of the equation of motion known as the Lorentz-Dirac equation contains higher order Schott term which leads to the appearance of the runaway solutions. We demonstrate effective computational ways to avoid such unphysical solutions and perform numerical integration of the dynamical equations. We show that in the ultrarelativistic case the Schott term is small and does not have considerable effect to the trajectory of a particle. We compare results with the covariant Landau-Lifshitz equation which is the first iteration of the Lorentz-Dirac equation. Even though the Landau-Lifshitz equation is thought to be approximative solution, we show that in realistic scenarios both approaches lead to identical results.

Consistency of multi-time Dirac equations with general interaction potentials

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

Deckert, Dirk-André, E-mail: deckert@math.lmu.de; Nickel, Lukas, E-mail: nickel@math.lmu.de

In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under suitable assumptions on the differentiability of possible solutions, we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills themore » physically desirable Poincaré invariance. We conclude that in this sense, Dirac’s multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue.« less

Landau quantization of Dirac fermions in graphene and its multilayers

NASA Astrophysics Data System (ADS)

Yin, Long-Jing; Bai, Ke-Ke; Wang, Wen-Xiao; Li, Si-Yu; Zhang, Yu; He, Lin

2017-08-01

When electrons are confined in a two-dimensional (2D) system, typical quantum-mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum-mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.

Position, spin, and orbital angular momentum of a relativistic electron

NASA Astrophysics Data System (ADS)

Bliokh, Konstantin Y.; Dennis, Mark R.; Nori, Franco

2017-08-01

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We consider two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the Zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K. Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011), 10.1103/PhysRevLett.107.174802] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S. M. Barnett, Phys. Rev. Lett. 118, 114802 (2017), 10.1103/PhysRevLett.118.114802].

Discovering intermediate mass sterile neutrinos through τ-→π-μ-e+ν (or ν ¯ ) decay

NASA Astrophysics Data System (ADS)

Kim, C. S.; López Castro, G.; Sahoo, Dibyakrupa

2017-10-01

Distinguishing the Dirac and Majorana nature of neutrinos remains one of the most important tasks in neutrino physics. By assuming that the τ-→π-μ-e+ν (or ν ¯ ) decay is resonantly enhanced by the exchange of an intermediate mass sterile neutrino N , we show that the energy spectrum of emitted pions and muons can be used to easily distinguish between the Dirac and Majorana nature of N . This method takes advantage of the fact that the flavor of light neutrinos is not identified in the tau decay under consideration. We find that it is particularly advantageous, because of no competing background events, to search for N in the mass range me+mμ≤mN≤mμ+mπ, where mX denotes the mass of particle X ∈{e ,μ ,π ,N }.

The effective fine-structure constant of freestanding graphene measured in graphite.

PubMed

Reed, James P; Uchoa, Bruno; Joe, Young Il; Gan, Yu; Casa, Diego; Fradkin, Eduardo; Abbamonte, Peter

2010-11-05

Electrons in graphene behave like Dirac fermions, permitting phenomena from high-energy physics to be studied in a solid-state setting. A key question is whether or not these fermions are critically influenced by Coulomb correlations. We performed inelastic x-ray scattering experiments on crystals of graphite and applied reconstruction algorithms to image the dynamical screening of charge in a freestanding graphene sheet. We found that the polarizability of the Dirac fermions is amplified by excitonic effects, improving screening of interactions between quasiparticles. The strength of interactions is characterized by a scale-dependent, effective fine-structure constant, α(g)* (k,ω), the value of which approaches 0.14 ± 0.092 ~ 1/7 at low energy and large distances. This value is substantially smaller than the nominal α(g) = 2.2, suggesting that, on the whole, graphene is more weakly interacting than previously believed.

Josephson current signatures of the Majorana flat bands on the surface of time-reversal-invariant Weyl and Dirac semimetals

NASA Astrophysics Data System (ADS)

Chen, Anffany; Pikulin, Dmitry I.; Franz, Marcel

A linear Josephson junction mediated by the surface states of a time-reversal-invariant Weyl or Dirac semimetal localizes Majorana flat bands protected by the time-reversal symmetry. We show that as a result, the Josephson current exhibits a discontinuous jump at π phase difference which can serve as an experimental signature of the Majorana bands. The magnitude of the jump scales proportionally to the junction length and the momentum space distance between the Weyl nodes projected onto the junction. It also exhibits a characteristic dependence on the junction orientation. We demonstrate that the jump is robust against the effects of non-zero temperature and weak non-magnetic disorder. This work was supported by NSERC and CIfAR. In addition A.C. acknowledges support by the 2016 Boulder Summer School for Condensed Matter and Materials Physics through NSF Grant DMR-13001648.

Phase Transitions of the Polariton Condensate in 2D Dirac Materials

NASA Astrophysics Data System (ADS)

Lee, Ki Hoon; Lee, Changhee; Min, Hongki; Chung, Suk Bum

2018-04-01

For the quantum well in an optical microcavity, the interplay of the Coulomb interaction and the electron-photon (e -ph) coupling can lead to the hybridizations of the exciton and the cavity photon known as polaritons, which can form the Bose-Einstein condensate above a threshold density. Additional physics due to the nontrivial Berry phase comes into play when the quantum well consists of the gapped two-dimensional Dirac material such as the transition metal dichalcogenide MoS2 or WSe2 . Specifically, in forming the polariton, the e -ph coupling from the optical selection rule due to the Berry phase can compete against the Coulomb electron-electron (e -e ) interaction. We find that this competition gives rise to a rich phase diagram for the polariton condensate involving both topological and symmetry breaking phase transitions, with the former giving rise to the quantum anomalous Hall and the quantum spin Hall phases.

Phase Transitions of the Polariton Condensate in 2D Dirac Materials.

PubMed

Lee, Ki Hoon; Lee, Changhee; Min, Hongki; Chung, Suk Bum

2018-04-13

For the quantum well in an optical microcavity, the interplay of the Coulomb interaction and the electron-photon (e-ph) coupling can lead to the hybridizations of the exciton and the cavity photon known as polaritons, which can form the Bose-Einstein condensate above a threshold density. Additional physics due to the nontrivial Berry phase comes into play when the quantum well consists of the gapped two-dimensional Dirac material such as the transition metal dichalcogenide MoS_{2} or WSe_{2}. Specifically, in forming the polariton, the e-ph coupling from the optical selection rule due to the Berry phase can compete against the Coulomb electron-electron (e-e) interaction. We find that this competition gives rise to a rich phase diagram for the polariton condensate involving both topological and symmetry breaking phase transitions, with the former giving rise to the quantum anomalous Hall and the quantum spin Hall phases.

Tripartite nonlocality for an open Dirac system in the background of Schwarzschild space-time

NASA Astrophysics Data System (ADS)

Ding, Zhi-Yong; Shi, Jia-Dong; Wu, Tao; He, Juan

2017-12-01

In this paper, the behavior of the tripartite nonlocality for a Dirac system in the background of Schwarzschild space-time is studied. It is shown that the nonlocality of the ultimate physical accessible state always decreases as the Hawking effect increases monotonically, which is independent of the number of particles located near the event horizon. Besides, the more particles there are located near the event horizon, the more difficult the violation of the Svetlichny inequality becomes. Furthermore, we investigate the property of these particles suffering from a non-Markovian environment, and derive that the nonlocality decreases quickly with the increasing decoherence time accompanied by damping revivals. To preserve tripartite nonlocality in the non-Markovian environment, we propose a scheme by means of prior weak measurement and post measurement reversal. It is worth noticing that the effect is better for larger measurement strengths, while it induces smaller success probability.

Electronic properties of 8 - Pmmn borophene

DOE PAGES

Lopez-Bezanilla, Alejandro; Littlewood, Peter B.

2016-06-15

First-principles calculations on monolayer 8-Pmmn borophene are reported to reveal unprecedented electronic properties in a two-dimensional material. Based on a Born effective charge analysis, 8-Pmmn borophene is the first single-element-based monolayered material exhibiting two sublattices with substantial ionic features. We observed Dirac cones are actually formed by the p(z) orbitals of one of the inequivalent sublattices composed of uniquely four atoms, yielding an underlying hexagonal network topologically equivalent to distorted graphene. One significant physical outcome of this effect includes the possibility of converting metallic 8-Pmmn borophene into an indirect band gap semiconductor by means of external shear stress. Furthermore, themore » stability of the strained structures are supported by a phonon frequency analysis. The Dirac cones are sensitive to the formation of vacancies only in the inequivalent sublattice electronically active at the Fermi level.« less

Effect of wave function on the proton induced L XRP cross sections for {sub 62}Sm and {sub 74}W

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

Shehla,; Kaur, Rajnish; Kumar, Anil

The L{sub k}(k= 1, α, β, γ) X-ray production cross sections have been calculated for {sub 74}W and {sub 62}Sm at different incident proton energies ranging 1-5 MeV using theoretical data sets of different physical parameters, namely, the Li(i=1-3) sub-shell X-ray emission rates based on the Dirac-Fork (DF) model, the fluorescence and Coster Kronig yields based on the Dirac- Hartree-Slater (DHS) model and two sets the proton ionization cross sections based on the DHS model and the ECPSSR in order to assess the influence of the wave function on the XRP cross sections. The calculated cross sections have been compared withmore » the measured cross sections reported in the recent compilation to check the reliability of the calculated values.« less

Three-component fermions with surface Fermi arcs in tungsten carbide

NASA Astrophysics Data System (ADS)

Ma, J.-Z.; He, J.-B.; Xu, Y.-F.; Lv, B. Q.; Chen, D.; Zhu, W.-L.; Zhang, S.; Kong, L.-Y.; Gao, X.; Rong, L.-Y.; Huang, Y.-B.; Richard, P.; Xi, C.-Y.; Choi, E. S.; Shao, Y.; Wang, Y.-L.; Gao, H.-J.; Dai, X.; Fang, C.; Weng, H.-M.; Chen, G.-F.; Qian, T.; Ding, H.

2018-04-01

Topological Dirac and Weyl semimetals not only host quasiparticles analogous to the elementary fermionic particles in high-energy physics, but also have a non-trivial band topology manifested by gapless surface states, which induce exotic surface Fermi arcs1,2. Recent advances suggest new types of topological semimetal, in which spatial symmetries protect gapless electronic excitations without high-energy analogues3-11. Here, using angle-resolved photoemission spectroscopy, we observe triply degenerate nodal points near the Fermi level of tungsten carbide with space group P 6 ¯m 2 (no. 187), in which the low-energy quasiparticles are described as three-component fermions distinct from Dirac and Weyl fermions. We further observe topological surface states, whose constant-energy contours constitute pairs of `Fermi arcs' connecting to the surface projections of the triply degenerate nodal points, proving the non-trivial topology of the newly identified semimetal state.

Mobility spectrum analytical approach for intrinsic band picture of Ba(FeAs)2

NASA Astrophysics Data System (ADS)

Huynh, K. K.; Tanabe, Y.; Urata, T.; Heguri, S.; Tanigaki, K.; Kida, T.; Hagiwara, M.

2014-09-01

Unconventional high temperature superconductivity as well as three-dimensional bulk Dirac cone quantum states arising from the unique d-orbital topology have comprised an intriguing research area in physics. Here we apply a special analytical approach using a mobility spectrum, in which the carrier number is conveniently described as a function of mobility without any hypothesis, both on the types and the numbers of carriers, for the interpretations of longitudinal and transverse electric transport of high quality single crystal Ba(FeAs)2 in a wide range of magnetic fields. We show that the majority carriers are accommodated in large parabolic hole and electron pockets with very different topology as well as remarkably different mobility spectra, whereas the minority carriers reside in Dirac quantum states with the largest mobility as high as 70,000 cm2(Vs)-1. The deduced mobility spectra are discussed and compared to the reported sophisticated first principle band calculations.

Topological Dirac line nodes and superconductivity coexist in SnSe at high pressure

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

Chen, Xuliang; Lu, Pengchao; Wang, Xuefei

2017-10-01

We report on the discovery of a pressure-induced topological and superconducting phase of SnSe, a material which attracts much attention recently due to its superior thermoelectric properties. In situ high-pressure electrical transport and synchrotron x-ray diffraction measurements show that the superconductivity emerges along with the formation of a CsCl-type structural phase of SnSe above around 27 GPa, with a maximum critical temperature of 3.2 K at 39 GPa. Based on ab initio calculations, this CsCl-type SnSe is predicted to be a Dirac line-node (DLN) semimetal in the absence of spin-orbit coupling, whose DLN states are protected by the coexistence ofmore » time-reversal and inversion symmetries. These results make CsCl-type SnSe an interesting model platform with simple crystal symmetry to study the interplay of topological physics and superconductivity.« less

First Experimental Realization of the Dirac Oscillator

NASA Astrophysics Data System (ADS)

Franco-Villafañe, J. A.; Sadurní, E.; Barkhofen, S.; Kuhl, U.; Mortessagne, F.; Seligman, T. H.

2013-10-01

We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yield the spectrum of the one-dimensional Dirac oscillator with and without a mass term. The flexibility of the experimental setup allows the implementation of other one-dimensional Dirac-type equations.

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

NASA Astrophysics Data System (ADS)

Dai, Jian; Song, Xing-Chang

2001-07-01

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

CALL FOR PAPERS: Progress in Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

2003-11-01

This is a call for contributions to a Special Issue of Journal of Physics A: Mathematical and General entitled `Statistical Physics of Disordered Systems: from Real Materials to Optimization and Codes'. This issue should be a place for high quality original work. We stress the fact that we are interested in having the topic interpreted broadly: we would like to have contributions ranging from equilibrium and dynamical studies of spin glasses, glassy behaviour in amorphous materials, and low temperature physics, to applications in non-conventional areas such as error correcting codes, image analysis and reconstruction, optimization, and algorithms based on statistical mechanical ideas. We believe that we have arrived at a very exciting moment for the development of this multidisciplinary approach, and that this issue will be of a high standard and prove to be a very useful tool in the future. The Editorial Board has invited E Marinari, H Nishimori and F Ricci-Tersenghi to serve as Guest Editors for the Special Issue. Their criteria for acceptance of contributions are the following: bullet The subject of the paper should relate to the statistical physics of disordered systems. bullet Contributions will be refereed and processed according to the usual procedures of the journal. bullet Papers should be original (they should not be simply reviews of authors' own work that is already published elsewhere). bullet Review articles will be considered for inclusion in the Special Issue only in very special cases. The editors will analyse potential proposals of reviews, and if needed they will ask for some review contributions. The guidelines for the preparation of contributions are the following: bullet The deadline for submission of contributions is 31 March 2003. This deadline will allow the Special Issue to appear in about October 2003. bullet There is a nominal page limit of 15 printed pages (approximately 9000 words) per research contribution. The contributions that have been approved by the Guest Editors as review articles will have a limit of 30 printed pages (18000 words). Papers exceeding these limits may be accepted at the discretion of the Guest Editors. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. bullet Contributions to the Special Issue should if possible be submitted electronically at www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue -- Statistical Physics of Disordered Systems'. Submissions should ideally be in either standard LaTeX form or Microsoft Word. Please see the web site for further information on electronic submissions. bullet Authors unable to submit electronically may send hard copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing the electronic code on floppy disk if available and quoting `JPhysA Special Issue -- Statistical Physics of Disordered Systems'. bullet All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This Special Issue will be published in both paper and online editions of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue in addition to the usual 25 free offprints of their article. E Marinari, H Nishimori and F Ricci-Tersenghi Guest Editors

Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

NASA Astrophysics Data System (ADS)

Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.

2018-04-01

We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.

Light trapping and circularly polarization at a Dirac point in 2D plasma photonic crystals

NASA Astrophysics Data System (ADS)

Li, Qian; Hu, Lei; Mao, Qiuping; Jiang, Haiming; Hu, Zhijia; Xie, Kang; Wei, Zhang

2018-03-01

Light trapping at the Dirac point in 2D plasma photonic crystal has been obtained. The new localized mode, Dirac mode, is attributable to neither photonic bandgap nor total internal reflection. It exhibits a unique algebraic profile and possesses a high-Q factor resonator of about 105. The Dirac point could be modulated by tuning the filling factor, plasma frequency and plasma cyclotron frequency, respectively. When a magnetic field parallel to the wave vector is applied, Dirac modes for right circularly polarized and left circularly polarized waves could be obtained at different frequencies, and the Q factor could be tuned. This property will add more controllability and flexibility to the design and modulation of novel photonic devices. It is also valuable for the possibilities of Dirac modes in photonic crystal containing other kinds of metamaterials.

Using OSG Computing Resources with (iLC)Dirac

NASA Astrophysics Data System (ADS)

Sailer, A.; Petric, M.; CLICdp Collaboration

2017-10-01

CPU cycles for small experiments and projects can be scarce, thus making use of all available resources, whether dedicated or opportunistic, is mandatory. While enabling uniform access to the LCG computing elements (ARC, CREAM), the DIRAC grid interware was not able to use OSG computing elements (GlobusCE, HTCondor-CE) without dedicated support at the grid site through so called ‘SiteDirectors’, which directly submit to the local batch system. This in turn requires additional dedicated effort for small experiments on the grid site. Adding interfaces to the OSG CEs through the respective grid middleware is therefore allowing accessing them within the DIRAC software without additional site-specific infrastructure. This enables greater use of opportunistic resources for experiments and projects without dedicated clusters or an established computing infrastructure with the DIRAC software. To allow sending jobs to HTCondor-CE and legacy Globus computing elements inside DIRAC the required wrapper classes were developed. Not only is the usage of these types of computing elements now completely transparent for all DIRAC instances, which makes DIRAC a flexible solution for OSG based virtual organisations, but it also allows LCG Grid Sites to move to the HTCondor-CE software, without shutting DIRAC based VOs out of their site. In these proceedings we detail how we interfaced the DIRAC system to the HTCondor-CE and Globus computing elements and explain the encountered obstacles and solutions developed, and how the linear collider community uses resources in the OSG.

Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux

NASA Astrophysics Data System (ADS)

Cariglia, Marco

2012-10-01

The Eisenhart-Duval lift allows embedding nonrelativistic theories into a Lorentzian geometrical setting. In this paper we study the lift from the point of view of the Dirac equation and its hidden symmetries. We show that dimensional reduction of the Dirac equation for the Eisenhart-Duval metric in general gives rise to the nonrelativistic Lévy-Leblond equation in lower dimension. We study in detail in which specific cases the lower dimensional limit is given by the Dirac equation, with scalar and vector flux, and the relation between lift, reduction, and the hidden symmetries of the Dirac equation. While there is a precise correspondence in the case of the lower dimensional massive Dirac equation with no flux, we find that for generic fluxes it is not possible to lift or reduce all solutions and hidden symmetries. As a by-product of this analysis, we construct new Lorentzian metrics with special tensors by lifting Killing-Yano and closed conformal Killing-Yano tensors and describe the general conformal Killing-Yano tensor of the Eisenhart-Duval lift metrics in terms of lower dimensional forms. Last, we show how, by dimensionally reducing the higher dimensional operators of the massless Dirac equation that are associated with shared hidden symmetries, it is possible to recover hidden symmetry operators for the Dirac equation with flux.

Spatial fluctuations of helical Dirac fermions on the surface of topological insulators

NASA Astrophysics Data System (ADS)

Beidenkopf, Haim

2013-03-01

Strong topological insulators are materials that host exotic states on their surfaces due to a topological band inversion in their bulk band structure. These surface states have Dirac dispersion as if they were massless relativistic particles, and are assured to remain metallic by time reversal symmetry. The helical spin texture associated with the Dirac dispersion prohibits backscattering, which we have imaged using scanning tunneling microscopy (STM) and spectroscopic mappings. This topological protection can be lifted by time-reversal breaking perturbations that induce a gap at the Dirac point and cant the helical spin texture. Massive Dirac electrons had been visualized by angular resolved photo emission spectroscopy in magnetically doped topological insulators. While we do not identify a gapped spectrum in our STM measurements of similar compounds, we do find a dominating electrostatic response to the charged content of those dopants. In their presence the Dirac spectrum exhibits strong spatial fluctuations. As a result translational invariance is broken over a characteristic length scale and the Dirac-point energy is only locally defined. Possible global manifestations of these local fluctuations will be discussed, as well as alternative avenues for breaking time reversal symmetry while maintaining the integrity of the Dirac spectrum. This work was supported by NSF, NSF-MRSEC, and DARPA.

Data Mining for 3D Organic Dirac Materials

NASA Astrophysics Data System (ADS)

Geilhufe, R. Matthias; Borysov, Stanislav S.; Bouhon, Adrien; Balatsky, Alexander V.

The study of Dirac materials, i.e. materials where the low-energy fermionic excitations behave as massless Dirac particles has been of ongoing interest for more than two decades. Such massless Dirac fermions are characterized by a linear dispersion relation with respect to the particle momentum. A combined study using group theory and data mining within the Organic Materials Database leads to the discovery of stable Dirac-point nodes and Dirac line-nodes within the electronic band structure in the class of 3-dimensional organic crystals. The nodes are protected by crystalline symmetry. As a result of this study, we present band structure calculations and symmetry analysis for previously synthesized organic materials. In all these materials, the Dirac nodes are well separated within the energy and located near the Fermi surface, which opens up a possibility for their direct experimental observation. The authors acknowledge support by the US Department of Energy, BES E3B7, the swedish Research Council Grant No. 638-2013-9243, the Knut and Alice Wallenberg Foundation, and the European Research Council (FP/2207-2013)/ERC Grant Agreement No. DM-321031.

Electrodynamic properties of the semimetallic Dirac material SrMnB i2 : Two-carrier-model analysis

NASA Astrophysics Data System (ADS)

Park, H. J.; Park, Byung Cheol; Lee, Min-Cheol; Jeong, D. W.; Park, Joonbum; Kim, Jun Sung; Ji, Hyo Seok; Shim, J. H.; Kim, K. W.; Moon, S. J.; Kim, Hyeong-Do; Cho, Deok-Yong; Noh, T. W.

2017-10-01

The electrodynamics of free carriers in the semimetallic Dirac material SrMnB i2 was investigated using optical spectroscopy and first-principles calculations. Using a two-carrier-model analysis, the total free-carrier response was successfully decomposed into individual contributions from Dirac fermions and non-Dirac free carriers. Possible roles of chiral pseudospin, spin-orbit interaction (SOI), antiferromagnetism, and electron-phonon (e -p h ) coupling in the Dirac fermion transport were also addressed. The Dirac fermions possess a low scattering rate of ˜10 meV at low temperature and thereby experience coherent transport. However, at high temperatures, we observed that the Dirac fermion transport becomes significantly incoherent, possibly due to strong e -p h interactions. The SOI-induced gap and antiferromagnetism play minor roles in the electrodynamics of the free carriers in SrMnB i2 . We also observed a seemingly optical-gap-like feature near 120 meV, which emerges at low temperatures but becomes filled in with increasing temperature. This gap-filling phenomenon is ascribed to phonon-assisted indirect transitions promoted at high temperatures.

First-Principles Prediction of Spin-Polarized Multiple Dirac Rings in Manganese Fluoride

NASA Astrophysics Data System (ADS)

Jiao, Yalong; Ma, Fengxian; Zhang, Chunmei; Bell, John; Sanvito, Stefano; Du, Aijun

2017-07-01

Spin-polarized materials with Dirac features have sparked great scientific interest due to their potential applications in spintronics. But such a type of structure is very rare and none has been fabricated. Here, we investigate the already experimentally synthesized manganese fluoride (MnF3 ) as a novel spin-polarized Dirac material by using first-principles calculations. MnF3 exhibits multiple Dirac cones in one spin orientation, while it behaves like a large gap semiconductor in the other spin channel. The estimated Fermi velocity for each cone is of the same order of magnitude as that in graphene. The 3D band structure further reveals that MnF3 possesses rings of Dirac nodes in the Brillouin zone. Such a spin-polarized multiple Dirac ring feature is reported for the first time in an experimentally realized material. Moreover, similar band dispersions can be also found in other transition metal fluorides (e.g., CoF3 , CrF3 , and FeF3 ). Our results highlight a new interesting single-spin Dirac material with promising applications in spintronics and information technologies.

First-Principles Prediction of Spin-Polarized Multiple Dirac Rings in Manganese Fluoride.

PubMed

Jiao, Yalong; Ma, Fengxian; Zhang, Chunmei; Bell, John; Sanvito, Stefano; Du, Aijun

2017-07-07

Spin-polarized materials with Dirac features have sparked great scientific interest due to their potential applications in spintronics. But such a type of structure is very rare and none has been fabricated. Here, we investigate the already experimentally synthesized manganese fluoride (MnF_{3}) as a novel spin-polarized Dirac material by using first-principles calculations. MnF_{3} exhibits multiple Dirac cones in one spin orientation, while it behaves like a large gap semiconductor in the other spin channel. The estimated Fermi velocity for each cone is of the same order of magnitude as that in graphene. The 3D band structure further reveals that MnF_{3} possesses rings of Dirac nodes in the Brillouin zone. Such a spin-polarized multiple Dirac ring feature is reported for the first time in an experimentally realized material. Moreover, similar band dispersions can be also found in other transition metal fluorides (e.g., CoF_{3}, CrF_{3}, and FeF_{3}). Our results highlight a new interesting single-spin Dirac material with promising applications in spintronics and information technologies.

Relativistic Photoionization Computations with the Time Dependent Dirac Equation

DTIC Science & Technology

2016-10-12

fields often occurs in the relativistic regime. A complete description of this phenomenon requires both relativistic and quantum mechanical treatment...photoionization, or other relativis- tic quantum electronics problems. While the Klein-Gordon equation captures much of the relevant physics, especially...for moderately heavy ions (Z 137), it does neglect the spin polarization of the electron. This memo parallels [1], but replaces the Klein-Gordon

Wave Functions for Time-Dependent Dirac Equation under GUP

NASA Astrophysics Data System (ADS)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

Seesaw roadmap to neutrino mass and dark matter

NASA Astrophysics Data System (ADS)

Centelles Chuliá, Salvador; Srivastava, Rahul; Valle, José W. F.

2018-06-01

We describe the many pathways to generate Majorana and Dirac neutrino mass through generalized dimension-5 operators a la Weinberg. The presence of new scalars beyond the Standard Model Higgs doublet implies new possible field contractions, which are required in the case of Dirac neutrinos. We also notice that, in the Dirac neutrino case, the extra symmetries needed to ensure the Dirac nature of neutrinos can also be made responsible for stability of dark matter.

On the spring and mass of the Dirac oscillator

NASA Technical Reports Server (NTRS)

Crawford, James P.

1993-01-01

The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.

Dirac structures in nonequilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Yoshimura, Hiroaki

2018-01-01

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equations for nonequilibrium thermodynamics admit an intrinsic formulation in terms of Dirac structures, both on the Lagrangian and the Hamiltonian settings. In the absence of irreversible processes, these Dirac structures reduce to canonical Dirac structures associated with canonical symplectic forms on phase spaces. Our geometric formulation of nonequilibrium thermodynamic thus consistently extends the geometric formulation of mechanics, to which it reduces in the absence of irreversible processes. The Dirac structures are associated with the variational formulation of nonequilibrium thermodynamics developed in the work of Gay-Balmaz and Yoshimura, J. Geom. Phys. 111, 169-193 (2017a) and are induced from a nonlinear nonholonomic constraint given by the expression of the entropy production of the system.

Optical analogue of relativistic Dirac solitons in binary waveguide arrays

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

Tran, Truong X., E-mail: truong.tran@mpl.mpg.de; Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen; Longhi, Stefano

2014-01-15

We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An opticalmore » analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.« less

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

PubMed Central

Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi

2016-01-01

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials. PMID:27578363

High efficiency and non-Richardson thermionics in three dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Huang, Sunchao; Sanderson, Matthew; Zhang, Yan; Zhang, Chao

2017-10-01

Three dimensional (3D) topological materials have a linear energy dispersion and exhibit many electronic properties superior to conventional materials such as fast response times, high mobility, and chiral transport. In this work, we demonstrate that 3D Dirac materials also have advantages over conventional semiconductors and graphene in thermionic applications. The low emission current suffered in graphene due to the vanishing density of states is enhanced by an increased group velocity in 3D Dirac materials. Furthermore, the thermal energy carried by electrons in 3D Dirac materials is twice of that in conventional materials with a parabolic electron energy dispersion. As a result, 3D Dirac materials have the best thermal efficiency or coefficient of performance when compared to conventional semiconductors and graphene. The generalized Richardson-Dushman law in 3D Dirac materials is derived. The law exhibits the interplay of the reduced density of states and enhanced emission velocity.

Quantum Hall effect in a bulk antiferromagnet EuMnBi2 with magnetically confined two-dimensional Dirac fermions.

PubMed

Masuda, Hidetoshi; Sakai, Hideaki; Tokunaga, Masashi; Yamasaki, Yuichi; Miyake, Atsushi; Shiogai, Junichi; Nakamura, Shintaro; Awaji, Satoshi; Tsukazaki, Atsushi; Nakao, Hironori; Murakami, Youichi; Arima, Taka-hisa; Tokura, Yoshinori; Ishiwata, Shintaro

2016-01-01

For the innovation of spintronic technologies, Dirac materials, in which low-energy excitation is described as relativistic Dirac fermions, are one of the most promising systems because of the fascinating magnetotransport associated with extremely high mobility. To incorporate Dirac fermions into spintronic applications, their quantum transport phenomena are desired to be manipulated to a large extent by magnetic order in a solid. We report a bulk half-integer quantum Hall effect in a layered antiferromagnet EuMnBi2, in which field-controllable Eu magnetic order significantly suppresses the interlayer coupling between the Bi layers with Dirac fermions. In addition to the high mobility of more than 10,000 cm(2)/V s, Landau level splittings presumably due to the lifting of spin and valley degeneracy are noticeable even in a bulk magnet. These results will pave a route to the engineering of magnetically functionalized Dirac materials.

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

NASA Astrophysics Data System (ADS)

Tateishi, Ikuma; Matsuura, Hiroyasu

2018-07-01

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

Graphene Dirac point tuned by ferroelectric polarization field

NASA Astrophysics Data System (ADS)

Wang, Xudong; Chen, Yan; Wu, Guangjian; Wang, Jianlu; Tian, Bobo; Sun, Shuo; Shen, Hong; Lin, Tie; Hu, Weida; Kang, Tingting; Tang, Minghua; Xiao, Yongguang; Sun, Jinglan; Meng, Xiangjian; Chu, Junhao

2018-04-01

Graphene has received numerous attention for future nanoelectronics and optoelectronics. The Dirac point is a key parameter of graphene that provides information about its carrier properties. There are lots of methods to tune the Dirac point of graphene, such as chemical doping, impurities, defects, and disorder. In this study, we report a different approach to tune the Dirac point of graphene using a ferroelectric polarization field. The Dirac point can be adjusted to near the ferroelectric coercive voltage regardless its original position. We have ensured this phenomenon by temperature-dependent experiments, and analyzed its mechanism with the theory of impurity correlation in graphene. Additionally, with the modulation of ferroelectric polymer, the current on/off ratio and mobility of graphene transistor both have been improved. This work provides an effective method to tune the Dirac point of graphene, which can be readily used to configure functional devices such as p-n junctions and inverters.

Spin symmetry in the Dirac sea derived from the bare nucleon-nucleon interaction

NASA Astrophysics Data System (ADS)

Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan

2018-06-01

The spin symmetry in the Dirac sea has been investigated with relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. Taking the nucleus 16O as an example and comparing the theoretical results with the data, the definition of the single-particle potential in the Dirac sea is studied in detail. It is found that if the single-particle states in the Dirac sea are treated as occupied states, the ground state properties are in better agreement with experimental data. Moreover, in this case, the spin symmetry in the Dirac sea is better conserved and it is more consistent with the findings using phenomenological relativistic density functionals.

Decay Rates and Probability Estimatesfor Massive Dirac Particlesin the Kerr-Newman Black Hole Geometry

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr-Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in L∞ {loc} at least at the rate t-5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].

Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

Chiral Anomaly from Strain-Induced Gauge Fields in Dirac and Weyl Semimetals

NASA Astrophysics Data System (ADS)

Pikulin, D. I.; Chen, Anffany; Franz, M.

2016-10-01

Dirac and Weyl semimetals form an ideal platform for testing ideas developed in high-energy physics to describe massless relativistic particles. One such quintessentially field-theoretic idea of the chiral anomaly already resulted in the prediction and subsequent observation of the pronounced negative magnetoresistance in these novel materials for parallel electric and magnetic fields. Here, we predict that the chiral anomaly occurs—and has experimentally observable consequences—when real electromagnetic fields E and B are replaced by strain-induced pseudo-electromagnetic fields e and b . For example, a uniform pseudomagnetic field b is generated when a Weyl semimetal nanowire is put under torsion. In accordance with the chiral anomaly equation, we predict a negative contribution to the wire resistance proportional to the square of the torsion strength. Remarkably, left- and right-moving chiral modes are then spatially segregated to the bulk and surface of the wire forming a "topological coaxial cable." This produces hydrodynamic flow with potentially very long relaxation time. Another effect we predict is the ultrasonic attenuation and electromagnetic emission due to a time-periodic mechanical deformation causing pseudoelectric field e . These novel manifestations of the chiral anomaly are most striking in the semimetals with a single pair of Weyl nodes but also occur in Dirac semimetals such as Cd3 As2 and Na3Bi and Weyl semimetals with unbroken time-reversal symmetry.

Spin force and torque in non-relativistic Dirac oscillator on a sphere

NASA Astrophysics Data System (ADS)

Shikakhwa, M. S.

2018-03-01

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin-orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.

Bulk Fermi Surfaces of the Dirac Type-II Semimetallic Candidates M Al3 (Where M =V , Nb, and Ta)

NASA Astrophysics Data System (ADS)

Chen, K.-W.; Lian, X.; Lai, Y.; Aryal, N.; Chiu, Y.-C.; Lan, W.; Graf, D.; Manousakis, E.; Baumbach, R. E.; Balicas, L.

2018-05-01

We report a de Haas-van Alphen (dHvA) effect study on the Dirac type-II semimetallic candidates M Al3 (where, M =V , Nb and Ta). The angular dependence of their Fermi surface (FS) cross-sectional areas reveals a remarkably good agreement with our first-principles calculations. Therefore, dHvA supports the existence of tilted Dirac cones with Dirac type-II nodes located at 100, 230 and 250 meV above the Fermi level ɛF for VAl3 , NbAl3 and TaAl3 respectively, in agreement with the prediction of broken Lorentz invariance in these compounds. However, for all three compounds we find that the cyclotron orbits on their FSs, including an orbit nearly enclosing the Dirac type-II node, yield trivial Berry phases. We explain this via an analysis of the Berry phase where the position of this orbit, relative to the Dirac node, is adjusted within the error implied by the small disagreement between our calculations and the experiments. We suggest that a very small amount of doping could displace ɛF to produce topologically nontrivial orbits encircling their Dirac node(s).

A unified physical model of Seebeck coefficient in amorphous oxide semiconductor thin-film transistors

NASA Astrophysics Data System (ADS)

Lu, Nianduan; Li, Ling; Sun, Pengxiao; Banerjee, Writam; Liu, Ming

2014-09-01

A unified physical model for Seebeck coefficient was presented based on the multiple-trapping and release theory for amorphous oxide semiconductor thin-film transistors. According to the proposed model, the Seebeck coefficient is attributed to the Fermi-Dirac statistics combined with the energy dependent trap density of states and the gate-voltage dependence of the quasi-Fermi level. The simulation results show that the gate voltage, energy disorder, and temperature dependent Seebeck coefficient can be well described. The calculation also shows a good agreement with the experimental data in amorphous In-Ga-Zn-O thin-film transistor.

Counter-diabatic driving for Dirac dynamics

NASA Astrophysics Data System (ADS)

Fan, Qi-Zhen; Cheng, Xiao-Hang; Chen, Xi

2018-03-01

In this paper, we investigate the fast quantum control of Dirac equation dynamics by counter-diabatic driving, sharing the concept of shortcut to adiabaticity. We systematically calculate the counter-diabatic terms in different Dirac systems, like graphene and trapped ions. Specially, the fast and robust population inversion processes are achieved in Dirac system, taking into account the quantum simulation with trapped ions. In addition, the population transfer between two bands can be suppressed by counter-diabatic driving in graphene system, which might have potential applications in opt-electric devices.

Magnetotransport study of Dirac fermions in YbMnBi 2 antiferromagnet

DOE PAGES

Wang, Aifeng; Zaliznyak, I.; Ren, Weijun; ...

2016-10-15

We report quantum transport and Dirac fermions in YbMnBi 2 single crystals. YbMnBi 2 is a layered material with anisotropic conductivity and magnetic order below 290 K. Magnetotransport properties, nonzero Berry phase, and small cyclotron mass indicate the presence of Dirac fermions. Lastly, angular-dependent magnetoresistance indicates a possible quasi-two-dimensional Fermi surface, whereas the deviation from the nontrivial Berry phase expected for Dirac states suggests the contribution of parabolic bands at the Fermi level or spin-orbit coupling.

CALL FOR PAPERS: Progress in Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

2003-12-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General dedicated to the subject of Supersymmetric Quantum Mechanics as featured in the International Conference in Supersymmetric Quantum Mechanics (PSQM03), 15--19 July 2003, University of Valladolid, Spain (http://metodos.fam.cie.uva.es/~susy_qm_03/). Participants at that meeting, as well as other researchers working in this area or in related fields, are invited to submit a research paper to this issue. The Editorial Board has invited Irina Areféva, David J Fernández, Véronique Hussin, Javier Negro, Luis M Nieto and Boris F Samsonov to act as Guest Editors for the special issue. Their criteria for acceptance of contributions are as follows: bullet The subject of the paper should be in the general area covered by the PSQM03 conference. bullet Contributions will be refereed and processed according to the usual mechanisms of the journal. bullet Papers should present substantial new results (they should not be simply reviews of authors' own work that is already published elsewhere). The guidelines for the preparation of contributions are as follows: bullet DEADLINE for submission of contributions is 15 January 2004. This deadline will allow the special issue to appear in approximately September 2004. bullet There is a page limit of 15 pages per research contribution. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. bullet Contributions to the special issue should if possible be submitted electronically at www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA special issue --- PSQM03'. Submissions should ideally be in either standard LaTeX form or Microsoft Word. Please see the web site for further information on electronic submissions. bullet Authors unable to submit by email may send hard copy contributions to: Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing the electronic code if available and mentioning `PSQM03 special issue'. bullet All contributions should be accompanied by a readme file or covering letter giving the postal and e-mail addresses for correspondence. Any subsequent change of address should be notified to the publishing office. The corresponding author of each contribution will receive a complimentary copy of the issue. Irina Areféva, David J Fernández, Véronique Hussin, Javier Negro, Luis M Nieto and Boris F Samsonov Guest Editors

The development of solar systems - Physical and cosmological considerations

NASA Astrophysics Data System (ADS)

Treder, H.-J.

Present knowledge of the evolution of the universe is addressed in terms of various philosophies, in particular Kantian philosophy. The formation of the solar system according to the theories of Kant and Laplace is reviewed and evaluated in terms of the time necessary to accomplish it. The significance of the Mach-Einstein ideas concerning inertia and Dirac's (1927) notion of a changing gravitational constant in this context is also considered.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Dirac cone pairs in silicene induced by interface Si-Ag hybridization: A first-principles effective band study

NASA Astrophysics Data System (ADS)

Lian, Chao; Meng, Sheng

2017-06-01

Using density functional theory combined with orbital-selective band unfolding techniques, we study the effective band structure of silicene (3 ×3 )/Ag(111) (4 ×4 ) structure. Consistent with the ARPES spectra recently obtained by [Feng et al. Proc. Natl. Acad. Sci. USA 113, 14656 (2016), 10.1073/pnas.1613434114], we observe six pairs of Dirac cones near the boundary of the Brillouin zone (BZ) of Ag (1 ×1 ) , while no Dirac cone is observed inside the BZ. Furthermore, we find that these Dirac cones are induced by the interfacial Si-Ag hybridization, mainly composed of Si pz orbitals and Ag s p bands, which is intrinsically different from the Dirac cones in free-standing silicene.

Evolution of magnetic Dirac bosons in a honeycomb lattice

NASA Astrophysics Data System (ADS)

Boyko, D.; Balatsky, A. V.; Haraldsen, J. T.

2018-01-01

We examine the presence and evolution of magnetic Dirac nodes in the Heisenberg honeycomb lattice. Using linear spin theory, we evaluate the collinear phase diagram as well as the change in the spin dynamics with various exchange interactions. We show that the ferromagnetic structure produces bosonic Dirac and Weyl points due to the competition between the interactions. Furthermore, it is shown that the criteria for magnetic Dirac nodes are coupled to the magnetic structure and not the overall crystal symmetry, where the breaking of inversion symmetry greatly affects the antiferromagnetic configurations. The tunability of the nodal points through variation of the exchange parameters leads to the possibility of controlling Dirac symmetries through an external manipulation of the orbital interactions.

Use of Fermi-Dirac statistics for defects in solids

NASA Astrophysics Data System (ADS)

Johnson, R. A.

1981-12-01

The Fermi-Dirac distribution function is an approximation describing a special case of Boltzmann statistics. A general occupation probability formula is derived and a criterion given for the use of Fermi-Dirac statistics. Application to classical problems of defects in solids is discussed.

Electric and magnetic superlattices in trilayer graphene

NASA Astrophysics Data System (ADS)

Uddin, Salah; Chan, K. S.

2016-01-01

The properties of one dimensional Kronig-Penney type of periodic electric and vector potential on ABC-trilayer graphene superlattices are investigated. The energy spectra obtained with periodic vector potentials shows the emergence of extra Dirac points in the energy spectrum with finite energies. For identical barrier and well widths, the original as well as the extra Dirac points are located in the ky = 0 plane. An asymmetry between the barrier and well widths causes a shift in the extra Dirac points away from the ky = 0 plane. Extra Dirac points having same electron hole crossing energy as that of the original Dirac point as well as finite energy Dirac points are generated in the energy spectrum when periodic electric potential is applied to the system. By applying electric and vector potential together, the symmetry of the energy spectrum about the Fermi level is broken. A tunable band gap is induced in the energy spectrum by applying both electric and vector potential simultaneously with different barrier and well widths.

Photonic crystal surface-emitting lasers enabled by an accidental Dirac point

DOEpatents

Chua, Song Liang; Lu, Ling; Soljacic, Marin

2014-12-02

A photonic-crystal surface-emitting laser (PCSEL) includes a gain medium electromagnetically coupled to a photonic crystal whose energy band structure exhibits a Dirac cone of linear dispersion at the center of the photonic crystal's Brillouin zone. This Dirac cone's vertex is called a Dirac point; because it is at the Brillouin zone center, it is called an accidental Dirac point. Tuning the photonic crystal's band structure (e.g., by changing the photonic crystal's dimensions or refractive index) to exhibit an accidental Dirac point increases the photonic crystal's mode spacing by orders of magnitudes and reduces or eliminates the photonic crystal's distributed in-plane feedback. Thus, the photonic crystal can act as a resonator that supports single-mode output from the PCSEL over a larger area than is possible with conventional PCSELs, which have quadratic band edge dispersion. Because output power generally scales with output area, this increase in output area results in higher possible output powers.

Topological edge states in ultra thin Bi(110) puckered crystal lattice

NASA Astrophysics Data System (ADS)

Wang, Baokai; Hsu, Chuanghan; Chang, Guoqing; Lin, Hsin; Bansil, Arun

We discuss the electronic structure of a 2-ML Bi(110) film with a crystal structure similar to that of black phosphorene. In the absence of Spin-Orbit coupling (SOC), the film is found to be a semimetal with two kinds of Dirac cones, which are classified by their locations in the Brillouin zone. All Dirac nodes are protected by crystal symmetry and carry non-zero winding numbers. When considering ribbons, along specific directions, projections of Dirac nodes serve as starting or ending points of edge bands depending on the sign of their carried winding number. After the inclusion of the SOC, all Dirac nodes are gapped out. Correspondingly, the edge states connecting Dirac nodes split and cross each other, and thus form a Dirac node at the boundary of the 1D Brillouin zone, which suggests that the system is a Quantum Spin Hall insulator. The nontrivial Quantum Spin Hall phase is also confirmed by counting the product of parities of the occupied bands at time-reversal invariant points.

C4N3H monolayer: A two-dimensional organic Dirac material with high Fermi velocity

NASA Astrophysics Data System (ADS)

Pan, Hongzhe; Zhang, Hongyu; Sun, Yuanyuan; Li, Jianfu; Du, Youwei; Tang, Nujiang

2017-11-01

Searching for two-dimensional (2D) organic Dirac materials, which have more adaptable practical applications compared with inorganic ones, is of great significance and has been ongoing. However, only two such materials with low Fermi velocity have been discovered so far. Herein, we report the design of an organic monolayer with C4N3H stoichiometry that possesses fascinating structure and good stability in its free-standing state. More importantly, we demonstrate that this monolayer is a semimetal with anisotropic Dirac cones and very high Fermi velocity. This Fermi velocity is roughly one order of magnitude larger than the largest velocity ever reported in 2D organic Dirac materials, and it is comparable to that in graphene. The Dirac states in this monolayer arise from the extended π -electron conjugation system formed by the overlapping 2 pz orbitals of carbon and nitrogen atoms. Our finding paves the way to a search for more 2D organic Dirac materials with high Fermi velocity.

Magnetoinfrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac Fermions in ZrTe 5

DOE PAGES

R. Y. Chen; Gu, G. D.; Chen, Z. G.; ...

2015-10-22

We present a magnetoinfrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe 5. We observe clear transitions between Landau levels and their further splitting under a magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D massless Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe 5 is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides direct, bulk spectroscopic evidence that a relatively weakmore » magnetic field can produce a sizable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. As a result, our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under the current magnetic field configuration.« less

Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2

PubMed Central

Liu, Jinyu; Hu, Jin; Cao, Huibo; Zhu, Yanglin; Chuang, Alyssa; Graf, D.; Adams, D. J.; Radmanesh, S. M. A.; Spinu, L.; Chiorescu, I.; Mao, Zhiqiang

2016-01-01

Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0; m0, mass of free electron), high quantum mobility (1280 cm2V−1S−1) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons. PMID:27466151

Dirac-Kähler particle in Riemann spherical space: boson interpretation

NASA Astrophysics Data System (ADS)

Ishkhanyan, A. M.; Florea, O.; Ovsiyuk, E. M.; Red'kov, V. M.

2015-11-01

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed.

Electronic structure, Dirac points and Fermi arc surface states in three-dimensional Dirac semimetal Na3Bi from angle-resolved photoemission spectroscopy

NASA Astrophysics Data System (ADS)

Aiji, Liang; Chaoyu, Chen; Zhijun, Wang; Youguo, Shi; Ya, Feng; Hemian, Yi; Zhuojin, Xie; Shaolong, He; Junfeng, He; Yingying, Peng; Yan, Liu; Defa, Liu; Cheng, Hu; Lin, Zhao; Guodong, Liu; Xiaoli, Dong; Jun, Zhang; M, Nakatake; H, Iwasawa; K, Shimada; M, Arita; H, Namatame; M, Taniguchi; Zuyan, Xu; Chuangtian, Chen; Hongming, Weng; Xi, Dai; Zhong, Fang; Xing-Jiang, Zhou

2016-07-01

The three-dimensional (3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A 3Bi (A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission (ARPES) measurements on the two cleaved surfaces, (001) and (100), of Na3Bi. On the (001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k x -k y plane and by varying the photon energy to get access to different out-of-plane k z s. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the (100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the (100) plane. We directly observe two isolated 3D Dirac nodes on the (100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ˜150 meV before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na3Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the 3D Dirac cones, on the possible formation of surface reconstruction of the (001) surface, and on the issue of basic Brillouin zone selection for the (100) surface. Project supported by the National Natural Science Foundation of China (Grant No. 11574367), the National Basic Research Program of China (Grant Nos. 2013CB921700, 2013CB921904, and 2015CB921300), and the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB07020300). The synchrotron radiation experiments have been done under the HiSOR Proposal numbers, 12-B-47 and 13-B-16.

Electron-hole asymmetry, Dirac fermions, and quantum magnetoresistance in BaMnBi 2

DOE PAGES

Li, Lijun; Wang, Kefeng; Graf, D.; ...

2016-03-28

Here, we report two-dimensional quantum transport and Dirac fermions in BaMnBi 2 single crystals. BaMnBi 2 is a layered bad metal with highly anisotropic conductivity and magnetic order below 290 K. Magnetotransport properties, nonzero Berry phase, small cyclotron mass, and the first-principles band structure calculations indicate the presence of Dirac fermions in Bi square nets. Quantum oscillations in the Hall channel suggest the presence of both electron and hole pockets, whereas Dirac and parabolic states coexist at the Fermi level.

Variational Integrators for Interconnected Lagrange-Dirac Systems

NASA Astrophysics Data System (ADS)

Parks, Helen; Leok, Melvin

2017-10-01

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange-Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange-Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange-Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67-98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529-562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).

Large optical conductivity of Dirac semimetal Fermi arc surface states

NASA Astrophysics Data System (ADS)

Shi, Li-kun; Song, Justin C. W.

2017-08-01

Fermi arc surface states, a hallmark of topological Dirac semimetals, can host carriers that exhibit unusual dynamics distinct from that of their parent bulk. Here we find that Fermi arc carriers in intrinsic Dirac semimetals possess a strong and anisotropic light-matter interaction. This is characterized by a large Fermi arc optical conductivity when light is polarized transverse to the Fermi arc; when light is polarized along the Fermi arc, Fermi arc optical conductivity is significantly muted. The large surface spectral weight is locked to the wide separation between Dirac nodes and persists as a large Drude weight of Fermi arc carriers when the system is doped. As a result, large and anisotropic Fermi arc conductivity provides a novel means of optically interrogating the topological surfaces states of Dirac semimetals.

Is there a connection between “dark” and “light” physics?

NASA Astrophysics Data System (ADS)

Lake, Matthew J.

2017-08-01

In the early-mid 20th century Dirac and Zel’dovich were among the first scientists to suggest an intimate connection between cosmology and atomic physics. Though a revolutionary proposal for its time, Dirac’s Large Number Hypothesis (1937) adopted a standard assumption of the day, namely, the non-existence of the cosmological constant term (Λ = 0). As a result, its implementation necessitated extreme violence to the theory of general relativity - something few physicists were prepared to sacrifice in favour of ‘numerology’ - requiring a time-dependent gravitational coupling of the form G(t) ˜ 1/t. Zel’dovich’s insight (1968) was to realise that a small but nonzero cosmological term (Λ > 0) allowed the present day radius of the Universe to be identified with the de Sitter radius, {r}{{U}}≃ {l}{{dS}}≃ 1/\\sqrt{{{Λ }}}, which removed the need for time-dependence in the fundamental couplings. Thus, he obtained the formula Λ ≃ m 6 G 2/ℏ4, where m is a mass scale characterising the relative strengths of the gravitational and electromagnetic interactions, which he identified with the proton mass m p. In this paper, we review a number of recent arguments which, instead, suggest the identification m = m e/α e, where m e is the electron mass and α e = e 2/ℏc ≃ 1/137 is the usual fine structure constant. We note that these are of a physical nature and, therefore, represent an attempt to lift previous arguments à la Dirac from the realm of numerology into the realm of empirical science. If valid, such arguments suggest an intimate connection, not only between the macroscopic and microscopic worlds, but, perhaps even more surprisingly, between the very essence of “dark” and “light” physics.

Search for Magnetic Monopoles with the MoEDAL Forward Trapping Detector in 13 TeV Proton-Proton Collisions at the LHC

NASA Astrophysics Data System (ADS)

Acharya, B.; Alexandre, J.; Baines, S.; Benes, P.; Bergmann, B.; Bernabéu, J.; Branzas, H.; Campbell, M.; Caramete, L.; Cecchini, S.; de Montigny, M.; De Roeck, A.; Ellis, J. R.; Fairbairn, M.; Felea, D.; Flores, J.; Frank, M.; Frekers, D.; Garcia, C.; Hirt, A. M.; Janecek, J.; Kalliokoski, M.; Katre, A.; Kim, D.-W.; Kinoshita, K.; Korzenev, A.; Lacarrère, D. H.; Lee, S. C.; Leroy, C.; Lionti, A.; Mamuzic, J.; Margiotta, A.; Mauri, N.; Mavromatos, N. E.; Mermod, P.; Mitsou, V. A.; Orava, R.; Parker, B.; Pasqualini, L.; Patrizii, L.; Pǎvǎlaş, G. E.; Pinfold, J. L.; Popa, V.; Pozzato, M.; Pospisil, S.; Rajantie, A.; Ruiz de Austri, R.; Sahnoun, Z.; Sakellariadou, M.; Sarkar, S.; Semenoff, G.; Shaa, A.; Sirri, G.; Sliwa, K.; Soluk, R.; Spurio, M.; Srivastava, Y. N.; Suk, M.; Swain, J.; Tenti, M.; Togo, V.; Tuszyński, J. A.; Vento, V.; Vives, O.; Vykydal, Z.; Whyntie, T.; Widom, A.; Willems, G.; Yoon, J. H.; Zgura, I. S.; MoEDAL Collaboration

2017-02-01

MoEDAL is designed to identify new physics in the form of long-lived highly ionizing particles produced in high-energy LHC collisions. Its arrays of plastic nuclear-track detectors and aluminium trapping volumes provide two independent passive detection techniques. We present here the results of a first search for magnetic monopole production in 13 TeV proton-proton collisions using the trapping technique, extending a previous publication with 8 TeV data during LHC Run 1. A total of 222 kg of MoEDAL trapping detector samples was exposed in the forward region and analyzed by searching for induced persistent currents after passage through a superconducting magnetometer. Magnetic charges exceeding half the Dirac charge are excluded in all samples and limits are placed for the first time on the production of magnetic monopoles in 13 TeV p p collisions. The search probes mass ranges previously inaccessible to collider experiments for up to five times the Dirac charge.

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.

Relativistic particle in a box: Klein-Gordon versus Dirac equations

NASA Astrophysics Data System (ADS)

Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

2018-03-01

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.

Finite-size correction scheme for supercell calculations in Dirac-point two-dimensional materials.

PubMed

Rocha, C G; Rocha, A R; Venezuela, P; Garcia, J H; Ferreira, M S

2018-06-19

Modern electronic structure calculations are predominantly implemented within the super cell representation in which unit cells are periodically arranged in space. Even in the case of non-crystalline materials, defect-embedded unit cells are commonly used to describe doped structures. However, this type of computation becomes prohibitively demanding when convergence rates are sufficiently slow and may require calculations with very large unit cells. Here we show that a hitherto unexplored feature displayed by several 2D materials may be used to achieve convergence in formation- and adsorption-energy calculations with relatively small unit-cell sizes. The generality of our method is illustrated with Density Functional Theory calculations for different 2D hosts doped with different impurities, all of which providing accuracy levels that would otherwise require enormously large unit cells. This approach provides an efficient route to calculating the physical properties of 2D systems in general but is particularly suitable for Dirac-point materials doped with impurities that break their sublattice symmetry.

Quantum self-gravitating collapsing matter in a quantum geometry

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge

2016-09-01

The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole.

Running coupling from gluon and ghost propagators in the Landau gauge: Yang-Mills theories with adjoint fermions

NASA Astrophysics Data System (ADS)

Bergner, Georg; Piemonte, Stefano

2018-04-01

Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N =1 supersymmetric Yang-Mills (SYM) theory and minimal walking technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N =1 SYM, minimal walking technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to compute the running coupling in the MiniMom scheme. We analyze several different ensembles of lattice Monte Carlo simulations for the SU(2) adjoint QCD with Nf=1 /2 ,1 ,3 /2 , and 2 Dirac fermions. We show how the running of the coupling changes as the number of interacting fermions is increased towards the conformal window.

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

Blennow, Mattias; Clementz, Stefan, E-mail: emb@kth.se, E-mail: scl@kth.se

Current problems with the solar model may be alleviated if a significant amount of dark matter from the galactic halo is captured in the Sun. We discuss the capture process in the case where the dark matter is a Dirac fermion and the background halo consists of equal amounts of dark matter and anti-dark matter. By considering the case where dark matter and anti-dark matter have different cross sections on solar nuclei as well as the case where the capture process is considered to be a Poisson process, we find that a significant asymmetry between the captured dark particles andmore » anti-particles is possible even for an annihilation cross section in the range expected for thermal relic dark matter. Since the captured number of particles are competitive with asymmetric dark matter models in a large range of parameter space, one may expect solar physics to be altered by the capture of Dirac dark matter. It is thus possible that solutions to the solar composition problem may be searched for in these type of models.« less

Giant Hall Photoconductivity in Narrow-Gapped Dirac Materials

NASA Astrophysics Data System (ADS)

Song, Justin C. W.; Kats, Mikhail A.

2016-12-01

Carrier dynamics acquire a new character in the presence of Bloch-band Berry curvature, which naturally arises in gapped Dirac materials (GDMs). Here we argue that photoresponse in GDMs with small band gaps is dramatically enhanced by Berry curvature. This manifests in a giant and saturable Hall photoconductivity when illuminated by circularly polarized light. Unlike Hall motion arising from a Lorentz force in a magnetic field, which impedes longitudinal carrier motion, Hall photoconductivity arising from Berry curvature can boost longitudinal carrier transport. In GDMs, this results in a helicity-dependent photoresponse in the Hall regime, where photoconductivity is dominated by its Hall component. We find that the induced Hall conductivity per incident irradiance is enhanced by up to six orders of magnitude when moving from the visible regime (with corresponding band gaps) to the far infrared. These results suggest that narrow-gap GDMs are an ideal test-bed for the unique physics that arise in the presence of Berry curvature, and open a new avenue for infrared and terahertz optoelectronics.

Extremely Large Magnetoresistance in a Topological Semimetal Candidate Pyrite PtBi2

NASA Astrophysics Data System (ADS)

Gao, Wenshuai; Hao, Ningning; Zheng, Fa-Wei; Ning, Wei; Wu, Min; Zhu, Xiangde; Zheng, Guolin; Zhang, Jinglei; Lu, Jianwei; Zhang, Hongwei; Xi, Chuanying; Yang, Jiyong; Du, Haifeng; Zhang, Ping; Zhang, Yuheng; Tian, Mingliang

2017-06-01

While pyrite-type PtBi2 with a face-centered cubic structure has been predicted to be a three-dimensional (3D) Dirac semimetal, experimental study of its physical properties remains absent. Here we report the angular-dependent magnetoresistance measurements of a PtBi2 single crystal under high magnetic fields. We observed extremely large unsaturated magnetoresistance (XMR) up to (11.2 ×106)% at T =1.8 K in a magnetic field of 33 T, which is comparable to the previously reported Dirac materials, such as WTe2 , LaSb, and NbP. The crystals exhibit an ultrahigh mobility and significant Shubnikov-de Hass quantum oscillations with a nontrivial Berry phase. The analysis of Hall resistivity indicates that the XMR can be ascribed to the nearly compensated electron and hole. Our experimental results associated with the ab initio calculations suggest that pyrite PtBi2 is a topological semimetal candidate that might provide a platform for exploring topological materials with XMR in noble metal alloys.

Dirac dark matter and b →s ℓ+ℓ- with U(1) gauge symmetry

NASA Astrophysics Data System (ADS)

Celis, Alejandro; Feng, Wan-Zhe; Vollmann, Martin

2017-02-01

We revisit the possibility of a Dirac fermion dark matter candidate in the light of current b →s ℓ+ℓ- anomalies by investigating a minimal extension of the Standard Model with a horizontal U(1 ) ' local symmetry. Dark matter stability is protected by a remnant Z2 symmetry arising after spontaneous symmetry breaking of U(1 ) '. The associated Z' gauge boson can accommodate current hints of new physics in b →s ℓ+ℓ- decays, and acts as a vector portal between dark matter and the visible sector. We find that the model is severely constrained by a combination of precision measurements at flavor factories, LHC searches for dilepton resonances, as well as direct and indirect dark matter searches. Despite this, viable regions of the parameter space accommodating the observed dark matter relic abundance and the b →s ℓ+ℓ-anomalies still persist for dark matter and Z ' masses in the TeV range.

Gigantic Surface Lifetime of an Intrinsic Topological Insulator

DOE PAGES

Neupane, Madhab; Xu, Su-Yang; Ishida, Yukiaki; ...

2015-09-09

We report that the interaction between light and novel two-dimensional electronic states holds promise to realize new fundamental physics and optical devices. Here, we use pump-probe photoemission spectroscopy to study the optically excited Dirac surface states in the bulk-insulating topological insulator Bi 2Te 2Se and reveal optical properties that are in sharp contrast to those of bulk-metallic topological insulators. We observe a gigantic optical lifetime exceeding 4 μs (1 μs=10 more » $${-}$$6 s) for the surface states in Bi 2Te 2Se, whereas the lifetime in most topological insulators, such as Bi2Se3, has been limited to a few picoseconds (1 ps=10 $${-}$$12 s). Moreover, we discover a surface photovoltage, a shift of the chemical potential of the Dirac surface states, as large as 100 mV. Lastly, our results demonstrate a rare platform to study charge excitation and relaxation in energy and momentum space in a two-dimensional system.« less

Effect of strain on the electronic structure of graphene

NASA Astrophysics Data System (ADS)

Martinez, Edgar; Cifuentes, Eduardo; de Coss, Romeo

2008-03-01

Graphene has been attracting interest due to its remarkable physical properties resulting from an electron spectrum resembling relativistic dynamics (Dirac fermions). Thus, is desirable to know methods for controling the charge carriers in graphene. In this work, we propose that the electronic properties of graphene can be modulated via isotropic and uniaxial strain. We have studied the electronic structure of graphene under mechanical deformation by means of first principles calculations. We present results for the charge distribution, electronic density of states, and band structure. We focus the analysis on the behavior of the Dirac cones and the number of the charge carriers as a function of strain. We find that an isotropic tensile strain increases the effective mass of carriers and an isotropic compression strain decrease it. Uniaxial tensile strain induce a similar behavior, as strain increase effective mass increase. Thus, our results show that strain allows controllable tuning of the graphene electronic properties. This research was supported by Consejo Nacional de Ciencia y Tecnolog'ia (Conacyt) under Grant No. 43830-F.

Direct evidence of interaction-induced Dirac cones in a monolayer silicene/Ag(111) system

PubMed Central

Feng, Ya; Liu, Defa; Feng, Baojie; Liu, Xu; Zhao, Lin; Xie, Zhuojin; Liu, Yan; Liang, Aiji; Hu, Cheng; Hu, Yong; He, Shaolong; Liu, Guodong; Zhang, Jun; Chen, Chuangtian; Xu, Zuyan; Chen, Lan; Wu, Kehui; Liu, Yu-Tzu; Lin, Hsin; Huang, Zhi-Quan; Hsu, Chia-Hsiu; Chuang, Feng-Chuan; Bansil, Arun; Zhou, X. J.

2016-01-01

Silicene, analogous to graphene, is a one-atom-thick 2D crystal of silicon, which is expected to share many of the remarkable properties of graphene. The buckled honeycomb structure of silicene, along with enhanced spin-orbit coupling, endows silicene with considerable advantages over graphene in that the spin-split states in silicene are tunable with external fields. Although the low-energy Dirac cone states lie at the heart of all novel quantum phenomena in a pristine sheet of silicene, a hotly debated question is whether these key states can survive when silicene is grown or supported on a substrate. Here we report our direct observation of Dirac cones in monolayer silicene grown on a Ag(111) substrate. By performing angle-resolved photoemission measurements on silicene(3 × 3)/Ag(111), we reveal the presence of six pairs of Dirac cones located on the edges of the first Brillouin zone of Ag(111), which is in sharp contrast to the expected six Dirac cones centered at the K points of the primary silicene(1 × 1) Brillouin zone. Our analysis shows clearly that the unusual Dirac cone structure we have observed is not tied to pristine silicene alone but originates from the combined effects of silicene(3 × 3) and the Ag(111) substrate. Our study thus identifies the case of a unique type of Dirac cone generated through the interaction of two different constituents. The observation of Dirac cones in silicene/Ag(111) opens a unique materials platform for investigating unusual quantum phenomena and for applications based on 2D silicon systems. PMID:27930314

Direct evidence of interaction-induced Dirac cones in a monolayer silicene/Ag(111) system

NASA Astrophysics Data System (ADS)

Feng, Ya; Liu, Defa; Feng, Baojie; Liu, Xu; Zhao, Lin; Xie, Zhuojin; Liu, Yan; Liang, Aiji; Hu, Cheng; Hu, Yong; He, Shaolong; Liu, Guodong; Zhang, Jun; Chen, Chuangtian; Xu, Zuyan; Chen, Lan; Wu, Kehui; Liu, Yu-Tzu; Lin, Hsin; Huang, Zhi-Quan; Hsu, Chia-Hsiu; Chuang, Feng-Chuan; Bansil, Arun; Zhou, X. J.

2016-12-01

Silicene, analogous to graphene, is a one-atom-thick 2D crystal of silicon, which is expected to share many of the remarkable properties of graphene. The buckled honeycomb structure of silicene, along with enhanced spin-orbit coupling, endows silicene with considerable advantages over graphene in that the spin-split states in silicene are tunable with external fields. Although the low-energy Dirac cone states lie at the heart of all novel quantum phenomena in a pristine sheet of silicene, a hotly debated question is whether these key states can survive when silicene is grown or supported on a substrate. Here we report our direct observation of Dirac cones in monolayer silicene grown on a Ag(111) substrate. By performing angle-resolved photoemission measurements on silicene(3 × 3)/Ag(111), we reveal the presence of six pairs of Dirac cones located on the edges of the first Brillouin zone of Ag(111), which is in sharp contrast to the expected six Dirac cones centered at the K points of the primary silicene(1 × 1) Brillouin zone. Our analysis shows clearly that the unusual Dirac cone structure we have observed is not tied to pristine silicene alone but originates from the combined effects of silicene(3 × 3) and the Ag(111) substrate. Our study thus identifies the case of a unique type of Dirac cone generated through the interaction of two different constituents. The observation of Dirac cones in silicene/Ag(111) opens a unique materials platform for investigating unusual quantum phenomena and for applications based on 2D silicon systems.

Understanding and Controlling the Electronic Properties of Graphene Using Scanning Probe Microscopy

DTIC Science & Technology

2014-07-21

Dirac point in gated bilayer graphene, Applied Physics Letters, (12 2009): 243502. doi : 10.1063/1.3275755 Brian J. LeRoy, Adam T. Roberts, Rolf...of soliton motion and stacking in trilayer graphene, Nature Materials , (04 2014): 0. doi : 10.1038/nmat3965 Matthew Yankowitz, Joel I-Jan Wang...of bilayer graphene via quasiparticle scattering, APL Materials , (09 2014): 92503. doi : Matthew Yankowitz, Fenglin Wang, Chun Ning Lau, Brian J

Notes on oscillator-like interactions of various spin relativistic particles

NASA Technical Reports Server (NTRS)

Dvoeglazov, Valeri V.; Delsolmesa, Antonio

1995-01-01

The equations for various spin particles with oscillator-like interactions are discussed in this talk. Topics discussed include: (1) comment on 'The Klein-Gordon Oscillator'; (2) the Dirac oscillator in quaternion form; (3) the Dirac-Dowker oscillator; (4) the Weinberg oscillator; and (5) note on the two-body Dirac oscillator.

Quantum oscillations in the type-II Dirac semi-metal candidate PtSe2

NASA Astrophysics Data System (ADS)

Yang, Hao; Schmidt, Marcus; Süss, Vicky; Chan, Mun; Balakirev, Fedor F.; McDonald, Ross D.; Parkin, Stuart S. P.; Felser, Claudia; Yan, Binghai; Moll, Philip J. W.

2018-04-01

Three-dimensional topological semi-metals carry quasiparticle states that mimic massless relativistic Dirac fermions, elusive particles that have never been observed in nature. As they appear in the solid body, they are not bound to the usual symmetries of space-time and thus new types of fermionic excitations that explicitly violate Lorentz-invariance have been proposed, the so-called type-II Dirac fermions. We investigate the electronic spectrum of the transition-metal dichalcogenide PtSe2 by means of quantum oscillation measurements in fields up to 65 T. The observed Fermi surfaces agree well with the expectations from band structure calculations, that recently predicted a type-II Dirac node to occur in this material. A hole- and an electron-like Fermi surface dominate the semi-metal at the Fermi level. The quasiparticle mass is significantly enhanced over the bare band mass value, likely by phonon renormalization. Our work is consistent with the existence of type-II Dirac nodes in PtSe2, yet the Dirac node is too far below the Fermi level to support free Dirac–fermion excitations.

Quasi-Dirac neutrino oscillations

NASA Astrophysics Data System (ADS)

Anamiati, Gaetana; Fonseca, Renato M.; Hirsch, Martin

2018-05-01

Dirac neutrino masses require two distinct neutral Weyl spinors per generation, with a special arrangement of masses and interactions with charged leptons. Once this arrangement is perturbed, lepton number is no longer conserved and neutrinos become Majorana particles. If these lepton number violating perturbations are small compared to the Dirac mass terms, neutrinos are quasi-Dirac particles. Alternatively, this scenario can be characterized by the existence of pairs of neutrinos with almost degenerate masses, and a lepton mixing matrix which has 12 angles and 12 phases. In this work we discuss the phenomenology of quasi-Dirac neutrino oscillations and derive limits on the relevant parameter space from various experiments. In one parameter perturbations of the Dirac limit, very stringent bounds can be derived on the mass splittings between the almost degenerate pairs of neutrinos. However, we also demonstrate that with suitable changes to the lepton mixing matrix, limits on such mass splittings are much weaker, or even completely absent. Finally, we consider the possibility that the mass splittings are too small to be measured and discuss bounds on the new, nonstandard lepton mixing angles from current experiments for this case.

Spin Nernst effect and intrinsic magnetization in two-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Gusynin, V. P.; Sharapov, S. G.; Varlamov, A. A.

2015-05-01

We begin with a brief description of the role of the Nernst-Ettingshausen effect in the studies of the high-temperature superconductors and Dirac materials such as graphene. The theoretical analysis of the NE effect is involved because the standard Kubo formalism has to be modified by the presence of magnetization currents in order to satisfy the third law of thermodynamics. A new generation of the low-buckled Dirac materials is expected to have a strong spin Nernst effect that represents the spintronics analog of the NE effect. These Dirac materials can be considered as made of two independent electron subsystems of the two-component gapped Dirac fermions. For each subsystem the gap breaks a time-reversal symmetry and thus plays a role of an effective magnetic field. We explicitly demonstrate how the correct thermoelectric coefficient emerges both by the explicit calculation of the magnetization and by a formal cancelation in the modified Kubo formula. We conclude by showing that the nontrivial dependences of the spin Nersnt signal on the carrier concentration and electric field applied are expected in silicene and other low-buckled Dirac materials.

Magnons in a honeycomb ferromagnet

NASA Astrophysics Data System (ADS)

Banerjee, Saikat

The original discovery of the Dirac electron dispersion in graphene led naturally to the question of Dirac cone stability with respect to interactions, and the Coulomb interaction between electrons was shown to induce a logarithmic renormalization of the Dirac dispersion. With the rapid expansion of the list of Dirac fermion compounds, the concept of bosonic Dirac materials has emerged. At the single particle level, these materials closely resemble the fermionic counterparts. However, the changed particle statistics affects the stability of Dirac cones differently. Here we study the effect of interactions focusing on the honeycomb ferromagnet - where the quasi-particles are magnetic spin waves (magnons). We demonstrate that magnon-magnon interactions lead to a significant renormalization of the bare band structure. We also address the question of the edge and surface states for a finite system. We applied these results to ferromagnetic CrBr3, where the Cr3+ atoms are arranged in weakly coupled honeycomb layers. Our theory qualitatively accounts for the unexplained anomalies in neutron scattering data from 40 years ago for CrBr3 and hereby expand the theory of ferromagnets beyond the standard Dyson theory.

Tuning Electrostatic Potentials for Imaging the Quantum Properties of Massless Dirac Fermions in Graphene

NASA Astrophysics Data System (ADS)

Wong, Dillon

Graphene, a two-dimensional (2D) honeycomb lattice of sp 2-bonded carbon atoms, is renowned for its many extraordinary properties. Not only does it have an extremely high carrier mobility, exceptional mechanical strength, and fascinating optical behavior, graphene additionally has an interesting energy-momentum relationship that is emergent from its space group symmetry. Graphene's low-energy electronic excitations consist of quasiparticles whose energies disperse linearly with wavevector and obey a 2D massless Dirac equation with a modified speed of light. This fortuitous circumstance allows for the exploration of ultra-relativistic phenomena using conventional tabletop techniques common to solid state physics and material science. Here I discuss experiments that probe these ultra-relativistic effects via application of scanning tunneling microscopy (STM) and spectroscopy (STS) to graphene field-effect transistors (FETs) in proximity with charged impurities. The first part of this dissertation focuses on the ultra-relativistic Coulomb problem. Depending on the strength of the potential, the Coulomb problem for massless Dirac particles is divided into two regimes: the subcritical and the supercritical. The subcritical regime is characterized by an electron-hole asymmetry in the local density of states (LDOS) and, unlike in nonrelativistic quantum mechanics, does not support bound states. In contrast, the supercritical regime hosts quasi-bound states that are analogous to "atomic collapse" orbits predicted to occur in atoms with nuclear charge Z > 170. By using an STM tip to directly position calcium (Ca) impurities on a graphene surface, we assembled "artificial nuclei" and observed a transition between the subcritical and supercritical regimes with increasing nuclear charge. We also investigated the screening of these charged impurities by massless Dirac fermions while varying the graphene carrier concentration with an electrostatic gate. The second part of this dissertation focuses on the ultra-relativistic harmonic oscillator. We developed a method for manipulating charged defects inside the boron nitride (BN) substrate underneath graphene to construct circular graphene p-n junctions. These p-n junctions were effectively quantum dots that electrostatically trapped graphene's relativistic charge carriers, and we imaged the interference patterns corresponding to this quantum confinement. The observed energy-level spectra in our p-n junctions closely matched a theoretical spectrum obtained by solving the 2D massless Dirac equation with a quadratic potential, allowing us to identify each observed state with principal and angular momentum quantum numbers. The results discussed here provide insight into fundamental aspects of relativistic quantum mechanics and into graphene properties pertinent to technological applications. In particular, graphene's response to electrostatic potentials determines the scope in which its charge carriers can be directed and harnessed for useful purposes. Furthermore, many of the results contained in this dissertation are expected to generalize to other Dirac materials.

La genèse du concept de champ quantique

NASA Astrophysics Data System (ADS)

Darrigol, O.

This is a historical study of the roots of a concept which has proved to be essential in modern particle physics : the concept of quantum field. The first steps were accomplished by two young theoreticians : Pascual Jordan quantized the free electromagnetic field in 1925 by means of the formal rules of the just discovered matrix mechanics, and Paul Dirac quantized the whole system charges + field in 1927. Using Dirac's equation for electrons (1928) and Jordan's idea of quantized matter waves (second quantization), Werner Heisenberg and Wolfgang Pauli provided in 1929-1930 an extension of Dirac's radiation theory and the proof of its relativistic invariance. Meanwhile Enrico Fermi discovered independently a more elegant and pedagogical formulation. To appreciate the degree of historical necessity of the quantization of fields, and the value of contemporaneous critics to this approach, it was necessary to investigate some of the history of the old radiation theory. We present the various arguments however provisional or naïve or wrong they could be in retrospect. So we hope to contribute to a more vivid picture of notions which, once deprived of their historical setting, might seem abstruse to the modern user. Nous présentons une étude historique des origines d'un concept devenu essentiel dans la physique moderne des particules : le concept de champ quantique. Deux jeunes théoriciens franchirent les premières étapes : Pascual Jordan quantifia le champ électromagnétique en 1925 grâce aux règles formelles de la mécanique des matrices naissante, et Paul Dirac quantifia le système complet charges + champ en 1927. Au moyen de l'équation de l'électron de Dirac (1928) et de l'idée de Jordan d'ondes de matière quantifiées (deuxième quantification), Werner Heisenberg et Wolfgang Pauli donnèrent en 1929-1930 une extension de la théorie du rayonnement de Dirac et la preuve de son invariance relativiste. Pendant ce temps Enrico Fermi découvrit indépendamment une formulation plus élégante et plus pédagogique. Pour apprécier le degré de nécessité historique de la quantification des champs et la valeur des critiques contemporaines à cette approche, nous avons dû analyser quelques points de l'histoire de l'ancienne théorie du rayonnement. Nous présentons les divers arguments quelque provisoires, naïfs ou faux qu'ils puissent sembler aujourd'hui. Ainsi nous espérons brosser un tableau plus vivant de notions menacées d'hermétisme si l'on oublie leurs fondements historiques.

Dirac State in Giant Magnetoresistive Materials

NASA Astrophysics Data System (ADS)

Wu, Y.; Jo, N. H.; Ochi, M.; Huang, L.; Mou, D.; Kong, T.; Mun, E.; Wang, L.; Lee, Y.; Bud'Ko, S. L.; Canfield, P. C.; Trivedi, N.; Arito, R.; Kaminski, A.

We use ultrahigh resolution, tunable, vacuum ultraviolet laser-based angle-resolved photoemission spectroscopy (ARPES) to study the electronic properties of materials that recently were discovered to display titanic magnetoresistance. We find that that several of these materials have Dirac-like features in their band structure. In some materials those features are ``ordinary'' Dirac cones, while in others the linear Dirac dispersion of two crossing bands forms a linear object in 3D momentum space. Our observation poses an important question about the role of Dirac dispersion in the unusually high, non-saturating magnetoresistance of these materials. Research was supported by the US DOE, Office of Basic Energy Sciences under Contract No. DE-AC02-07CH11358; Gordon and Betty Moore Foundation EPiQS Initiative (Grant No. GBMF4411); CEM, a NSF MRSEC, under Grant No. DMR-1420451.

Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems

NASA Astrophysics Data System (ADS)

Milletarı, Mirco; Offidani, Manuel; Ferreira, Aires; Raimondi, Roberto

2017-12-01

We present a theoretical analysis of two-dimensional Dirac-Rashba systems in the presence of disorder and external perturbations. We unveil a set of exact symmetry relations (Ward identities) that impose strong constraints on the spin dynamics of Dirac fermions subject to proximity-induced interactions. This allows us to demonstrate that an arbitrary dilute concentration of scalar impurities results in the total suppression of nonequilibrium spin Hall currents when only Rashba spin-orbit coupling is present. Remarkably, a finite spin Hall conductivity is restored when the minimal Dirac-Rashba model is supplemented with a spin-valley interaction. The Ward identities provide a systematic way to predict the emergence of the spin Hall effect in a wider class of Dirac-Rashba systems of experimental relevance and represent an important benchmark for testing the validity of numerical methodologies.

Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus

NASA Astrophysics Data System (ADS)

Kim, Jimin; Baik, Seung Su; Jung, Sung Won; Sohn, Yeongsup; Ryu, Sae Hee; Choi, Hyoung Joon; Yang, Bohm-Jung; Kim, Keun Su

2017-12-01

We report the realization of novel symmetry-protected Dirac fermions in a surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely tunable band gap of black phosphorus by the surface Stark effect is employed to achieve a surprisingly large band inversion up to ˜0.6 eV . High-resolution angle-resolved photoemission spectra directly reveal the pair creation of Dirac points and their movement along the axis of the glide-mirror symmetry. Unlike graphene, the Dirac point of black phosphorus is stable, as protected by space-time inversion symmetry, even in the presence of spin-orbit coupling. Our results establish black phosphorus in the inverted regime as a simple model system of 2D symmetry-protected (topological) Dirac semimetals, offering an unprecedented opportunity for the discovery of 2D Weyl semimetals.

Dirac Fermions in Borophene

NASA Astrophysics Data System (ADS)

Feng, Baojie; Sugino, Osamu; Liu, Ro-Ya; Zhang, Jin; Yukawa, Ryu; Kawamura, Mitsuaki; Iimori, Takushi; Kim, Howon; Hasegawa, Yukio; Li, Hui; Chen, Lan; Wu, Kehui; Kumigashira, Hiroshi; Komori, Fumio; Chiang, Tai-Chang; Meng, Sheng; Matsuda, Iwao

2017-03-01

Honeycomb structures of group IV elements can host massless Dirac fermions with nontrivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer structures. We present a detailed investigation of the β12 sheet, which is a borophene structure that can form spontaneously on a Ag(111) surface. Our tight-binding analysis revealed that the lattice of the β12 sheet could be decomposed into two triangular sublattices in a way similar to that for a honeycomb lattice, thereby hosting Dirac cones. Furthermore, each Dirac cone could be split by introducing periodic perturbations representing overlayer-substrate interactions. These unusual electronic structures were confirmed by angle-resolved photoemission spectroscopy and validated by first-principles calculations. Our results suggest monolayer boron as a new platform for realizing novel high-speed low-dissipation devices.

Elastic gauge fields and Hall viscosity of Dirac magnons

NASA Astrophysics Data System (ADS)

Ferreiros, Yago; Vozmediano, María A. H.

2018-02-01

We analyze the coupling of elastic lattice deformations to the magnon degrees of freedom of magnon Dirac materials. For a honeycomb ferromagnet we find that, as happens in the case of graphene, elastic gauge fields appear coupled to the magnon pseudospinors. For deformations that induce constant pseudomagnetic fields, the spectrum around the Dirac nodes splits into pseudo-Landau levels. We show that when a Dzyaloshinskii-Moriya interaction is considered, a topological gap opens in the system and a Chern-Simons effective action for the elastic degrees of freedom is generated. Such a term encodes a phonon Hall viscosity response, entirely generated by quantum fluctuations of magnons living in the vicinity of the Dirac points. The magnon Hall viscosity vanishes at zero temperature, and grows as temperature is raised and the states around the Dirac points are increasingly populated.

Dirac directional emission in anisotropic zero refractive index photonic crystals.

PubMed

He, Xin-Tao; Zhong, Yao-Nan; Zhou, You; Zhong, Zhi-Chao; Dong, Jian-Wen

2015-08-14

A certain class of photonic crystals with conical dispersion is known to behave as isotropic zero-refractive-index medium. However, the discrete building blocks in such photonic crystals are limited to construct multidirectional devices, even for high-symmetric photonic crystals. Here, we show multidirectional emission from low-symmetric photonic crystals with semi-Dirac dispersion at the zone center. We demonstrate that such low-symmetric photonic crystal can be considered as an effective anisotropic zero-refractive-index medium, as long as there is only one propagation mode near Dirac frequency. Four kinds of Dirac multidirectional emitters are achieved with the channel numbers of five, seven, eleven, and thirteen, respectively. Spatial power combination for such kind of Dirac directional emitter is also verified even when multiple sources are randomly placed in the anisotropic zero-refractive-index photonic crystal.

The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry

PubMed Central

He, Wen-Yu; Chan, C. T.

2015-01-01

We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes. The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The Dirac nodes can be unbuckled through breaking the mirror symmetry and a photonic analog of Chern insulator can be achieved through time reversal symmetry breaking. Breaking time reversal symmetry can lead to unidirectional helical edge states and breaking mirror symmetry can reduce the band gap to amplify the finite size effect, providing ways to engineer helical edge states. PMID:25640993

Dirac directional emission in anisotropic zero refractive index photonic crystals

PubMed Central

He, Xin-Tao; Zhong, Yao-Nan; Zhou, You; Zhong, Zhi-Chao; Dong, Jian-Wen

2015-01-01

A certain class of photonic crystals with conical dispersion is known to behave as isotropic zero-refractive-index medium. However, the discrete building blocks in such photonic crystals are limited to construct multidirectional devices, even for high-symmetric photonic crystals. Here, we show multidirectional emission from low-symmetric photonic crystals with semi-Dirac dispersion at the zone center. We demonstrate that such low-symmetric photonic crystal can be considered as an effective anisotropic zero-refractive-index medium, as long as there is only one propagation mode near Dirac frequency. Four kinds of Dirac multidirectional emitters are achieved with the channel numbers of five, seven, eleven, and thirteen, respectively. Spatial power combination for such kind of Dirac directional emitter is also verified even when multiple sources are randomly placed in the anisotropic zero-refractive-index photonic crystal. PMID:26271208

Singular solution of the Feller diffusion equation via a spectral decomposition.

PubMed

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

PubMed

Reiher, Markus; Wolf, Alexander

2004-12-08

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented. (c) 2004 American Institute of Physics.

Cr doping induced negative transverse magnetoresistance in C d3A s2 thin films

NASA Astrophysics Data System (ADS)

Liu, Yanwen; Tiwari, Rajarshi; Narayan, Awadhesh; Jin, Zhao; Yuan, Xiang; Zhang, Cheng; Chen, Feng; Li, Liang; Xia, Zhengcai; Sanvito, Stefano; Zhou, Peng; Xiu, Faxian

2018-02-01

The magnetoresistance of a material conveys various dynamic information about charge and spin carriers, inspiring both fundamental studies in physics and practical applications such as magnetic sensors, data storage, and spintronic devices. Magnetic impurities play a crucial role in the magnetoresistance as they induce exotic states of matter such as the quantum anomalous Hall effect in topological insulators and tunable ferromagnetic phases in dilute magnetic semiconductors. However, magnetically doped topological Dirac semimetals are hitherto lacking. Here, we report a systematic study of Cr-doped C d3A s2 thin films grown by molecular-beam epitaxy. With the Cr doping, C d3A s2 thin films exhibit unexpected negative transverse magnetoresistance and strong quantum oscillations, bearing a trivial Berry's phase and an enhanced effective mass. More importantly, with ionic gating the magnetoresistance of Cr-doped C d3A s2 thin films can be drastically tuned from negative to positive, demonstrating the strong correlation between electrons and the localized spins of the Cr impurities, which we interpret through the formation of magnetic polarons. Such a negative magnetoresistance under perpendicular magnetic field and its gate tunability have not been observed previously in the Dirac semimetal C d3A s2 . The Cr-induced topological phase transition and the formation of magnetic polarons in C d3A s2 provide insights into the magnetic interaction in Dirac semimetals as well as their potential applications in spintronics.

Singular solution of the Feller diffusion equation via a spectral decomposition

NASA Astrophysics Data System (ADS)

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

Band nesting, massive Dirac fermions, and valley Landé and Zeeman effects in transition metal dichalcogenides: A tight-binding model

NASA Astrophysics Data System (ADS)

Bieniek, Maciej; Korkusiński, Marek; Szulakowska, Ludmiła; Potasz, Paweł; Ozfidan, Isil; Hawrylak, Paweł

2018-02-01

We present here the minimal tight-binding model for a single layer of transition metal dichalcogenides (TMDCs) MX 2(M , metal; X , chalcogen) which illuminates the physics and captures band nesting, massive Dirac fermions, and valley Landé and Zeeman magnetic field effects. TMDCs share the hexagonal lattice with graphene but their electronic bands require much more complex atomic orbitals. Using symmetry arguments, a minimal basis consisting of three metal d orbitals and three chalcogen dimer p orbitals is constructed. The tunneling matrix elements between nearest-neighbor metal and chalcogen orbitals are explicitly derived at K ,-K , and Γ points of the Brillouin zone. The nearest-neighbor tunneling matrix elements connect specific metal and sulfur orbitals yielding an effective 6 ×6 Hamiltonian giving correct composition of metal and chalcogen orbitals but not the direct gap at K points. The direct gap at K , correct masses, and conduction band minima at Q points responsible for band nesting are obtained by inclusion of next-neighbor Mo-Mo tunneling. The parameters of the next-nearest-neighbor model are successfully fitted to MX 2(M =Mo ; X =S ) density functional ab initio calculations of the highest valence and lowest conduction band dispersion along K -Γ line in the Brillouin zone. The effective two-band massive Dirac Hamiltonian for MoS2, Landé g factors, and valley Zeeman splitting are obtained.

Topology-optimized dual-polarization Dirac cones

NASA Astrophysics Data System (ADS)

Lin, Zin; Christakis, Lysander; Li, Yang; Mazur, Eric; Rodriguez, Alejandro W.; Lončar, Marko

2018-02-01

We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which exhibit dual-polarization Dirac cones. We present photonic crystals of different symmetry types, such as fourfold and sixfold rotational symmetries, with Dirac cones at different points within the Brillouin zone. The demonstrated and related optimization techniques open avenues to band-structure engineering and manipulating the propagation of light in periodic media, with possible applications to exotic optical phenomena such as effective zero-index media and topological photonics.

Observerʼs mathematics applications to quantum mechanics

NASA Astrophysics Data System (ADS)

Khots, B.; Khots, D.

2014-12-01

When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in the contemporary study of nature. This work considers physical aspects in a setting of arithmetic, algebra, geometry, analysis, and topology provided by Observer's Mathematics (see www.mathrelativity.com). In this paper, we consider Dirac equations for free electrons. Certain results and communications pertaining to solutions of these problems are provided.

Dirac equation in Kerr-NUT-(A)dS spacetimes: Intrinsic characterization of separability in all dimensions

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Krtouš, Pavel; Kubizňák, David

2011-07-01

We intrinsically characterize separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions. Namely, we explicitly demonstrate that, in such spacetimes, there exists a complete set of first-order mutually commuting operators, one of which is the Dirac operator, that allows for common eigenfunctions which can be found in a separated form and correspond precisely to the general solution of the Dirac equation found by Oota and Yasui [Phys. Lett. BPYLBAJ0370-2693 659, 688 (2008)10.1016/j.physletb.2007.11.057]. Since all the operators in the set can be generated from the principal conformal Killing-Yano tensor, this establishes the (up-to-now) missing link among the existence of hidden symmetry, presence of a complete set of commuting operators, and separability of the Dirac equation in these spacetimes.

Creation of half-metallic f -orbital Dirac fermion with superlight elements in orbital-designed molecular lattice

NASA Astrophysics Data System (ADS)

Cui, Bin; Huang, Bing; Li, Chong; Zhang, Xiaoming; Jin, Kyung-Hwan; Zhang, Lizhi; Jiang, Wei; Liu, Desheng; Liu, Feng

2017-08-01

Magnetism in solids generally originates from the localized d or f orbitals that are hosted by heavy transition-metal elements. Here, we demonstrate a mechanism for designing a half-metallic f -orbital Dirac fermion from superlight s p elements. Combining first-principles and model calculations, we show that bare and flat-band-sandwiched (FBS) Dirac bands can be created when C20 molecules are deposited into a two-dimensional hexagonal lattice, which are composed of f -molecular orbitals (MOs) derived from s p -atomic orbitals (AOs). Furthermore, charge doping of the FBS Dirac bands induces spontaneous spin polarization, converting the system into a half-metallic Dirac state. Based on this discovery, a model of a spin field effect transistor is proposed to generate and transport 100% spin-polarized carriers. Our finding illustrates a concept to realize exotic quantum states by manipulating MOs, instead of AOs, in orbital-designed molecular crystal lattices.

‘Parabolic’ trapped modes and steered Dirac cones in platonic crystals

PubMed Central

McPhedran, R. C.; Movchan, A. B.; Movchan, N. V.; Brun, M.; Smith, M. J. A.

2015-01-01

This paper discusses the properties of flexural waves governed by the biharmonic operator, and propagating in a thin plate pinned at doubly periodic sets of points. The emphases are on the design of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates for a finite set (cluster) of pinned points. The Dirac cone topologies we exhibit have at least two cones touching at a point in the reciprocal lattice, augmented by another band passing through the point. We show that these Dirac cones can be steered along symmetry lines in the Brillouin zone by varying the aspect ratio of rectangular lattices of pins, and that, as the cones are moved, the involved band surfaces tilt. We link Dirac points with a parabolic profile in their neighbourhood, and the characteristic of this parabolic profile decides the direction of propagation of the trapped mode in finite clusters. PMID:27547089

Photonic crystal surface-emitting lasers

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

Chua, Song Liang; Lu, Ling; Soljacic, Marin

2015-06-23

A photonic-crystal surface-emitting laser (PCSEL) includes a gain medium electromagnetically coupled to a photonic crystal whose energy band structure exhibits a Dirac cone of linear dispersion at the center of the photonic crystal's Brillouin zone. This Dirac cone's vertex is called a Dirac point; because it is at the Brillouin zone center, it is called an accidental Dirac point. Tuning the photonic crystal's band structure (e.g., by changing the photonic crystal's dimensions or refractive index) to exhibit an accidental Dirac point increases the photonic crystal's mode spacing by orders of magnitudes and reduces or eliminates the photonic crystal's distributed in-planemore » feedback. Thus, the photonic crystal can act as a resonator that supports single-mode output from the PCSEL over a larger area than is possible with conventional PCSELs, which have quadratic band edge dispersion. Because output power generally scales with output area, this increase in output area results in higher possible output powers.« less

Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials

NASA Astrophysics Data System (ADS)

Hübener, Hannes; Sentef, Michael A.; de Giovannini, Umberto; Kemper, Alexander F.; Rubio, Angel

2017-01-01

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

Dirac State in the FeB2 Monolayer with Graphene-Like Boron Sheet.

PubMed

Zhang, Haijun; Li, Yafei; Hou, Jianhou; Du, Aijun; Chen, Zhongfang

2016-10-12

By introducing the commonly utilized Fe atoms into a two-dimensional (2D) honeycomb boron network, we theoretically designed a new Dirac material of FeB 2 monolayer with a Fermi velocity in the same order of graphene. The electron transfer from Fe atoms to B networks not only effectively stabilizes the FeB 2 networks but also leads to the strong interaction between the Fe and B atoms. The Dirac state in FeB 2 system primarily arises from the Fe d orbitals and hybridized orbital from Fe-d and B-p states. The newly predicted FeB 2 monolayer has excellent dynamic and thermal stabilities and is also the global minimum of 2D FeB 2 system, implying its experimental feasibility. Our results are beneficial to further uncovering the mechanism of the Dirac cones and providing a feasible strategy for Dirac materials design.

Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials.

PubMed

Hübener, Hannes; Sentef, Michael A; De Giovannini, Umberto; Kemper, Alexander F; Rubio, Angel

2017-01-17

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na 3 Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

Creating stable Floquet–Weyl semimetals by laser-driving of 3D Dirac materials

PubMed Central

Hübener, Hannes; Sentef, Michael A.; De Giovannini, Umberto; Kemper, Alexander F.; Rubio, Angel

2017-01-01

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet–Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance. PMID:28094286

Dirac equation on a curved surface

NASA Astrophysics Data System (ADS)

Brandt, F. T.; Sánchez-Monroy, J. A.

2016-09-01

The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein-Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles.

Elemental Topological Dirac Semimetal: α -Sn on InSb(111)

DOE PAGES

Xu, Cai-Zhi; Chan, Yang-Hao; Chen, Yige; ...

2017-04-04

Three-dimensional (3D) topological Dirac semimetals (TDSs) are rare but important as a versatile platform for exploring exotic electronic properties and topological phase transitions. A quintessential feature of TDSs is 3D Dirac fermions associated with bulk electronic states near the Fermi level. We have observed such bulk Dirac cones in epitaxially grown α-Sn films on InSb(111), the first such TDS system realized in an elemental form, using angle-resolved photoemission spectroscopy. First-principles calculations confirm that epitaxial strain is key to the formation of the TDS phase. A phase diagram is established that connects the 3D TDS phase through a singular point ofmore » a zero-gap semimetal phase to a topological insulator phase. The nature of the Dirac cone crosses over from 3D to 2D as the film thickness is reduced.« less

A Fock space coupled cluster study on the electronic structure of the UO(2), UO(2) (+), U(4+), and U(5+) species.

PubMed

Infante, Ivan; Eliav, Ephraim; Vilkas, Marius J; Ishikawa, Yasuyuki; Kaldor, Uzi; Visscher, Lucas

2007-09-28

The ground and excited states of the UO(2) molecule have been studied using a Dirac-Coulomb intermediate Hamiltonian Fock-space coupled cluster approach (DC-IHFSCC). This method is unique in describing dynamic and nondynamic correlation energies at relatively low computational cost. Spin-orbit coupling effects have been fully included by utilizing the four-component Dirac-Coulomb Hamiltonian from the outset. Complementary calculations on the ionized systems UO(2) (+) and UO(2) (2+) as well as on the ions U(4+) and U(5+) were performed to assess the accuracy of this method. The latter calculations improve upon previously published theoretical work. Our calculations confirm the assignment of the ground state of the UO(2) molecule as a (3)Phi(2u) state that arises from the 5f(1)7s(1) configuration. The first state from the 5f(2) configuration is found above 10,000 cm(-1), whereas the first state from the 5f(1)6d(1) configuration is found at 5,047 cm(-1).

Drude Conductivity of Dirac Fermions in Graphene

DTIC Science & Technology

2010-01-01

interband transitions, as required by the sum rule. Our surprising observation indicates that many-body effects and Dirac fermion-impurity interactions...reduction of free electron oscillator strength is corroborated by corresponding changes in graphene interband transitions, as required by the sum...dimensions. Researchers have demonstrated in graphene exotic Dirac fermion phenomena ranging from anomalous quantum Hall effects 1,2 to Klein tunneling 3 in

Anomalous thermospin effect in the low-buckled Dirac materials

NASA Astrophysics Data System (ADS)

Gusynin, V. P.; Sharapov, S. G.; Varlamov, A. A.

2014-10-01

A strong spin Nernst effect with nontrivial dependences on the carrier concentration and electric field applied is expected in silicene and other low-buckled Dirac materials. These Dirac materials can be considered as being made of two independent electron subsystems of the two-component gapped Dirac fermions. For each subsystem, the gap breaks a time-reversal symmetry and thus plays the role of an effective magnetic field. Accordingly, the standard Kubo formalism has to be altered by including the effective magnetization in order to satisfy the third law of thermodynamics. We explicitly demonstrate this by calculating the magnetization and showing how the correct thermoelectric coefficient emerges.

Coulomb disorder in three-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Skinner, Brian

2015-03-01

In three-dimensional materials with a Dirac spectrum, weak short-ranged disorder is essentially irrelevant near the Dirac point. This is manifestly not the case for Coulomb disorder, where the long-ranged nature of the potential produced by charged impurities implies large fluctuations of the disorder potential even when impurities are sparse, and these fluctuations are screened by the formation of electron/hole puddles. Here I outline a theory of such nonlinear screening of Coulomb disorder in three-dimensional Dirac systems, and present results for the typical magnitude of the disorder potential, the corresponding density of states, and the size and density of electron/hole puddles. The resulting conductivity is also discussed.

A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices

NASA Astrophysics Data System (ADS)

AlQurashi, Ahmed; Selvakumar, C. R.

2018-06-01

There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

Designing Two-Dimensional Dirac Heterointerfaces of Few-Layer Graphene and Tetradymite-Type Sb2Te3 for Thermoelectric Applications.

PubMed

Jang, Woosun; Lee, Jiwoo; In, Chihun; Choi, Hyunyong; Soon, Aloysius

2017-12-06

Despite the ubiquitous nature of the Peltier effect in low-dimensional thermoelectric devices, the influence of finite temperature on the electronic structure and transport in the Dirac heterointerfaces of the few-layer graphene and layered tetradymite, Sb 2 Te 3 (which coincidently have excellent thermoelectric properties) are not well understood. In this work, using the first-principles density-functional theory calculations, we investigate the detailed atomic and electronic structure of these Dirac heterointerfaces of graphene and Sb 2 Te 3 and further re-examine the effect of finite temperature on the electronic band structures using a phenomenological temperature-broadening model based on Fermi-Dirac statistics. We then proceed to understand the underlying charge redistribution process in this Dirac heterointerfaces and through solving the Boltzmann transport equation, we present the theoretical evidence of electron-hole asymmetry in its electrical conductivity as a consequence of this charge redistribution mechanism. We finally propose that the hexagonal-stacked Dirac heterointerfaces are useful as efficient p-n junction building blocks in the next-generation thermoelectric devices where the electron-hole asymmetry promotes the thermoelectric transport by "hot" excited charge carriers.

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.

Superstatistics with different kinds of distributions in the deformed formalism

NASA Astrophysics Data System (ADS)

Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

2018-03-01

In this article, after first introducing superstatistics, the effective Boltzmann factor in a deformed formalism for modified Dirac delta, uniform, two-level and Gamma distributions is derived. Then we make use of the superstatistics for four important problems in physics and the thermodynamic properties of the system are calculated. All results in the limit case are reduced to ordinary statistical mechanics. Furthermore, effects of all parameters in the problems are calculated and shown graphically.

Fermion dipole moment and holography

NASA Astrophysics Data System (ADS)

Kulaxizi, Manuela; Rahman, Rakibur

2015-12-01

In the background of a charged AdS black hole, we consider a Dirac particle endowed with an arbitrary magnetic dipole moment. For non-zero charge and dipole coupling of the bulk fermion, we find that the dual boundary theory can be plagued with superluminal modes. Requiring consistency of the dual CFT amounts to constraining the strength of the dipole coupling by an upper bound. We briefly discuss the implications of our results for the physics of holographic non-Fermi liquids.

Executor Framework for DIRAC

NASA Astrophysics Data System (ADS)

Casajus Ramo, A.; Graciani Diaz, R.

2012-12-01

DIRAC framework for distributed computing has been designed as a group of collaborating components, agents and servers, with persistent database back-end. Components communicate with each other using DISET, an in-house protocol that provides Remote Procedure Call (RPC) and file transfer capabilities. This approach has provided DIRAC with a modular and stable design by enforcing stable interfaces across releases. But it made complicated to scale further with commodity hardware. To further scale DIRAC, components needed to send more queries between them. Using RPC to do so requires a lot of processing power just to handle the secure handshake required to establish the connection. DISET now provides a way to keep stable connections and send and receive queries between components. Only one handshake is required to send and receive any number of queries. Using this new communication mechanism DIRAC now provides a new type of component called Executor. Executors process any task (such as resolving the input data of a job) sent to them by a task dispatcher. This task dispatcher takes care of persisting the state of the tasks to the storage backend and distributing them among all the Executors based on the requirements of each task. In case of a high load, several Executors can be started to process the extra load and stop them once the tasks have been processed. This new approach of handling tasks in DIRAC makes Executors easy to replace and replicate, thus enabling DIRAC to further scale beyond the current approach based on polling agents.

Split Dirac Supersymmetry: An Ultraviolet Completion of Higgsino Dark Matter

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

Fox, Patrick J.; Kribs, Graham D.; Martin, Adam

2014-10-07

Motivated by the observation that the Higgs quartic coupling runs to zero at an intermediate scale, we propose a new framework for models of split supersymmetry, in which gauginos acquire intermediate scale Dirac masses ofmore » $$\\sim 10^{8-11}$$ GeV. Scalar masses arise from one-loop finite contributions as well as direct gravity-mediated contributions. Like split supersymmetry, one Higgs doublet is fine-tuned to be light. The scale at which the Dirac gauginos are introduced to make the Higgs quartic zero is the same as is necessary for gauge coupling unification. Thus, gauge coupling unification persists (nontrivially, due to adjoint multiplets), though with a somewhat higher unification scale $$\\gtrsim 10^{17}$$ GeV. The $$\\mu$$-term is naturally at the weak scale, and provides an opportunity for experimental verification. We present two manifestations of Split Dirac Supersymmetry. In the "Pure Dirac" model, the lightest Higgsino must decay through R-parity violating couplings, leading to an array of interesting signals in colliders. In the "Hypercharge Impure" model, the bino acquires a Majorana mass that is one-loop suppressed compared with the Dirac gluino and wino. This leads to weak scale Higgsino dark matter whose overall mass scale, as well as the mass splitting between the neutral components, is naturally generated from the same UV dynamics. We outline the challenges to discovering pseudo-Dirac Higgsino dark matter in collider and dark matter detection experiments.« less

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-09-01

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

PubMed

Akemann, Gernot; Wettig, Tilo

2004-03-12

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.

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

PubMed

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

2010-08-27

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

Dirac neutrinos and SN 1987A

NASA Technical Reports Server (NTRS)

Turner, Michael S.

1991-01-01

Previous work has shown that the cooling of SN 1987A excludes a Dirac-neutrino mass greater than theta(20 keV) for nu(sub e), nu(sub mu), or nu(sub tau). The emission of wrong-helicity, Dirac neutrinos from SN 1987A, is re-examined. It is concluded that the effect of a Dirac neutrino on the cooling of SN 1987A has been underestimated due to neutrino degeneracy and additional emission processes. The limit that follows from the cooling of SN 1987A is believed to be greater (probably much greater) than 10 keV. This result is significant in light of the recent evidence for a 17 keV mass eigenstate that mixes with the electron neutrino.

Observation of Antiprotons

DOE R&D Accomplishments Database

Chamberlain, Owen; Segre, Emilio; Wiegand, Clyde; Ypsilantis, Thomas

1955-10-19

One of the striking features of Dirac's theory of the electron was the appearance of solutions to his equations which required the existence of an antiparticle, later identified as the positron. The extension of the Dirac theory to the proton requires the existence of an antiproton, a particle which bears to the proton the same relationship as the positron to the electron. However, until experimental proof of the existence of the antiproton was obtained, it might be questioned whether a proton is a Dirac particle in the same sense as is the electron. For instance, the anomalous magnetic moment of the proton indicates that the simple Dirac equation does not give a complete description of the proton.

Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.

PubMed

Owerre, S A

2017-07-31

In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX 3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L  ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM  < J L and possess chiral magnon edge modes.

Anomalous Dirac point transport due to extended defects in bilayer graphene.

PubMed

Shallcross, Sam; Sharma, Sangeeta; Weber, Heiko B

2017-08-24

Charge transport at the Dirac point in bilayer graphene exhibits two dramatically different transport states, insulating and metallic, that occur in apparently otherwise indistinguishable experimental samples. We demonstrate that the existence of these two transport states has its origin in an interplay between evanescent modes, that dominate charge transport near the Dirac point, and disordered configurations of extended defects in the form of partial dislocations. In a large ensemble of bilayer systems with randomly positioned partial dislocations, the distribution of conductivities is found to be strongly peaked at both the insulating and metallic limits. We argue that this distribution form, that occurs only at the Dirac point, lies at the heart of the observation of both metallic and insulating states in bilayer graphene.In seemingly indistinguishable bilayer graphene samples, two distinct transport regimes, insulating and metallic, have been identified experimentally. Here, the authors demonstrate that these two states originate from the interplay between extended defects and evanescent modes at the Dirac point.

Majorana zero modes in Dirac semimetal Josephson junctions

NASA Astrophysics Data System (ADS)

Li, Chuan; de Boer, Jorrit; de Ronde, Bob; Huang, Yingkai; Golden, Mark; Brinkman, Alexander

We have realized proximity-induced superconductivity in a Dirac semimetal and revealed the topological nature of the superconductivity by the observation of Majorana zero modes. As a Dirac semimetal, Bi0.97Sb0.03 is used, where a three-dimensional Dirac cone exists in the bulk due to an accidental touching between conduction and valence bands. Electronic transport measurements on Hall-bars fabricated out of Bi0.97Sb0.03 flakes consistently show negative magnetoresistance for magnetic fields parallel to the current, which is associated with the chiral anomaly. In perpendicular magnetic fields, we see Shubnikov-de Haas oscillations that indicate very low carrier densities. The low Fermi energy and protection against backscattering in our Dirac semimetal Josephson junctions provide favorable conditions for a large contribution of Majorana zero modes to the supercurrent. In radiofrequency irradiation experiments, we indeed observe these Majorana zero modes in Nb-Bi0.97Sb0.03-Nb Josephson junctions as a 4 π periodic contribution to the current-phase relation.

Merging of the Dirac points in electronic artificial graphene

NASA Astrophysics Data System (ADS)

Feilhauer, J.; Apel, W.; Schweitzer, L.

2015-12-01

Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically that such a merging of the Dirac points can be observed in electronic artificial graphene created from a two-dimensional electron gas by application of a triangular lattice of repulsive antidots. Here, the effect of strain is modeled by tuning the distance between the repulsive potentials along the armchair direction. Our results show that the merging of the Dirac points should be observable in a recent experiment with molecular graphene.

Hydrogenated arsenenes as planar magnet and Dirac material

NASA Astrophysics Data System (ADS)

Zhang, Shengli; Hu, Yonghong; Hu, Ziyu; Cai, Bo; Zeng, Haibo

2015-07-01

Arsenene and antimonene are predicted to have 2.49 and 2.28 eV band gaps, which have aroused intense interest in the two-dimensional (2D) semiconductors for nanoelectronic and optoelectronic devices. Here, the hydrogenated arsenenes are reported to be planar magnet and 2D Dirac materials based on comprehensive first-principles calculations. The semi-hydrogenated (SH) arsenene is found to be a quasi-planar magnet, while the fully hydrogenated (FH) arsenene is a planar Dirac material. The buckling height of pristine arsenene is greatly decreased by the hydrogenation, resulting in a planar and relatively low-mass-density sheet. The electronic structures of arsenene are also evidently altered after hydrogenating from wide-band-gap semiconductor to metallic material for SH arsenene, and then to Dirac material for FH arsenene. The SH arsenene has an obvious magnetism, mainly contributed by the p orbital of the unsaturated As atom. Such magnetic and Dirac materials modified by hydrogenation of arsenene may have potential applications in future optoelectronic and spintronic devices.

Symmetry-enforced stability of interacting Weyl and Dirac semimetals

NASA Astrophysics Data System (ADS)

Carlström, Johan; Bergholtz, Emil J.

2018-04-01

The nodal and effectively relativistic dispersion featuring in a range of novel materials including two-dimensional graphene and three-dimensional Dirac and Weyl semimetals has attracted enormous interest during the past decade. Here, by studying the structure and symmetry of the diagrammatic expansion, we show that these nodal touching points are in fact perturbatively stable to all orders with respect to generic two-body interactions. For effective low-energy theories relevant for single and multilayer graphene, type-I and type-II Weyl and Dirac semimetals, as well as Weyl points with higher topological charge, this stability is shown to be a direct consequence of a spatial symmetry that anticommutes with the effective Hamiltonian while leaving the interaction invariant. A more refined argument is applied to the honeycomb lattice model of graphene showing that its Dirac points are also perturbatively stable to all orders. We also give examples of nodal Hamiltonians that acquire a gap from interactions as a consequence of symmetries different from those of Weyl and Dirac materials.

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

NASA Astrophysics Data System (ADS)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

Analytical study of mode degeneracy in non-Hermitian photonic crystals with TM-like polarization

NASA Astrophysics Data System (ADS)

Yin, Xuefan; Liang, Yong; Ni, Liangfu; Wang, Zhixin; Peng, Chao; Li, Zhengbin

2017-08-01

We present a study of the mode degeneracy in non-Hermitian photonic crystals (PC) with TM-like polarization and C4 v symmetry from the perspective of the coupled-wave theory (CWT). The CWT framework is extended to include TE-TM coupling terms which are critical for modeling the accidental triple degeneracy within non-Hermitian PC systems. We derive the analytical form of the wave function and the condition of Dirac-like-cone dispersion when radiation loss is relatively small. We find that, similar to a real Dirac cone, the Dirac-like cone in non-Hermitian PCs possesses good linearity and isotropy, even with a ring of exceptional points (EPs) inevitably existing in the vicinity of the second-order Γ point. However, the Berry phase remains zero at the Γ point, indicating the cone does not obey the Dirac equation and is only a Dirac-like cone. The topological modal interchange phenomenon and nonzero Berry phase of the EPs are also discussed.

Engineering and Probing Topological Properties of Dirac Semimetal Films by Asymmetric Charge Transfer.

PubMed

Villanova, John W; Barnes, Edwin; Park, Kyungwha

2017-02-08

Dirac semimetals (DSMs) have topologically robust three-dimensional Dirac (doubled Weyl) nodes with Fermi-arc states. In heterostructures involving DSMs, charge transfer occurs at the interfaces, which can be used to probe and control their bulk and surface topological properties through surface-bulk connectivity. Here we demonstrate that despite a band gap in DSM films, asymmetric charge transfer at the surface enables one to accurately identify locations of the Dirac-node projections from gapless band crossings and to examine and engineer properties of the topological Fermi-arc surface states connecting the projections, by simulating adatom-adsorbed DSM films using a first-principles method with an effective model. The positions of the Dirac-node projections are insensitive to charge transfer amount or slab thickness except for extremely thin films. By varying the amount of charge transfer, unique spin textures near the projections and a separation between the Fermi-arc states change, which can be observed by gating without adatoms.

Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

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

Cari, C., E-mail: carinln@yahoo.com; Suparmi, A., E-mail: carinln@yahoo.com

2014-09-30

Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.

Pathways to naturally small Dirac neutrino masses

DOE PAGES

Ma, Ernest; Popov, Oleg

2016-11-18

If neutrinos are truly Dirac fermions, the smallness of their masses may still be natural if certain symmetries exist beyond those of the standard model of quarks and leptons. We perform a systematic study of how this may occur at tree level and in one loop. As a result, we also propose a scotogenic version of the left-right gauge model with naturally small Dirac neutrino masses in one loop.

Kondo Effect in Dirac Systems

NASA Astrophysics Data System (ADS)

Yanagisawa, Takashi

2015-07-01

We investigate the Kondo effect in Dirac systems, where Dirac electrons interact with the localized spin via the s-d exchange coupling. The Dirac electron in solid state has the linear dispersion and is described typically by the Hamiltonian such as Hk = vk · σ for the wave number k where σj are Pauli matrices. We derived the formula of the Kondo temperature TK by means of the Green's function theory for small J. The TK is determined from a singularity of Green's functions in the form TK ≃ bar{D}exp ( - const./ρ |J|) when the exchange coupling |J| is small where bar{D} = D/√{1 + D2/(2μ )2} for a cutoff D and ρ is the density of states at the Fermi surface. When |μ| ≪ D, TK is proportional to |μ|: TK ≃ |μ| exp(-const./ρ|J|). The Kondo screening will, however, disappear when the Fermi surface shrinks to a point called the Dirac point, that is, TK vanishes when the chemical potential μ is just at the Dirac point. The resistivity and the specific heat exhibit a log-T singularity in the range TK < T ≪ |μ|/kB. Instead, for T ˜ O(|μ|) or T > |μ|, they never show log-T.

Signatures of evanescent transport in ballistic suspended graphene-superconductor junctions

PubMed Central

Kumaravadivel, Piranavan; Du, Xu

2016-01-01

In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles with linear energy dispersion. A particularly intriguing phenomenon arises with the intrinsic charge transport behavior at the Dirac point where the charge density approaches zero. In graphene, a 2-D Dirac fermion gas system, it was predicted that charge transport near the Dirac point is carried by evanescent modes, resulting in unconventional “pseudo-diffusive” charge transport even in the absence of disorder. In the past decade, experimental observation of this phenomenon remained challenging due to the presence of strong disorder in graphene devices which limits the accessibility of the low carrier density regime close enough to the Dirac point. Here we report transport measurements on ballistic suspended graphene-Niobium Josephson weak links that demonstrate a transition from ballistic to pseudo-diffusive like evanescent transport below a carrier density of ~1010 cm−2. Approaching the Dirac point, the sub-harmonic gap structures due to multiple Andreev reflections display a strong Fermi energy-dependence and become increasingly pronounced, while the normalized excess current through the superconductor-graphene interface decreases sharply. Our observations are in qualitative agreement with the long standing theoretical prediction for the emergence of evanescent transport mediated pseudo-diffusive transport in graphene. PMID:27080733

Orbital selective spin-texture in a topological insulator

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

Singh, Bahadur, E-mail: bahadursingh24@gmail.com; Prasad, R.

Three-dimensional topological insulators support a metallic non-trivial surface state with unique spin texture, where spin and momentum are locked perpendicular to each other. In this work, we investigate the orbital selective spin-texture associated with the topological surface states in Sb2Te{sub 3}, using the first principles calculations. Sb2Te{sub 3} is a strong topological insulator with a p-p type bulk band inversion at the Γ-point and supports a single topological metallic surface state with upper (lower) Dirac-cone has left (right) handed spin-texture. Here, we show that the topological surface state has an additional locking between the spin and orbitals, leading to anmore » orbital selective spin-texture. The out-of-plane orbitals (p{sub z} orbitals) have an isotropic orbital texture for both the Dirac cones with an associated left and right handed spin-texture for the upper and lower Dirac cones, respectively. In contrast, the in-planar orbital texture (p{sub x} and p{sub y} projections) is tangential for the upper Dirac-cone and is radial for the lower Dirac-cone surface state. The dominant in-planar orbital texture in both the Dirac cones lead to a right handed orbital-selective spin-texture.« less

Magnetotransport study of Dirac fermions in YbMnBi2 and CaMnBi2

NASA Astrophysics Data System (ADS)

Wang, Aifeng; Zaliznyak, Igor; Graf, David; Ren, Weijun; Wang, Kefeng; Wu, Lijun; Garlea, Ovidiu; Warren, John; Bozin, Emil; Zhu, Yimei; Petrovic, Cedomir

It is well known that AMnBi2 (A = alkaline earth) with two dimensional (2D) bismuth layer host quasi-2D Dirac states similar to graphene and topological insulators. The Dirac state is significantly affected by the alkaline earth in the block layer. Angle-resolved photoemission spectroscopy (ARPES) indicates that YbMnBi2 could be the first Weyl semimetal with time-reversal symmetry breaking, whereas the anisotropic Dirac state in SrMnBi2 can host a valley-polarized interlayer current through magnetic valley control. Here, we study in-plane magnetotransport in YbMnBi2, and interlayer magnetotransport in CaMnBi2. The angular-dependent magnetoresistance, nonzero Berry phase, and small cyclotron mass confirm the presence of Dirac fermion and quasi-2D fermi surface in YbMnBi2. The interlayer electronic transport in CaMnBi2 suggest valley polarized conduction and a Dirac state on the side wall of the warped cylindrical Fermi surface of CaMnBi2. Work at BNL was supported by the U.S. Department of Energy-BES, Division of Materials Science and Engineering, under Contract No. DE-SC0012704. Work at the National High Magnetic Field Laboratory is supported by the NSF Cooperative Agreement No. DMR-06541.

Massless Dirac fermions trapping in a quasi-one-dimensional n p n junction of a continuous graphene monolayer

NASA Astrophysics Data System (ADS)

Bai, Ke-Ke; Qiao, Jia-Bin; Jiang, Hua; Liu, Haiwen; He, Lin

2017-05-01

Massless Dirac fermions in graphene provide unprecedented opportunities to realize the Klein paradox, which is one of the most exotic and striking properties of relativistic particles. In the seminal theoretical work [M. I. Katsnelson et al., Nat. Phys. 2, 620 (2006), 10.1038/nphys384], it was predicted that the massless Dirac fermions can pass through one-dimensional (1D) potential barriers unimpededly at normal incidence. Such a result seems to preclude confinement of the massless Dirac fermions in graphene by using 1D potential barriers. Here, we demonstrate both experimentally and theoretically that massless Dirac fermions can be trapped in a quasi-1D n p n junction of a continuous graphene monolayer. Because of highly anisotropic transmission of the massless Dirac fermions at n-p junction boundaries (the so-called Klein tunneling in graphene), charge carriers incident at large oblique angles will be reflected from one edge of the junction with high probability and continue to bounce from the opposite edge. Consequently, these electrons are trapped for a finite time to form quasibound states in the quasi-1D n p n junction. The quasibound states seen as pronounced resonances are probed and the quantum interference patterns arising from these states are directly visualized in our scanning tunneling microscope measurements.

Can chaos be observed in quantum gravity?

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Höhn, Philipp A.; Koslowski, Tim A.; Nelson, Mike I.

2017-06-01

Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.

Integration of Cloud resources in the LHCb Distributed Computing

NASA Astrophysics Data System (ADS)

Úbeda García, Mario; Méndez Muñoz, Víctor; Stagni, Federico; Cabarrou, Baptiste; Rauschmayr, Nathalie; Charpentier, Philippe; Closier, Joel

2014-06-01

This contribution describes how Cloud resources have been integrated in the LHCb Distributed Computing. LHCb is using its specific Dirac extension (LHCbDirac) as an interware for its Distributed Computing. So far, it was seamlessly integrating Grid resources and Computer clusters. The cloud extension of DIRAC (VMDIRAC) allows the integration of Cloud computing infrastructures. It is able to interact with multiple types of infrastructures in commercial and institutional clouds, supported by multiple interfaces (Amazon EC2, OpenNebula, OpenStack and CloudStack) - instantiates, monitors and manages Virtual Machines running on this aggregation of Cloud resources. Moreover, specifications for institutional Cloud resources proposed by Worldwide LHC Computing Grid (WLCG), mainly by the High Energy Physics Unix Information Exchange (HEPiX) group, have been taken into account. Several initiatives and computing resource providers in the eScience environment have already deployed IaaS in production during 2013. Keeping this on mind, pros and cons of a cloud based infrasctructure have been studied in contrast with the current setup. As a result, this work addresses four different use cases which represent a major improvement on several levels of our infrastructure. We describe the solution implemented by LHCb for the contextualisation of the VMs based on the idea of Cloud Site. We report on operational experience of using in production several institutional Cloud resources that are thus becoming integral part of the LHCb Distributed Computing resources. Furthermore, we describe as well the gradual migration of our Service Infrastructure towards a fully distributed architecture following the Service as a Service (SaaS) model.

Hall effect in the presence of rotation

NASA Astrophysics Data System (ADS)

Zubkov, M. A.

2018-02-01

A rotating relativistic fermion system is considered. The consideration is based on the Dirac equation written in the laboratory (non-rotating) reference frame. Rotation in this approach gives rise to the effective magnetic and electric fields that act in the same way both on positive and negative electric charges. In the presence of external electric field in the given system the electric current appears orthogonal to both the electric field and the axis of rotation. The possible applications to the physics of quark-gluon plasma are discussed.

Quantum electron levels in the field of a charged black hole

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

Dokuchaev, V. I.; Eroshenko, Yu. N., E-mail: eroshenko@ms2.inr.ac.ru

2015-12-15

Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically self-consistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.

Physics based calculation of the fine structure constant

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

Lestone, John Paul

2009-01-01

We assume that the coupling between particles and photons is defined by a surface area and a temperature, and that the square of the temperature is the inverse of the surface area ({Dirac_h}=c= 1). By making assumptions regarding stimulated emission and effects associated with the finite length of a string that forms the particle surface, the fine structure constant is calculated to be {approx}1/137.04. The corresponding calculated fundamental unit of charge is 1.6021 x 10{sup -19} C.

The generator coordinate Dirac-Fock method for open-shell atomic systems

NASA Astrophysics Data System (ADS)

Malli, Gulzari L.; Ishikawa, Yasuyuki

1998-11-01

Recently we developed generator coordinate Dirac-Fock and Dirac-Fock-Breit methods for closed-shell systems assuming finite nucleus and have reported Dirac-Fock and Dirac-Fock-Breit energies for the atoms He through Nobelium (Z=102) [see Refs. Reference 10Reference 11Reference 12Reference 13]. In this paper, we generalize our earlier work on closed-shell systems and develop a generator coordinate Dirac-Fock method for open-shell systems. We present results for a number of representative open-shell heavy atoms (with nuclear charge Z>80) including the actinide and superheavy transactinide (with Z>103) atomic systems: Fr (Z=87), Ac (Z=89), and Lr (Z=103) to E113 (eka-thallium, Z=113). The high accuracy obtained in our open-shell Dirac-Fock calculations is similar to that of our closed-shell calculations, and we attribute it to the fact that the representation of the relativistic dynamics of an electron in a spherical ball finite nucleus near the origin in terms of our universal Gaussian basis set is as accurate as that provided by the numerical finite difference method. The DF SCF energies calculated by Desclaux [At. Data. Nucl. Data Tables 12, 311 (1973)] (apart from a typographic error for Fr pointed out here) are higher than those reported here for atoms of some of the superheavy transactinide elements by as much as 5 hartrees (136 eV). We believe that this is due to the use by Desclaux of much larger atomic masses than the currently accepted values for these elements.

Quantum entanglement in inhomogeneous 1D systems

NASA Astrophysics Data System (ADS)

Ramírez, Giovanni

2018-04-01

The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our inhomogeneous system, the inhomogeneity parameter, h, allows us to tune different regimes where a volumetric violation of the area law appears. We apply the strong disorder renormalization group to describe the maximally entangled state of the system in a strong inhomogeneity regime. Moreover, in a weak inhomogeneity regime, we use a continuum approximation to describe the state as a thermo-field double in a conformal field theory with an effective temperature which is proportional to the inhomogeneity parameter of the system. The latter description also shows that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = h2, providing another example of the relation between quantum entanglement and space-time geometry. The results we discuss here were already published before, but here we present a more didactic exposure of basic concepts of the rainbow system for the students attending the Latin American School of Physics "Marcos Moshinsky" 2017.

Rare-Region-Induced Avoided Quantum Criticality in Disordered Three-Dimensional Dirac and Weyl Semimetals

NASA Astrophysics Data System (ADS)

Pixley, J. H.; Huse, David A.; Das Sarma, S.

2016-04-01

We numerically study the effect of short-ranged potential disorder on massless noninteracting three-dimensional Dirac and Weyl fermions, with a focus on the question of the proposed (and extensively theoretically studied) quantum critical point separating semimetal and diffusive-metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian (H ) and exactly calculate the density of states (DOS) near zero energy, using a combination of Lanczos on H2 and the kernel polynomial method on H . We establish the existence of two distinct types of low-energy eigenstates contributing to the disordered density of states in the weak-disorder semimetal regime. These are (i) typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states and (ii) nonperturbative rare eigenstates that are weakly dispersive and quasilocalized in the real-space regions with the largest (and rarest) local random potential. Using twisted boundary conditions, we are able to systematically find and study these two (essentially independent) types of eigenstates. We find that the Dirac states contribute low-energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasilocalized eigenstates contribute a nonzero background DOS which is only weakly energy dependent near zero energy and is exponentially small at weak disorder. We also find that the expected semimetal to diffusive-metal quantum critical point is converted to an avoided quantum criticality that is "rounded out" by nonperturbative effects, with no signs of any singular behavior in the DOS at the energy of the clean Dirac point. However, the crossover effects of the avoided (or hidden) criticality manifest themselves in a so-called quantum critical fan region away from the Dirac energy. We discuss the implications of our results for disordered Dirac and Weyl semimetals, and reconcile the large body of existing numerical work showing quantum criticality with the existence of these nonperturbative effects.

Multiscale solvers and systematic upscaling in computational physics

NASA Astrophysics Data System (ADS)

Brandt, A.

2005-07-01

Multiscale algorithms can overcome the scale-born bottlenecks that plague most computations in physics. These algorithms employ separate processing at each scale of the physical space, combined with interscale iterative interactions, in ways which use finer scales very sparingly. Having been developed first and well known as multigrid solvers for partial differential equations, highly efficient multiscale techniques have more recently been developed for many other types of computational tasks, including: inverse PDE problems; highly indefinite (e.g., standing wave) equations; Dirac equations in disordered gauge fields; fast computation and updating of large determinants (as needed in QCD); fast integral transforms; integral equations; astrophysics; molecular dynamics of macromolecules and fluids; many-atom electronic structures; global and discrete-state optimization; practical graph problems; image segmentation and recognition; tomography (medical imaging); fast Monte-Carlo sampling in statistical physics; and general, systematic methods of upscaling (accurate numerical derivation of large-scale equations from microscopic laws).

Angular and polarization trails from effective interactions of Majorana neutrinos at the LHeC

NASA Astrophysics Data System (ADS)

Duarte, Lucía; Zapata, Gabriel; Sampayo, Oscar A.

2018-05-01

We study the possibility of the LHeC facility to disentangle different new physics contributions to the production of heavy sterile Majorana neutrinos in the lepton number violating channel e-p→ lj+ + 3 jets (l_j≡e ,μ ). This is done investigating the angular and polarization trails of effective operators with distinct Dirac-Lorentz structure contributing to the Majorana neutrino production, which parameterize new physics from a higher energy scale. We study an asymmetry in the angular distribution of the final anti-lepton and the initial electron polarization effect on the number of signal events produced by the vectorial and scalar effective interactions, finding both analyses could well separate their contributions.

Canonical methods in classical and quantum gravity: An invitation to canonical LQG

NASA Astrophysics Data System (ADS)

Reyes, Juan D.

2018-04-01

Loop Quantum Gravity (LQG) is a candidate quantum theory of gravity still under construction. LQG was originally conceived as a background independent canonical quantization of Einstein’s general relativity theory. This contribution provides some physical motivations and an overview of some mathematical tools employed in canonical Loop Quantum Gravity. First, Hamiltonian classical methods are reviewed from a geometric perspective. Canonical Dirac quantization of general gauge systems is sketched next. The Hamiltonian formultation of gravity in geometric ADM and connection-triad variables is then presented to finally lay down the canonical loop quantization program. The presentation is geared toward advanced undergradute or graduate students in physics and/or non-specialists curious about LQG.

Search for Magnetic Monopoles with the MoEDAL Forward Trapping Detector in 13 TeV Proton-Proton Collisions at the LHC.

PubMed

Acharya, B; Alexandre, J; Baines, S; Benes, P; Bergmann, B; Bernabéu, J; Branzas, H; Campbell, M; Caramete, L; Cecchini, S; de Montigny, M; De Roeck, A; Ellis, J R; Fairbairn, M; Felea, D; Flores, J; Frank, M; Frekers, D; Garcia, C; Hirt, A M; Janecek, J; Kalliokoski, M; Katre, A; Kim, D-W; Kinoshita, K; Korzenev, A; Lacarrère, D H; Lee, S C; Leroy, C; Lionti, A; Mamuzic, J; Margiotta, A; Mauri, N; Mavromatos, N E; Mermod, P; Mitsou, V A; Orava, R; Parker, B; Pasqualini, L; Patrizii, L; Păvălaş, G E; Pinfold, J L; Popa, V; Pozzato, M; Pospisil, S; Rajantie, A; Ruiz de Austri, R; Sahnoun, Z; Sakellariadou, M; Sarkar, S; Semenoff, G; Shaa, A; Sirri, G; Sliwa, K; Soluk, R; Spurio, M; Srivastava, Y N; Suk, M; Swain, J; Tenti, M; Togo, V; Tuszyński, J A; Vento, V; Vives, O; Vykydal, Z; Whyntie, T; Widom, A; Willems, G; Yoon, J H; Zgura, I S

2017-02-10

MoEDAL is designed to identify new physics in the form of long-lived highly ionizing particles produced in high-energy LHC collisions. Its arrays of plastic nuclear-track detectors and aluminium trapping volumes provide two independent passive detection techniques. We present here the results of a first search for magnetic monopole production in 13 TeV proton-proton collisions using the trapping technique, extending a previous publication with 8 TeV data during LHC Run 1. A total of 222 kg of MoEDAL trapping detector samples was exposed in the forward region and analyzed by searching for induced persistent currents after passage through a superconducting magnetometer. Magnetic charges exceeding half the Dirac charge are excluded in all samples and limits are placed for the first time on the production of magnetic monopoles in 13 TeV pp collisions. The search probes mass ranges previously inaccessible to collider experiments for up to five times the Dirac charge.

STM Studies of Spin-­Orbit Coupled Phases in Real-­ and Momentum-­Space

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

Madhavan, Vidya

The recently discovered class of spin-orbit coupled materials with interesting topological character are fascinating both from fundamental as well as application point of view. Two striking examples are 3D topological insulators (TIs) and topological crystalline insulators (TCIs). These materials host linearly dispersing (Dirac like) surface states with an odd number of Dirac nodes and are predicted to carry a quantized half-integer value of the axion field. The non-trivial topological properties of TIs and TCIs arise from strong spin-orbit coupling leading to an inverted band structure; which also leads to the chiral spin texture in momentum space. In this project wemore » used low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) to study materials with topological phases in real- and momentum-space. We studied both single crystals and thin films of topological materials which are susceptible to being tuned by doping, strain or gating, allowing us to explore their physical properties in the most interesting regimes and set the stage for future technological applications. .« less

Signatures of in-plane and out-of-plane magnetization generated by synchrotron radiation in magnetically doped and pristine topological insulators

NASA Astrophysics Data System (ADS)

Shikin, A. M.; Rybkina, A. A.; Estyunin, D. A.; Sostina, D. M.; Voroshnin, V. Yu.; Klimovskikh, I. I.; Rybkin, A. G.; Surnin, Yu. A.; Kokh, K. A.; Tereshchenko, O. E.; Petaccia, L.; Di Santo, G.; Skirdkov, P. N.; Zvezdin, K. A.; Zvezdin, A. K.; Kimura, A.; Chulkov, E. V.; Krasovskii, E. E.

2018-06-01

Possibility of in-plane and out-of-plane magnetization generated by synchrotron radiation (SR) in magnetically doped and pristine topological insulators (TIs) is demonstrated and studied by angle-resolved photoemission spectroscopy. We show experimentally and by ab initio calculations how nonequal depopulation of the Dirac cone (DC) states with opposite momenta in V-doped and pristine TIs generated by linearly polarized SR leads to the hole-generated uncompensated spin accumulation followed by the SR-induced magnetization via spin-torque effect. Moreover, the photoexcitation of the DC is asymmetric, and it varies with the photon energy. We find a relation between the photoexcitation asymmetry, the generated spin accumulation, and the induced in-plane and out-of-plane magnetic field. Experimentally the SR-generated in-plane and out-of-plane magnetization is confirmed by the k∥ shift of the DC position and by the gap opening at the Dirac point even above the Curie temperature. Theoretical predictions and estimations of the measurable physical quantities substantiate the experimental results.

Interplay of relativistic and nonrelativistic transport in atomically precise segmented graphene nanoribbons

DOE PAGES

Yannouleas, Constantine; Romanovsky, Igor; Landman, Uzi

2015-01-20

Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NEGF) conductance calculations and a Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. The continuum model reproduces themore » NEGF results, including optical Dirac Fabry-Pérot (FP) equidistant oscillations for massless relativistic carriers in metallic armchair SGNRs, and an unequally-spaced FP pattern for mixed armchair-zigzag SGNRs where carriers transit from a relativistic (armchair) to a nonrelativistic (zigzag) regime. This provides a unifying framework for analysis of coherent transport phenomena and interpretation of forthcoming experiments in SGNRs.« less

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra

PubMed Central

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-01-01

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail. PMID:24225900

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra.

PubMed

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-11-14

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail.

Topological Insulators in Ternary Compounds with a Honeycomb Lattice

NASA Astrophysics Data System (ADS)

Zhang, Hai-Jun; Chadov, Stanislav; Muchler, Lukas; Yan, Binghai; Qi, Xiao-Liang; Kübler, Jürgen; Zhang, Shou-Cheng; Felser, Claudia

2011-03-01

One of the most exciting subjects in solid state physics is a single layer of graphite which exhibits a variety of unconventional novel properties. The key feature of its electronic structure are linear dispersive bands which cross in a single point at the Fermi energy. This is so-called Dirac cone. The ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topological surface states. These materials exhibit the surface states formed by only a single Dirac cone at the G point together with the small direct band gap opened by a strong spin-orbit coupling (SOC) in the bulk. These materials are centro-symmetric, therefore, it is possible to determine the parity of their wave functions, and hence, their topological character. The work was supported by the supercomputing center at Stanford Institute Materials and Energy Science. The financial support of the DFG/ASPIMATT project (unit 1.2-A) is gratefully acknowledged.

Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials

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

Schulze-Halberg, Axel, E-mail: xbataxel@gmail.com; Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, IN 46408; Roy, Barnana, E-mail: barnana@isical.ac.in

2014-10-15

We introduce a method for constructing Darboux (or supersymmetric) pairs of pseudoscalar and scalar Dirac potentials that are associated with exceptional orthogonal polynomials. Properties of the transformed potentials and regularity conditions are discussed. As an application, we consider a pseudoscalar Dirac potential related to the Schrödinger model for the rationally extended radial oscillator. The pseudoscalar partner potentials are constructed under the first- and second-order Darboux transformations.

Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements

NASA Astrophysics Data System (ADS)

Bendory, Tamir; Eldar, Yonina C.

2015-12-01

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

Addressing the Majorana vs. Dirac Question Using Neutrino Decays

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

Kayser, Boris

We explain why it is so hard to determine whether neutrinos are Majorana or Dirac particles as long as the only neutrinos we study are ultra-relativistic. We then show how non-relativistic neutrinos could help, and focus on the angular distributions in the decays of an as-yet-to-be-discovered heavy neutrino $N$. We find that these angular distributions could very well tell us whether neutrinos are Majorana or Dirac particles.

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry

NASA Astrophysics Data System (ADS)

Yan, Mu-Lin

2012-06-01

The de Sitter invariant Special Relativity (dS-SR) is SR with constant curvature, and a natural extension of usual Einstein SR (E-SR). In this paper, we solve the dS-SR Dirac equation of Hydrogen by means of the adiabatic approach and the quasi-stationary perturbation calculations of QM. Hydrogen atom is located in the light cone of the Universe. FRW metric and ΛCDM cosmological model are used to discuss this issue. To the atom, effects of de Sitter space-time geometry described by Beltrami metric are taken into account. The dS-SR Dirac equation turns out to be a time dependent quantum Hamiltonian system. We reveal that: (i) The fundamental physics constants me, ℏ, e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α ≡ e2/(ℏc) keeps to be invariant; (ii) (2s1/2-2p1/2)-splitting due to dS-SR QM effects: By means of perturbation theory, that splitting ΔE(z) are calculated analytically, which belongs to Script O(1/R2)-physics of dS-SR QM. Numerically, we find that when |R| ≃ {103 Gly, 104 Gly, 105 Gly}, and z ≃ {1, or 2}, the ΔE(z) ≫ 1 (Lamb shift). This indicates that for these cases the hyperfine structure effects due to QED could be ignored, and the dS-SR fine structure effects are dominant. This effect could be used to determine the universal constant R in dS-SR, and be thought as a new physics beyond E-SR.

Spontaneous PT symmetry breaking in Dirac-Kronig-Penney crystals

NASA Astrophysics Data System (ADS)

Longhi, Stefano; Cannata, Francesco; Ventura, Alberto

2011-12-01

We introduce a non-Hermitian PT invariant extension of the Dirac-Kronig-Penney model, describing the motion of a Dirac quasiparticle in a locally periodic sequence of imaginary δ-Dirac barriers and wells, and propose its optical realization using superstructure fiber Bragg gratings with alternating regions of optical gain and absorption. For the infinite crystal, we determine the band structure and show that the PT phase is always broken. For a finite crystal, we derive analytical expressions for reflection and transmission probabilities, and show that the PT phase is unbroken below a finite threshold of the δ-barrier area. In the proposed optical realization, the onset of PT symmetry breaking in the finite crystal corresponds to the lasing condition for the grating superstructures.

Spectral distances on the doubled Moyal plane using Dirac eigenspinors

NASA Astrophysics Data System (ADS)

Kumar, Kaushlendra; Chakraborty, Biswajit

2018-04-01

We present here a novel method for computing spectral distances in the doubled Moyal plane in a noncommutative geometrical framework using Dirac eigenspinors, while solving the Lipschitz ball condition explicitly through matrices. The standard results of longitudinal, transverse, and hypotenuse distances between different pairs of pure states have been computed and the Pythagorean equality between them has been reproduced. The issue of the nonunital nature of the Moyal plane algebra is taken care of through a sequence of projection operators constructed from Dirac eigenspinors, which plays a crucial role throughout this paper. At the end, a toy model for a "Higgs field" has been constructed by fluctuating the Dirac operator and the variation on the transverse distance has been demonstrated, through an explicit computation.

Energy splitting of excitons in gapped Dirac materials

NASA Astrophysics Data System (ADS)

Xiao, Di; Zhou, Jianhui; Shan, Wenyu; Yao, Wang; Okamoto, Satoshi

2015-03-01

We show that there is an energy splitting between excitons with opposite angular momentum in gapped Dirac materials, such as monolayers of transition metal dichalcogenides and gapped surface states of topological insulators. This splitting can be traced back to the chiral nature of Dirac electrons. We also discuss the optical selection rule of excitons in gap Dirac materials and clarify the relationship to its single-particle counterpart. A simple estimation of the splitting (~ 10 meV) in monolayer transition metal dichalcogenides is given . Our result reveals the limitation of the venerable hydrogenic model of excitons, and highlights the importance of the Berry phase in This work is supported by DOE (No. DE-SC0012509), and AFOSR (No. FA9550-14-1-0277).

Landau-level spectroscopy of massive Dirac fermions in single-crystalline ZrTe5 thin flakes

NASA Astrophysics Data System (ADS)

Jiang, Y.; Dun, Z. L.; Zhou, H. D.; Lu, Z.; Chen, K.-W.; Moon, S.; Besara, T.; Siegrist, T. M.; Baumbach, R. E.; Smirnov, D.; Jiang, Z.

2017-07-01

We report infrared magnetospectroscopy studies on thin crystals of an emerging Dirac material ZrTe5 near the intrinsic limit. The observed structure of the Landau-level transitions and zero-field infrared absorption indicate a two-dimensional Dirac-like electronic structure, similar to that in graphene but with a small relativistic mass corresponding to a 9.4-meV energy gap. Measurements with circularly polarized light reveal a significant electron-hole asymmetry, which leads to splitting of the Landau-level transitions at high magnetic fields. Our model, based on the Bernevig-Hughes-Zhang effective Hamiltonian, quantitatively explains all observed transitions, determining the values of the Fermi velocity, Dirac mass (or gap), electron-hole asymmetry, and electron and hole g factors.

Three-dimensional organic Dirac-line materials due to nonsymmorphic symmetry: A data mining approach

NASA Astrophysics Data System (ADS)

Geilhufe, R. Matthias; Bouhon, Adrien; Borysov, Stanislav S.; Balatsky, Alexander V.

2017-01-01

A data mining study of electronic Kohn-Sham band structures was performed to identify Dirac materials within the Organic Materials Database. Out of that, the three-dimensional organic crystal 5,6-bis(trifluoromethyl)-2-methoxy-1 H -1,3-diazepine was found to host different Dirac-line nodes within the band structure. From a group theoretical analysis, it is possible to distinguish between Dirac-line nodes occurring due to twofold degenerate energy levels protected by the monoclinic crystalline symmetry and twofold degenerate accidental crossings protected by the topology of the electronic band structure. The obtained results can be generalized to all materials having the space group P 21/c (No. 14, C2h 5) by introducing three distinct topological classes.

Selective Dirac voltage engineering of individual graphene field-effect transistors for digital inverter and frequency multiplier integrations

NASA Astrophysics Data System (ADS)

Sul, Onejae; Kim, Kyumin; Jung, Yungwoo; Choi, Eunsuk; Lee, Seung-Beck

2017-09-01

The ambipolar band structure of graphene presents unique opportunities for novel electronic device applications. A cycle of gate voltage sweep in a conventional graphene transistor produces a frequency-doubled output current. To increase the frequency further, we used various graphene doping control techniques to produce Dirac voltage engineered graphene channels. The various surface treatments and substrate conditions produced differently doped graphene channels that were integrated on a single substrate and multiple Dirac voltages were observed by applying a single gate voltage sweep. We applied the Dirac voltage engineering techniques to graphene field-effect transistors on a single chip for the fabrication of a frequency multiplier and a logic inverter demonstrating analog and digital circuit application possibilities.

Selective Dirac voltage engineering of individual graphene field-effect transistors for digital inverter and frequency multiplier integrations.

PubMed

Sul, Onejae; Kim, Kyumin; Jung, Yungwoo; Choi, Eunsuk; Lee, Seung-Beck

2017-09-15

The ambipolar band structure of graphene presents unique opportunities for novel electronic device applications. A cycle of gate voltage sweep in a conventional graphene transistor produces a frequency-doubled output current. To increase the frequency further, we used various graphene doping control techniques to produce Dirac voltage engineered graphene channels. The various surface treatments and substrate conditions produced differently doped graphene channels that were integrated on a single substrate and multiple Dirac voltages were observed by applying a single gate voltage sweep. We applied the Dirac voltage engineering techniques to graphene field-effect transistors on a single chip for the fabrication of a frequency multiplier and a logic inverter demonstrating analog and digital circuit application possibilities.

CALL FOR PAPERS: Special Issue on `Geometric Numerical Integration of Differential Equations'

NASA Astrophysics Data System (ADS)

Quispel, G. R. W.; McLachlan, R. I.

2005-02-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Geometric Numerical Integration of Differential Equations'. This issue should be a repository for high quality original work. We are interested in having the topic interpreted broadly, that is, to include contributions dealing with symplectic or multisymplectic integration; volume-preserving integration; symmetry-preserving integration; integrators that preserve first integrals, Lyapunov functions, or dissipation; exponential integrators; integrators for highly oscillatory systems; Lie-group integrators, etc. Papers on geometric integration of both ODEs and PDEs will be considered, as well as application to molecular-scale integration, celestial mechanics, particle accelerators, fluid flows, population models, epidemiological models and/or any other areas of science. We believe that this issue is timely, and hope that it will stimulate further development of this new and exciting field. The Editorial Board has invited G R W Quispel and R I McLachlan to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are the following: • The subject of the paper should relate to geometric numerical integration in the sense described above. • Contributions will be refereed and processed according to the usual procedure of the journal. • Papers should be original; reviews of a work published elsewhere will not be accepted. The guidelines for the preparation of contributions are as follows: • The DEADLINE for submission of contributions is 1 September 2005. This deadline will allow the special issue to appear in late 2005 or early 2006. • There is a strict page limit of 16 printed pages (approximately 9600 words) per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. • Contributions to the special issue should if possible be submitted electronically by web upload at {www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue—Geometric Integration'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the web site for further information on electronic submissions. • Authors unable to submit electronically may send hard copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing the electronic code on floppy disk if available and quoting `JPhysA Special Issue—Geometric Integration'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue. G R W Quispel and R I McLachlan Guest Editors

Magnetotransport in Dirac metals: Chiral magnetic effect and quantum oscillations

DOE PAGES

Monteiro, Gustavo M.; Abanov, Alexander G.; Kharzeev, Dmitri E.

2015-10-08

Dirac metals are characterized by the linear dispersion of fermionic quasiparticles, with the Dirac point hidden inside a Fermi surface. We study the magnetotransport in these materials using chiral kinetic theory to describe within the same framework both the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations in the magnetoresistance due to the existence of the Fermi surface. Lastly, we discuss the relevance of obtained results to recent measurements on Cd 3As 2.

Large-basis ab initio no-core shell model and its application to {sup 12}C

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

Navratil, P.; Vary, J. P.; Barrett, B. R.

2000-11-01

We present the framework for the ab initio no-core nuclear shell model and apply it to obtain properties of {sup 12}C. We derive two-body effective interactions microscopically for specific model spaces from the realistic CD-Bonn and the Argonne V8' nucleon-nucleon (NN) potentials. We then evaluate binding energies, excitation spectra, radii, and electromagnetic transitions in the 0{Dirac_h}{Omega}, 2{Dirac_h}{Omega}, and 4{Dirac_h}{Omega} model spaces for the positive-parity states and the 1{Dirac_h}{Omega}, 3{Dirac_h}{Omega}, and 5{Dirac_h}{Omega} model spaces for the negative-parity states. Dependence on the model-space size, on the harmonic-oscillator frequency, and on the type of the NN potential, used for the effective interaction derivation,more » are studied. In addition, electromagnetic and weak neutral elastic charge form factors are calculated in the impulse approximation. Sensitivity of the form-factor ratios to the strangeness one-body form-factor parameters and to the influence of isospin-symmetry violation is evaluated and discussed. Agreement between theory and experiment is favorable for many observables, while others require yet larger model spaces and/or three-body forces. The limitations of the present results are easily understood by virtue of the trends established and previous phenomenological results.« less

Large linear magnetoresistance in a new Dirac material BaMnBi2

NASA Astrophysics Data System (ADS)

Wang, Yi-Yan; Yu, Qiao-He; Xia, Tian-Long

2016-10-01

Dirac semimetal is a class of materials that host Dirac fermions as emergent quasi-particles. Dirac cone-type band structure can bring interesting properties such as quantum linear magnetoresistance and large mobility in the materials. In this paper, we report the synthesis of high quality single crystals of BaMnBi2 and investigate the transport properties of the samples. BaMnBi2 is a metal with an antiferromagnetic transition at T N = 288 K. The temperature dependence of magnetization displays different behavior from CaMnBi2 and SrMnBi2, which suggests the possible different magnetic structure of BaMnBi2. The Hall data reveals electron-type carriers and a mobility μ(5 K) = 1500 cm2/V·s. Angle-dependent magnetoresistance reveals the quasi-two-dimensional (2D) Fermi surface in BaMnBi2. A crossover from semiclassical MR ˜ H 2 dependence in low field to MR ˜ H dependence in high field, which is attributed to the quantum limit of Dirac fermions, has been observed in magnetoresistance. Our results indicate the existence of Dirac fermions in BaMnBi2. Project supported by the National Natural Science Foundation of China (Grant No. 11574391), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grant No. 14XNLQ07).

Relativistic space-charge-limited current for massive Dirac fermions

NASA Astrophysics Data System (ADS)

Ang, Y. S.; Zubair, M.; Ang, L. K.

2017-04-01

A theory of relativistic space-charge-limited current (SCLC) is formulated to determine the SCLC scaling, J ∝Vα/Lβ , for a finite band-gap Dirac material of length L biased under a voltage V . In one-dimensional (1D) bulk geometry, our model allows (α ,β ) to vary from (2,3) for the nonrelativistic model in traditional solids to (3/2,2) for the ultrarelativistic model of massless Dirac fermions. For 2D thin-film geometry we obtain α =β , which varies between 2 and 3/2, respectively, at the nonrelativistic and ultrarelativistic limits. We further provide rigorous proof based on a Green's-function approach that for a uniform SCLC model described by carrier-density-dependent mobility, the scaling relations of the 1D bulk model can be directly mapped into the case of 2D thin film for any contact geometries. Our simplified approach provides a convenient tool to obtain the 2D thin-film SCLC scaling relations without the need of explicitly solving the complicated 2D problems. Finally, this work clarifies the inconsistency in using the traditional SCLC models to explain the experimental measurement of a 2D Dirac semiconductor. We conclude that the voltage scaling 3 /2 <α <2 is a distinct signature of massive Dirac fermions in a Dirac semiconductor and is in agreement with experimental SCLC measurements in MoS2.

Spectroscopic imaging scanning tunneling microscopy of a Dirac line node material ZrSiS

NASA Astrophysics Data System (ADS)

Zhou, Lihui; He, Qingyu; Queiroz, Raquel; Grüneis, Andreas; Schnyder, Andreas; Ast, Christian; Schoop, Leslie; Takagi, Hide; Rost, Andreas

3D Dirac materials are an intensive area of current condensed matter research. The related Dirac line node materials have come into focus due to many shared properties such as unconventional magneto-transport and the potential to host topologically nontrivial phases. ZrSiS is one of the first discovered materials of this new family, hosting a nodal line and an unconventional surface state. Spectroscopic imaging scanning tunneling microscopy (SI-STM) detects quasiparticle interference and has been extensively used to study the scattering mechanism and the band structures of exotic materials with high energy resolution at the atomic scale. Here in this presentation, we report the investigation of ZrSiS by SI-STM at the atomic scale, in combination with DFT calculations. We succeeded in visualizing the Dirac nodal line both in real and momentum space, adding key pieces of evidences confirming the existence of a nodal line in this material and highlighting its exceptional properties. The breaking of a non-symmorphic symmetry at the surface induces an unusual surface state whose dispersion was mapped. In particular, we observed spectroscopic signatures of a type-II Dirac fermion hosted by the surface state. Our data as seen by SI-STM has impact beyond ZrSiS providing crucial insights into the properties of Dirac line node materials in particular and non-symmorphic crystals in general.

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd₃As₂.

PubMed

Jeon, Sangjun; Zhou, Brian B; Gyenis, Andras; Feldman, Benjamin E; Kimchi, Itamar; Potter, Andrew C; Gibson, Quinn D; Cava, Robert J; Vishwanath, Ashvin; Yazdani, Ali

2014-09-01

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

Dynamical Localization for Discrete Anderson Dirac Operators

NASA Astrophysics Data System (ADS)

Prado, Roberto A.; de Oliveira, César R.; Carvalho, Silas L.

2017-04-01

We establish dynamical localization for random Dirac operators on the d-dimensional lattice, with d\\in { 1, 2, 3} , in the three usual regimes: large disorder, band edge and 1D. These operators are discrete versions of the continuous Dirac operators and consist in the sum of a discrete free Dirac operator with a random potential. The potential is a diagonal matrix formed by different scalar potentials, which are sequences of independent and identically distributed random variables according to an absolutely continuous probability measure with bounded density and of compact support. We prove the exponential decay of fractional moments of the Green function for such models in each of the above regimes, i.e., (j) throughout the spectrum at larger disorder, (jj) for energies near the band edges at arbitrary disorder and (jjj) in dimension one, for all energies in the spectrum and arbitrary disorder. Dynamical localization in theses regimes follows from the fractional moments method. The result in the one-dimensional regime contrast with one that was previously obtained for 1D Dirac model with Bernoulli potential.

DBI potential, DBI inflation action and general Lagrangian relative to phantom, K-essence and quintessence

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

Zhang, Qing; Huang, Yong-Chang, E-mail: ychuang@bjut.edu.cn

We derive a Dirac-Born-Infeld (DBI) potential and DBI inflation action by rescaling the metric. The determinant of the induced metric naturally includes the kinetic energy and the potential energy. In particular, the potential energy and kinetic energy can convert into each other in any order, which is in agreement with the limit of classical physics. This is quite different from the usual DBI action. We show that the Taylor expansion of the DBI action can be reduced into the form in the non-linear classical physics. These investigations are the support for the statement that the results of string theory aremore » consistent with quantum mechanics and classical physics. We deduce the Phantom, K-essence, Quintessence and Generalized Klein-Gordon Equation from the DBI model.« less

``Models'' CAVEAT EMPTOR!!!: ``Toy Models Too-Often Yield Toy-Results''!!!: Statistics, Polls, Politics, Economics, Elections!!!: GRAPH/Network-Physics: ``Equal-Distribution for All'' TRUMP-ED BEC ``Winner-Take-All'' ``Doctor Livingston I Presume?''

NASA Astrophysics Data System (ADS)

Preibus-Norquist, R. N. C.-Grover; Bush-Romney, G. W.-Willard-Mitt; Dimon, J. P.; Adelson-Koch, Sheldon-Charles-David-Sheldon; Krugman-Axelrod, Paul-David; Siegel, Edward Carl-Ludwig; D. N. C./O. F. P./''47''%/50% Collaboration; R. N. C./G. O. P./''53''%/49% Collaboration; Nyt/Wp/Cnn/Msnbc/Pbs/Npr/Ft Collaboration; Ftn/Fnc/Fox/Wsj/Fbn Collaboration; Lb/Jpmc/Bs/Boa/Ml/Wamu/S&P/Fitch/Moodys/Nmis Collaboration

2013-03-01

``Models''? CAVEAT EMPTOR!!!: ``Toy Models Too-Often Yield Toy-Results''!!!: Goldenfeld[``The Role of Models in Physics'', in Lects.on Phase-Transitions & R.-G.(92)-p.32-33!!!]: statistics(Silver{[NYTimes; Bensinger, ``Math-Geerks Clearly-Defeated Pundits'', LATimes, (11/9/12)])}, polls, politics, economics, elections!!!: GRAPH/network/net/...-PHYSICS Barabasi-Albert[RMP (02)] (r,t)-space VERSUS(???) [Where's the Inverse/ Dual/Integral-Transform???] (Benjamin)Franklin(1795)-Fourier(1795; 1897;1822)-Laplace(1850)-Mellin (1902) Brillouin(1922)-...(k,)-space, {Hubbard [The World According to Wavelets,Peters (96)-p.14!!!/p.246: refs.-F2!!!]},and then (2) Albert-Barabasi[]Bose-Einstein quantum-statistics(BEQS) Bose-Einstein CONDENSATION (BEC) versus Bianconi[pvt.-comm.; arXiv:cond-mat/0204506; ...] -Barabasi [???] Fermi-Dirac

Neutrino experiments

DOE PAGES

Lesko, K. T.

2004-02-24

This review examines a wide variety of experiments investigating neutrino interactions and neutrino properties from a variety of neutrino sources. We have witnessed remarkable progress in the past two years in settling long standing problems in neutrino physics and uncovering the first evidence for physics beyond the Standard Model in nearly 30 years. Here this paper briefly reviews this recent progress in the field of neutrino physics and highlights several significant experimental arenas and topics for the coming decade of particular interest. These highlighted experiments include the precision determination of oscillation parameters including θ 13, θ 12, Δm 12 2more » and Δm 23 2 as well as a number of fundamental properties are likely to be probed included nature of the neutrino (Majorana versus Dirac), the number of neutrino families and the neutrino’s absolute mass.« less

Characterization of the 1S-2S transition in antihydrogen.

PubMed

Ahmadi, M; Alves, B X R; Baker, C J; Bertsche, W; Capra, A; Carruth, C; Cesar, C L; Charlton, M; Cohen, S; Collister, R; Eriksson, S; Evans, A; Evetts, N; Fajans, J; Friesen, T; Fujiwara, M C; Gill, D R; Hangst, J S; Hardy, W N; Hayden, M E; Isaac, C A; Johnson, M A; Jones, J M; Jones, S A; Jonsell, S; Khramov, A; Knapp, P; Kurchaninov, L; Madsen, N; Maxwell, D; McKenna, J T K; Menary, S; Momose, T; Munich, J J; Olchanski, K; Olin, A; Pusa, P; Rasmussen, C Ø; Robicheaux, F; Sacramento, R L; Sameed, M; Sarid, E; Silveira, D M; Stutter, G; So, C; Tharp, T D; Thompson, R I; van der Werf, D P; Wurtele, J S

2018-05-01

In 1928, Dirac published an equation 1 that combined quantum mechanics and special relativity. Negative-energy solutions to this equation, rather than being unphysical as initially thought, represented a class of hitherto unobserved and unimagined particles-antimatter. The existence of particles of antimatter was confirmed with the discovery of the positron 2 (or anti-electron) by Anderson in 1932, but it is still unknown why matter, rather than antimatter, survived after the Big Bang. As a result, experimental studies of antimatter 3-7 , including tests of fundamental symmetries such as charge-parity and charge-parity-time, and searches for evidence of primordial antimatter, such as antihelium nuclei, have high priority in contemporary physics research. The fundamental role of the hydrogen atom in the evolution of the Universe and in the historical development of our understanding of quantum physics makes its antimatter counterpart-the antihydrogen atom-of particular interest. Current standard-model physics requires that hydrogen and antihydrogen have the same energy levels and spectral lines. The laser-driven 1S-2S transition was recently observed 8 in antihydrogen. Here we characterize one of the hyperfine components of this transition using magnetically trapped atoms of antihydrogen and compare it to model calculations for hydrogen in our apparatus. We find that the shape of the spectral line agrees very well with that expected for hydrogen and that the resonance frequency agrees with that in hydrogen to about 5 kilohertz out of 2.5 × 10 15 hertz. This is consistent with charge-parity-time invariance at a relative precision of 2 × 10 -12 -two orders of magnitude more precise than the previous determination 8 -corresponding to an absolute energy sensitivity of 2 × 10 -20 GeV.

Coherent Dirac plasmons in topological insulators

NASA Astrophysics Data System (ADS)

Mondal, Richarj; Arai, Akira; Saito, Yuta; Fons, Paul; Kolobov, Alexander V.; Tominaga, Junji; Hase, Muneaki

2018-04-01

We explore the ultrafast reflectivity response from photo-generated coupled phonon-surface Dirac plasmons in Sb2Te3 topological insulators several quintuple layers thick. The transient coherent phonon spectra obtained at different time frames exhibit a Fano-like asymmetric line shape of the A1g 2 mode, which is attributed to quantum interference between continuumlike coherent Dirac plasmons and phonons. By analyzing the time-dependent asymmetric line shape using the two-temperature model (TTM), it was determined that a Fano-like resonance persisted up to ≈1 ps after photo excitation with a relaxation profile dominated by Gaussian decay at ≤200 fs. The asymmetry parameter could be well described by the TTM for ≥200 fs, therefore suggesting the coherence time of the Dirac plasmon is ≈200 fs.

Electrostatic modulation of the electronic properties of Dirac semimetal Na3Bi thin films

NASA Astrophysics Data System (ADS)

Hellerstedt, Jack; Yudhistira, Indra; Edmonds, Mark T.; Liu, Chang; Collins, James; Adam, Shaffique; Fuhrer, Michael S.

2017-10-01

Large-area thin films of topological Dirac semimetal Na3Bi are grown on amorphous SiO2:Si substrates to realize a field-effect transistor with the doped Si acting as a back gate. As-grown films show charge carrier mobilities exceeding 7 000 cm2/V s and carrier densities below 3 ×1018cm-3 , comparable to the best thin-film Na3Bi . An ambipolar field effect and minimum conductivity are observed, characteristic of Dirac electronic systems. The results are quantitatively understood within a model of disorder-induced charge inhomogeneity in topological Dirac semimetals. The hole mobility is significantly larger than the electron mobility in Na3Bi which we ascribe to the inverted band structure. When present, these holes dominate the transport properties.

Birefringent breakup of Dirac fermions on a square optical lattice

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

Kennett, Malcolm P.; Komeilizadeh, Nazanin; Kaveh, Kamran

2011-05-15

We introduce a lattice model for fermions in a spatially periodic magnetic field that also has spatially periodic hopping amplitudes. We discuss how this model might be realized with cold atoms in an artificial magnetic field on a square optical lattice. When there is an average flux of half a flux quantum per plaquette, the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different ''speeds of light.'' These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of themore » effective low-energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain-wall topological defects.« less

The half-filled Landau level: The case for Dirac composite fermions

NASA Astrophysics Data System (ADS)

Geraedts, Scott D.; Zaletel, Michael P.; Mong, Roger S. K.; Metlitski, Max A.; Vishwanath, Ashvin; Motrunich, Olexei I.

2016-04-01

In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that “composite fermions”—bound states of an electron with two magnetic flux quanta—can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2kF backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.

Atomic structure calculations and identification of EUV and SXR spectral lines in Sr XXX

NASA Astrophysics Data System (ADS)

Goyal, Arun; Khatri, Indu; Aggarwal, Sunny; Singh, A. K.; Mohan, Man

2015-08-01

We report an extensive theoretical study of atomic data for Sr XXX in a wide range with L-shell electron excitations to the M-shell. We have calculated energy levels, wave-function compositions and lifetimes for lowest 113 fine structure levels and wavelengths of an extreme Ultraviolet (EUV) and soft X-ray (SXR) transitions. We have employed multi-configuration Dirac Fock method (MCDF) approach within the framework of Dirac-Coulomb Hamiltonian including quantum electrodynamics (QED) and Breit corrections. We have also presented the radiative data for electric and magnetic dipole (E1, M1) and quadrupole (E2, M2) transitions from the ground state. We have made comparisons with available energy levels compiled by NIST and achieve good agreement. But due to inadequate data in the literature, analogous relativistic distorted wave calculations have also been performed using flexible atomic code (FAC) to assess the reliability and accuracy of our results. Additionally, we have provided new atomic data for Sr XXX which is not published elsewhere in the literature and we believe that our results may be beneficial in fusion plasma research and astrophysical investigations and applications.

Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

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

Eelbode, D., E-mail: David.Eelbode@ua.ac.be; Raeymaekers, T., E-mail: Tim.Raeymaekers@UGent.be; Van der Jeugt, J., E-mail: Joris.VanderJeugt@UGent.be

2015-10-15

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.

Solar test of Dirac's large number hypothesis. [multiplicative creation model for solar evolution

NASA Technical Reports Server (NTRS)

Chin, C.-W.; Stothers, R.

1975-01-01

An investigation is conducted regarding the implications of Dirac's theories (1973, 1974) concerning the creation of new matter. It is found that Dirac's theory of multiplicative creation, but not his theory of additive creation, is not in contradiction with known facts about the sun. According to the theory of additive creation, matter is formed uniformly throughout space. The concept of multiplicative creation implies that existing matter multiplies itself in proportion to the amount of matter already present.

Topological Thouless pumping in graphene and 2D Dirac materials

NASA Astrophysics Data System (ADS)

Abergel, David; Pertsova, Anna

We present a comprehensive analysis of strain-induced topological Thouless pumping of charge and valley currents in graphene and 2D Dirac materials. We analyze the role of strain deformations with all possible symmetries and classify the charge and valley currents that are adiabatically pumped in response. These manifest as transport without an applied bias. The production of valley currents implies that strained Dirac materials are a candidate platform for valleytronic applications. Supported by ERC project DM-321031.

Tuning a Schottky Barrier in a Photoexcited Topological Insulator with Transient Dirac Cone Electron-Hole Asymmetry

DTIC Science & Technology

2014-01-06

S. Jia9, H.W. Ji9, R.J. Cava9 & M. Marsi1 The advent of Dirac materials has made it possible to realize two-dimensional gases of relativistic...ultrafast light pulses a relativistic nanoscale Schottky barrier, in a way that is impossible with conventional optoelectronic materials . DOI : 10.1038...topological insulator with transient Dirac cone electron-hole asymmetry. Nat. Commun. 5:3003 doi : 10.1038/ncomms4003 (2014). ARTICLE NATURE

Tunable superlattice in graphene to control the number of Dirac points.

PubMed

Dubey, Sudipta; Singh, Vibhor; Bhat, Ajay K; Parikh, Pritesh; Grover, Sameer; Sensarma, Rajdeep; Tripathi, Vikram; Sengupta, K; Deshmukh, Mandar M

2013-09-11

Superlattice in graphene generates extra Dirac points in the band structure and their number depends on the superlattice potential strength. Here, we have created a lateral superlattice in a graphene device with a tunable barrier height using a combination of two gates. In this Letter, we demonstrate the use of lateral superlattice to modify the band structure of graphene leading to the emergence of new Dirac cones. This controlled modification of the band structure persists up to 100 K.

Group-theoretical analysis of two-dimensional hexagonal materials

NASA Astrophysics Data System (ADS)

Minami, Susumu; Sugita, Itaru; Tomita, Ryosuke; Oshima, Hiroyuki; Saito, Mineo

2017-10-01

Two-dimensional hexagonal materials such as graphene and silicene have highly symmetric crystal structures and Dirac cones at the K point, which induce novel electronic properties. In this report, we calculate their electronic structures by using density functional theory and analyze their band structures on the basis of the group theory. Dirac cones frequently appear when the symmetry at the K point is high; thus, two-dimensional irreducible representations are included. We discuss the relationship between symmetry and the appearance of the Dirac cone.

Domain wall fermion QCD with the exact one flavor algorithm

DOE PAGES

Jung, C.; Kelly, C.; Mawhinney, R. D.; ...

2018-03-13

Lattice QCD calculations including the effects of one or more nondegenerate sea quark flavors are conventionally performed using the rational hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant ofmore » $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$, where $$\\mathcal{D}$$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$—in particular, no square root is necessary—enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors—such as the strange or charm—computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $$\\mathrm{{\\Delta}}I=1/2$$ $$K{\\rightarrow}{\\pi}{\\pi}$$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $$\\mathcal{D}$$ , and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD Collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to reuse the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our $2+1$ flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.« less

Domain wall fermion QCD with the exact one flavor algorithm

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

Jung, C.; Kelly, C.; Mawhinney, R. D.

Lattice QCD calculations including the effects of one or more nondegenerate sea quark flavors are conventionally performed using the rational hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant ofmore » $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$, where $$\\mathcal{D}$$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$—in particular, no square root is necessary—enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors—such as the strange or charm—computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $$\\mathrm{{\\Delta}}I=1/2$$ $$K{\\rightarrow}{\\pi}{\\pi}$$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $$\\mathcal{D}$$ , and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD Collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to reuse the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our $2+1$ flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.« less

Band warping, band non-parabolicity, and Dirac points in electronic and lattice structures

NASA Astrophysics Data System (ADS)

Resca, Lorenzo; Mecholsky, Nicholas A.; Pegg, Ian L.

2017-10-01

We illustrate at a fundamental level the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. We point out a robust presence of pairs of topologically induced Dirac points in a primitive-rectangular lattice using a p-type tight-binding approximation. We analyze two-dimensional primitive-rectangular and square Bravais lattices with implications that are expected to generalize to more complex structures. Band warping is shown to arise at the onset of a singular transition to a crystal lattice with a larger symmetry group, which allows the possibility of irreducible representations of higher dimensions, hence band degeneracy, at special symmetry points in reciprocal space. Band warping is incompatible with a multi-dimensional Taylor series expansion, whereas band non-parabolicities are associated with multi-dimensional Taylor series expansions to all orders. Still band non-parabolicities may merge into band warping at the onset of a larger symmetry group. Remarkably, while still maintaining a clear connection with that merging, band non-parabolicities may produce pairs of conical intersections at relatively low-symmetry points. Apparently, such conical intersections are robustly maintained by global topology requirements, rather than any local symmetry protection. For two p-type tight-binding bands, we find such pairs of conical intersections drifting along the edges of restricted Brillouin zones of primitive-rectangular Bravais lattices as lattice constants vary relatively to each other, until these conical intersections merge into degenerate warped bands at high-symmetry points at the onset of a square lattice. The conical intersections that we found appear to have similar topological characteristics as Dirac points extensively studied in graphene and other topological insulators, even though our conical intersections have none of the symmetry complexity and protection afforded by the latter more complex structures.

Domain wall fermion QCD with the exact one flavor algorithm

NASA Astrophysics Data System (ADS)

Jung, C.; Kelly, C.; Mawhinney, R. D.; Murphy, D. J.

2018-03-01

Lattice QCD calculations including the effects of one or more nondegenerate sea quark flavors are conventionally performed using the rational hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of D†D , where D is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of D†D —in particular, no square root is necessary—enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors—such as the strange or charm—computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the Δ I =1 /2 K →π π matrix elements on lattice ensembles with G -parity boundary conditions, since G -parity is associated with a doubling of the number of quark flavors described by D , and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD Collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to reuse the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2 +1 flavor G -parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.

Spin-1 Dirac-Weyl fermions protected by bipartite symmetry

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

Lin, Zeren; School of Physics, Peking University, Beijing 100871; Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn

2015-12-07

We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K′ in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T{sub 3}, an extensivelymore » studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K′.« less

Absence of Dirac states in BaZnBi 2 induced by spin-orbit coupling

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

Ren, Weijun; Wang, Aifeng; Graf, D.

We report magnetotransport properties of BaZnBi 2 single crystals. Whereas electronic structure features Dirac states, such states are removed from the Fermi level by spin-orbit coupling (SOC) and consequently electronic transport is dominated by the small hole and electron pockets. Our results are consistent with not only three-dimensional, but also with quasi-two-dimensional portions of the Fermi surface. The SOC-induced gap in Dirac states is much larger when compared to isostructural SrMnBi 2. This suggests that not only long-range magnetic order, but also mass of the alkaline-earth atoms A in ABX 2 ( A = alkaline-earth, B = transition-metal, and Xmore » = Bi/Sb) are important for the presence of low-energy states obeying the relativistic Dirac equation at the Fermi surface.« less

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Shot noise in systems with semi-Dirac points

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

Zhai, Feng; Wang, Juan

2014-08-14

We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L{sup 1∕2}. Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly withmore » L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points.« less

A Case Study Of Organic Dirac Materials -

NASA Astrophysics Data System (ADS)

Commeau, Benjamin; Geilhufe, Matthias; Fernando, Gayanath; Balatsky, Alexander

Dirac Materials are characterized by linear band crossings within the electronic band structure. Most research of Dirac materials has been dedicated towards inorganic materials, e.g., binary chalcogenides as toplogical insulators, the Weyl semimetal TaAs or graphene. The purpose of this study is to investigate the formation of Dirac points in organic materials under pressure and mechanical strain. We study multiple structural phases of the organic charge-transfer salt (BEDT-TTF)2I3. We numerically calculate the relaxed band structure near the Fermi level along different k-space directions. Once the relaxed ion structure is obtained, we pick different cell parameters to shrink and investigate the changes in the band structure. We discuss band structure degeneracies protected by crystalline and other symmetries, if any. Quantum Espresso and VASP codes were used to calculate and validate our results.

Small Fermi surfaces and strong correlation effects in Dirac materials with holography

NASA Astrophysics Data System (ADS)

Seo, Yunseok; Song, Geunho; Park, Chanyong; Sin, Sang-Jin

2017-10-01

Recent discovery of transport anomaly in graphene demonstrated that a system known to be weakly interacting may become strongly correlated if system parameter (s) can be tuned such that fermi surface is sufficiently small. We study the strong correlation effects in the transport coefficients of Dirac materials doped with magnetic impurity under the magnetic field using holographic method. The experimental data of magneto-conductivity are well fit by our theory, however, not much data are available for other transports of Dirac material in such regime. Therefore, our results on heat transport, thermo-electric power and Nernst coefficients are left as predictions of holographic theory for generic Dirac materials in the vicinity of charge neutral point with possible surface gap. We give detailed look over each magneto-transport observable and 3Dplots to guide future experiments.

Absence of Dirac states in BaZnBi 2 induced by spin-orbit coupling

DOE PAGES

Ren, Weijun; Wang, Aifeng; Graf, D.; ...

2018-01-22

We report magnetotransport properties of BaZnBi 2 single crystals. Whereas electronic structure features Dirac states, such states are removed from the Fermi level by spin-orbit coupling (SOC) and consequently electronic transport is dominated by the small hole and electron pockets. Our results are consistent with not only three-dimensional, but also with quasi-two-dimensional portions of the Fermi surface. The SOC-induced gap in Dirac states is much larger when compared to isostructural SrMnBi 2. This suggests that not only long-range magnetic order, but also mass of the alkaline-earth atoms A in ABX 2 ( A = alkaline-earth, B = transition-metal, and Xmore » = Bi/Sb) are important for the presence of low-energy states obeying the relativistic Dirac equation at the Fermi surface.« less

FFT-split-operator code for solving the Dirac equation in 2+1 dimensions

NASA Astrophysics Data System (ADS)

Mocken, Guido R.; Keitel, Christoph H.

2008-06-01

The main part of the code presented in this work represents an implementation of the split-operator method [J.A. Fleck, J.R. Morris, M.D. Feit, Appl. Phys. 10 (1976) 129-160; R. Heather, Comput. Phys. Comm. 63 (1991) 446] for calculating the time-evolution of Dirac wave functions. It allows to study the dynamics of electronic Dirac wave packets under the influence of any number of laser pulses and its interaction with any number of charged ion potentials. The initial wave function can be either a free Gaussian wave packet or an arbitrary discretized spinor function that is loaded from a file provided by the user. The latter option includes Dirac bound state wave functions. The code itself contains the necessary tools for constructing such wave functions for a single-electron ion. With the help of self-adaptive numerical grids, we are able to study the electron dynamics for various problems in 2+1 dimensions at high spatial and temporal resolutions that are otherwise unachievable. Along with the position and momentum space probability density distributions, various physical observables, such as the expectation values of position and momentum, can be recorded in a time-dependent way. The electromagnetic spectrum that is emitted by the evolving particle can also be calculated with this code. Finally, for planning and comparison purposes, both the time-evolution and the emission spectrum can also be treated in an entirely classical relativistic way. Besides the implementation of the above-mentioned algorithms, the program also contains a large C++ class library to model the geometric algebra representation of spinors that we use for representing the Dirac wave function. This is why the code is called "Dirac++". Program summaryProgram title: Dirac++ or (abbreviated) d++ Catalogue identifier: AEAS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 474 937 No. of bytes in distributed program, including test data, etc.: 4 128 347 Distribution format: tar.gz Programming language: C++ Computer: Any, but SMP systems are preferred Operating system: Linux and MacOS X are actively supported by the current version. Earlier versions were also tested successfully on IRIX and AIX Number of processors used: Generally unlimited, but best scaling with 2-4 processors for typical problems RAM: 160 Megabytes minimum for the examples given here Classification: 2.7 External routines: FFTW Library [3,4], Gnu Scientific Library [5], bzip2, bunzip2 Nature of problem: The relativistic time evolution of wave functions according to the Dirac equation is a challenging numerical task. Especially for an electron in the presence of high intensity laser beams and/or highly charged ions, this type of problem is of considerable interest to atomic physicists. Solution method: The code employs the split-operator method [1,2], combined with fast Fourier transforms (FFT) for calculating any occurring spatial derivatives, to solve the given problem. An autocorrelation spectral method [6] is provided to generate a bound state for use as the initial wave function of further dynamical studies. Restrictions: The code in its current form is restricted to problems in two spatial dimensions. Otherwise it is only limited by CPU time and memory that one can afford to spend on a particular problem. Unusual features: The code features dynamically adapting position and momentum space grids to keep execution time and memory requirements as small as possible. It employs an object-oriented approach, and it relies on a Clifford algebra class library to represent the mathematical objects of the Dirac formalism which we employ. Besides that it includes a feature (typically called "checkpointing") which allows the resumption of an interrupted calculation. Additional comments: Along with the program's source code, we provide several sample configuration files, a pre-calculated bound state wave function, and template files for the analysis of the results with both MatLab and Igor Pro. Running time: Running time ranges from a few minutes for simple tests up to several days, even weeks for real-world physical problems that require very large grids or very small time steps. References:J.A. Fleck, J.R. Morris, M.D. Feit, Time-dependent propagation of high energy laser beams through the atmosphere, Appl. Phys. 10 (1976) 129-160. R. Heather, An asymptotic wavefunction splitting procedure for propagating spatially extended wavefunctions: Application to intense field photodissociation of H +2, Comput. Phys. Comm. 63 (1991) 446. M. Frigo, S.G. Johnson, FFTW: An adaptive software architecture for the FFT, in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3, IEEE, 1998, pp. 1381-1384. M. Frigo, S.G. Johnson, The design and implementation of FFTW3, in: Proceedings of the IEEE, vol. 93, IEEE, 2005, pp. 216-231. URL: http://www.fftw.org/. M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, GNU Scientific Library Reference Manual, second ed., Network Theory Limited, 2006. URL: http://www.gnu.org/software/gsl/. M.D. Feit, J.A. Fleck, A. Steiger, Solution of the Schrödinger equation by a spectral method, J. Comput. Phys. 47 (1982) 412-433.

Examples of the Zeroth Theorem of the History of Science

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

Jackson, J.D.

2007-08-24

The zeroth theorem of the history of science, enunciated byE. P. Fischer, states that a discovery (rule,regularity, insight) namedafter someone (often) did not originate with that person. I present fiveexamples from physics: the Lorentz condition partial muAmu = 0 definingthe Lorentz gauge of the electromagnetic potentials; the Dirac deltafunction, delta(x); the Schumann resonances of the earth-ionospherecavity; the Weizsacker-Williams method of virtual quanta; the BMTequation of spin dynamics. I give illustrated thumbnail sketches of boththe true and reputed discoverers and quote from their "discovery"publications.

'Quantum interference with slits' revisited

NASA Astrophysics Data System (ADS)

Rothman, Tony; Boughn, Stephen

2011-01-01

Marcella has presented a straightforward technique employing the Dirac formalism to calculate single- and double-slit interference patterns. He claims that no reference is made to classical optics or scattering theory and that his method therefore provides a purely quantum mechanical description of these experiments. He also presents his calculation as if no approximations are employed. We show that he implicitly makes the same approximations found in classical treatments of interference and that no new physics has been introduced. At the same time, some of the quantum mechanical arguments Marcella gives are, at best, misleading.

Data-driven discovery of new Dirac semimetal materials

NASA Astrophysics Data System (ADS)

Yan, Qimin; Chen, Ru; Neaton, Jeffrey

In recent years, a significant amount of materials property data from high-throughput computations based on density functional theory (DFT) and the application of database technologies have enabled the rise of data-driven materials discovery. In this work, we initiate the extension of the data-driven materials discovery framework to the realm of topological semimetal materials and to accelerate the discovery of novel Dirac semimetals. We implement current available and develop new workflows to data-mine the Materials Project database for novel Dirac semimetals with desirable band structures and symmetry protected topological properties. This data-driven effort relies on the successful development of several automatic data generation and analysis tools, including a workflow for the automatic identification of topological invariants and pattern recognition techniques to find specific features in a massive number of computed band structures. Utilizing this approach, we successfully identified more than 15 novel Dirac point and Dirac nodal line systems that have not been theoretically predicted or experimentally identified. This work is supported by the Materials Project Predictive Modeling Center through the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-05CH11231.

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

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

Unver, O.; Gurtug, O.

2010-10-15

Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence,more » the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.« less

Melting of Domain Wall in Charge Ordered Dirac Electron of Organic Conductor α-(BEDT-TTF)2I3

NASA Astrophysics Data System (ADS)

Ohki, Daigo; Matsuno, Genki; Omori, Yukiko; Kobayashi, Akito

2018-05-01

The origin of charge order melting is identified by using the real space dependent mean-field theory in the extended Hubbard model describing an organic Dirac electron system α-(BEDT-TTF)2I3. In this model, the width of a domain wall which arises between different types of the charge ordered phase exhibits a divergent increase with decreasing the strength of electron-electron correlations. By analyzing the finite-size effect carefully, it is shown that the divergence coincides with a topological transition where a pair of Dirac cones merges in keeping with a finite gap. It is also clarified that the gap opening point and the topological transition point are different, which leads to the existence of an exotic massive Dirac electron phase with melted-type domain wall and gapless edge states. The present result also indicated that multiple metastable states are emerged in massive Dirac Electron phase. In the trivial charge ordered phase, the gapless domain-wall bound state takes place instead of the gapless edge states, accompanying with a form change of the domain wall from melted-type into hyperbolic-tangent-type.

Dirac field and gravity in NC SO(2,3)_\\star model

NASA Astrophysics Data System (ADS)

Gočanin, Dragoljub; Radovanović, Voja

2018-03-01

Action for the Dirac spinor field coupled to gravity on noncommutative (NC) Moyal-Weyl spacetime is obtained without prior knowledge of the metric tensor. We emphasize gauge origins of gravity and its interaction with fermions by demonstrating that a classical action invariant under SO(2, 3) gauge transformations can be exactly reduced to the Dirac action in curved spacetime after breaking the original symmetry down to the local Lorentz SO(1, 3) symmetry. The commutative SO(2, 3) invariant action can be straightforwardly deformed via Moyal-Weyl \\star -product to its NC SO(2,3)_\\star invariant version which can be expanded perturbatively in powers of the deformation parameter using the Seiberg-Witten map. The NC gravity-matter couplings in the expansion arise as an effect of the gauge symmetry breaking. We calculate in detail the first order NC correction to the classical Dirac action in curved spacetime and show that it does not vanish. Moreover, linear NC effects are apparent even in flat spacetime. We analyse NC deformation of the Dirac equation, Feynman propagator and dispersion relation for electrons in Minkowski spacetime and conclude that constant NC background acts as a birefringent medium for electrons propagating in it.

Tinene: a two-dimensional Dirac material with a 72 meV band gap.

PubMed

Cai, Bo; Zhang, Shengli; Hu, Ziyu; Hu, Yonghong; Zou, Yousheng; Zeng, Haibo

2015-05-21

Dirac materials have attracted great interest for both fundamental research and electronic devices due to their unique band structures, but the usual near zero bandgap of graphene results in a poor on-off ratio in the corresponding transistors. Here, we report on tinene, monolayer gray tin, as a new two-dimensional material with both Dirac characteristics and a remarkable 72 meV bandgap based on density functional theory calculations. Compared with silicene and germanene, tinene has a similar hexagonal honeycomb monolayer structure, but it has an obviously larger buckling height (∼0.70 Å). Interestingly, such a moderate buckling structure results in phonon dispersion without appreciable imaginary modes, indicating the strong dynamic stability of tinene. Significantly, a distinct transformation is discovered from the band structure that six Dirac cones would appear at high symmetry K points in the first Brillouin zone when gray tin is thinned from the bulk to monolayer, but a bandgap as large as 72 meV is still preserved. Considering the recent successful realization of silicene and germanene with a similar structure, the predicted stable tinene with Dirac characteristics and a suitable bandgap is a possibility for the "more than Moore" materials and devices.

Detection of sub-MeV dark matter with three-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Hochberg, Yonit; Kahn, Yonatan; Lisanti, Mariangela; Zurek, Kathryn M.; Grushin, Adolfo G.; Ilan, Roni; Griffin, Sinéad M.; Liu, Zhen-Fei; Weber, Sophie F.; Neaton, Jeffrey B.

2018-01-01

We propose the use of three-dimensional Dirac materials as targets for direct detection of sub-MeV dark matter. Dirac materials are characterized by a linear dispersion for low-energy electronic excitations, with a small band gap of O (meV ) if lattice symmetries are broken. Dark matter at the keV scale carrying kinetic energy as small as a few meV can scatter and excite an electron across the gap. Alternatively, bosonic dark matter as light as a few meV can be absorbed by the electrons in the target. We develop the formalism for dark matter scattering and absorption in Dirac materials and calculate the experimental reach of these target materials. We find that Dirac materials can play a crucial role in detecting dark matter in the keV to MeV mass range that scatters with electrons via a kinetically mixed dark photon, as the dark photon does not develop an in-medium effective mass. The same target materials provide excellent sensitivity to absorption of light bosonic dark matter in the meV to hundreds of meV mass range, superior to all other existing proposals when the dark matter is a kinetically mixed dark photon.

Inertial Mass from Spin Nonlinearity

NASA Astrophysics Data System (ADS)

Cohen, Marcus

The inertial mass of a Fermion shows up as chiral cross-coupling in its Dirac system. No scalar term can invariantly couple left and right chirality fields; the Dirac matrices must be spin tensors of mixed chirality. We show how such tensor couplings could arise from nonlinear mixing of four spinor fields, two representing the local electron fields and two inertial spinor fields sourced in the distant masses. We thus give a model that implements Mach's principle. Following Mendel Sachs,1 we let the inertial spinors factor the moving spacetime tetrads qα(x) and bar {q}α (x) that appear in the Dirac operator. The inertial spinors do more than set the spacetime "stage;" they are players in the chiral dynamics. Specifically, we show how the massive Dirac system arises as the envelope modulation equations coupling left and right chirality electron fields on a Friedmann universe via nonlinear "spin gratings" with the inertial spinor fields. These gratings implement Penrose's "mass-scatterings," which keep the null zig-zags of the bispinor wave function confined to a timelike world tube. Local perturbations to the inertial spinor fields appear in the Dirac system as Abelian and non-Abelian vector potentials.

Job monitoring on DIRAC for Belle II distributed computing

NASA Astrophysics Data System (ADS)

Kato, Yuji; Hayasaka, Kiyoshi; Hara, Takanori; Miyake, Hideki; Ueda, Ikuo

2015-12-01

We developed a monitoring system for Belle II distributed computing, which consists of active and passive methods. In this paper we describe the passive monitoring system, where information stored in the DIRAC database is processed and visualized. We divide the DIRAC workload management flow into steps and store characteristic variables which indicate issues. These variables are chosen carefully based on our experiences, then visualized. As a result, we are able to effectively detect issues. Finally, we discuss the future development for automating log analysis, notification of issues, and disabling problematic sites.

On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

NASA Astrophysics Data System (ADS)

Hulko, Artem

2018-03-01

In this paper we define a one-dimensional discrete Dirac operator on Z . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on Z . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole Z.

Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

NASA Astrophysics Data System (ADS)

Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

2018-03-01

The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

Group theoretical approach to the Dirac operator on S 2

NASA Astrophysics Data System (ADS)

Gutiérrez, Sergio; Huet, Idrish

2018-04-01

In this revision we outline the group theoretical approach to formulate and solve the eigenvalue problem of the Dirac operator on the round 2-sphere conceived as the right coset S 2 = SU(2)/U(1). Starting from general symmetry considerations we illustrate the formulation of the Dirac operator through left action or right action differential operators, whose properties on a right coset are quite different. The construction of the spinor space and the solution of the spectral problem using group theoretical methods is also presented.

Particle-like solutions of the Einstein-Dirac-Maxwell equations

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-08-01

We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.

Spin and Valley Noise in Two-Dimensional Dirac Materials

NASA Astrophysics Data System (ADS)

Tse, Wang-Kong; Saxena, A.; Smith, D. L.; Sinitsyn, N. A.

2014-07-01

We develop a theory for optical Faraday rotation noise in two-dimensional Dirac materials. In contrast to spin noise in conventional semiconductors, we find that the Faraday rotation fluctuations are influenced not only by spins but also the valley degrees of freedom attributed to intervalley scattering processes. We illustrate our theory with two-dimensional transition-metal dichalcogenides and discuss signatures of spin and valley noise in the Faraday noise power spectrum. We propose optical Faraday noise spectroscopy as a technique for probing both spin and valley relaxation dynamics in two-dimensional Dirac materials.

Scattering of Dirac waves off Kerr black holes

NASA Astrophysics Data System (ADS)

Chakrabarti, Sandip K.; Mukhopadhyay, Banibrata

2000-10-01

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry into radial and angular parts. Here we solve the complete wave equation and find out how the Dirac wave scatters off Kerr black holes. The eigenfunctions, eigenvalues and reflection and transmission co-efficients are computed. We compare the solutions with several parameters to show how a spinning black hole recognizes the mass and energy of incoming waves. Very close to the horizon the solutions become independent of the particle parameters, indicating the universality of the behaviour.

The unity of the fundamental interactions

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

Zichichi, A.

1983-01-01

This book offers a collection of authoritative papers which provides the reader with a plenary survey of some of the latest developments in the field of high-energy interactions. The contributing physicists offer a comprehensive review of recent significant findings from both theoretical and experimental studies in high-energy interactions. Topics include the end of the high-energy frontier, monopoles, numerical studies of gauge field theories, expectations for the next generation of experiments, unified models, cosmology, supersymmetry, neutrino physics at Fermilab, heavy flavor production in the highest-energy (pp) interactions, b-quark physics, hadron production in e/sup +/e/sup -/ annihilation, the search for new particlesmore » and electroweak interference effects in e/sup +/e/sup -/ interactions, CP violation, and high-energy soft (pp) interactions. Includes essays by Edward Teller and P.A.M. Dirac on their lives as physicists, and one by E.P. Wigner on ''the glorious days of physics.''« less

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

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

Inglis, Shaun, E-mail: sminglis@utas.edu.au; Jarvis, Peter, E-mail: Peter.Jarvis@utas.edu.au

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We showmore » how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form. - Highlights: • Maxwell–Dirac equations derived in manifestly gauge invariant tensor form. • Invariant scalar and four vector fields for four Poincaré subgroups derived, including two unusual cases. • Symmetry reduction imposed on Maxwell–Dirac equations under example subgroups. • Magnetic monopole arises for spherically symmetric case, consistent with charge quantization condition.« less

Unique Fock quantization of a massive fermion field in a cosmological scenario

NASA Astrophysics Data System (ADS)

Cortez, Jerónimo; Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.

2016-04-01

It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive at this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a nontrivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set.

Weiss oscillations and particle-hole symmetry at the half-filled Landau level

NASA Astrophysics Data System (ADS)

Cheung, Alfred K. C.; Raghu, S.; Mulligan, Michael

2017-06-01

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal ±e2/2 h at half filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son [Son, Phys. Rev. X 5, 031027 (2015), 10.1103/PhysRevX.5.031027]. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field the oscillations occur symmetrically as the electron density is varied about half filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long-wavelength physics.

Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices

NASA Astrophysics Data System (ADS)

Zhu, Yan-Qing; Zhang, Dan-Wei; Yan, Hui; Xing, Ding-Yu; Zhu, Shi-Liang

2017-09-01

The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct two- and three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconventional integer pseudospin, beyond the Dirac-Weyl-Majorana fermions, are an exotic kind of fermions named as Maxwell fermions. We demonstrate that the systems have rich topological features. For instance, the threefold degenerate points called Maxwell points may have quantized Berry phases and anomalous quantum Hall effects with spin-momentum locking may appear in topological Maxwell insulators in the two-dimensional lattices. In three dimensions, Maxwell points may have nontrivial monopole charges of ±2 with two Fermi arcs connecting them, and the merging of the Maxwell points leads to topological phase transitions. Finally, we propose realistic schemes for realizing the model Hamiltonians and detecting the topological properties of the emergent Maxwell quasiparticles in optical lattices.

Weiss oscillations and particle-hole symmetry at the half-filled Landau level

DOE PAGES

Cheung, Alfred K. C.; Raghu, S.; Mulligan, Michael

2017-06-15

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal ± e 2/2h at half filling. Here, we study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son [Son, Phys. Rev. X 5, 031027 (2015)]. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field the oscillations occur symmetrically as the electron density is varied about half filling. Wemore » find an approximate “sum rule” obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long-wavelength physics.« less

Weiss oscillations and particle-hole symmetry at the half-filled Landau level

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

Cheung, Alfred K. C.; Raghu, S.; Mulligan, Michael

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal ± e 2/2h at half filling. Here, we study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son [Son, Phys. Rev. X 5, 031027 (2015)]. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field the oscillations occur symmetrically as the electron density is varied about half filling. Wemore » find an approximate “sum rule” obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long-wavelength physics.« less

Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

NASA Astrophysics Data System (ADS)

Wills, John M.; Mattsson, Ann E.

2012-02-01

Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Visualizing the Topologically Induced States of Strongly Correlated Electrons in SmB6

NASA Astrophysics Data System (ADS)

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

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

M ξ, M αβ, M γ and M m X-ray production cross-sections for elements with 71⩽ z⩽92 at 5.96 keV photon energy

NASA Astrophysics Data System (ADS)

Sharma, Manju; Sharma, Veena; Kumar, Sanjeev; Puri, S.; Singh, Nirmal

2006-11-01

The M ξ, M αβ, M γ and M m X-ray production (XRP) cross-sections have been measured for the elements with 71⩽ Z⩽92 at 5.96 keV incident photon energy satisfying EM1< Einc< EL3, where EM1(L3) is the M 1(L 3) subshell binding energy. These XRP cross-sections have been calculated using photoionization cross-sections based on the relativistic Dirac-Hartree-Slater (RDHS) model with three sets of X-ray emission rates, fluorescence, Coster-Kronig and super Coster-Kronig yields based on (i) the non-relativistic Hartree-Slater (NRHS) potential model, (ii) the RDHS model and (iii) the relativistic Dirac-Fock (RDF) model. For the third set, the M i ( i=1-5) subshell fluorescence yields have been calculated using the RDF model-based X-ray emission rates and total widths reevaluated to incorporate the RDF model-based radiative widths. The measured cross-sections have been compared with the calculated values to check the applicability of the physical parameters based on different models.

Accurate Determination of the Quasiparticle and Scaling Properties Surrounding the Quantum Critical Point of Disordered Three-Dimensional Dirac Semimetals.

PubMed

Fu, Bo; Zhu, Wei; Shi, Qinwei; Li, Qunxiang; Yang, Jinlong; Zhang, Zhenyu

2017-04-07

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behavior is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. We further show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.

Accurate Determination of the Quasiparticle and Scaling Properties Surrounding the Quantum Critical Point of Disordered Three-dimensional Dirac Semimetals

DOE PAGES

Fu, Bo; Zhu, Wei; Shi, Qinwei; ...

2017-04-03

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behaviormore » is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. Furthermore, we show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.« less

White dwarfs, the Galaxy and Dirac's cosmology

NASA Technical Reports Server (NTRS)

Stothers, R.

1976-01-01

The additive and multiplicative versions of Dirac's cosmological hypothesis relating the gravitational constant variation with elapsed time and number of particles populating the universe is invoked to account for the deficiency or absence of white dwarfs fainter than about 0.0001 solar luminosity. An estimate is made of white dwarf luminosity in accordance with the two evolutionary models, and it is conjectured that some old white dwarfs with high space velocities may be on the verge of gravitational collapse. Lack of a special mechanism to produce the vast numbers of black holes or other dead stars accounting for 'missing matter' in the vicinity of the sun and in the galactic halo is noted in Dirac's multiplicative model. Results indicate that either Dirac's theory is untenable, or that radiation and heating are of some unknown nature, or that the process of creation of new matter requires a corresponding input of energy.

Large leptonic Dirac CP phase from broken democracy with random perturbations

NASA Astrophysics Data System (ADS)

Ge, Shao-Feng; Kusenko, Alexander; Yanagida, Tsutomu T.

2018-06-01

A large value of the leptonic Dirac CP phase can arise from broken democracy, where the mass matrices are democratic up to small random perturbations. Such perturbations are a natural consequence of broken residual S3 symmetries that dictate the democratic mass matrices at leading order. With random perturbations, the leptonic Dirac CP phase has a higher probability to attain a value around ± π / 2. Comparing with the anarchy model, broken democracy can benefit from residual S3 symmetries, and it can produce much better, realistic predictions for the mass hierarchy, mixing angles, and Dirac CP phase in both quark and lepton sectors. Our approach provides a general framework for a class of models in which a residual symmetry determines the general features at leading order, and where, in the absence of other fundamental principles, the symmetry breaking appears in the form of random perturbations.

Dirac-electron-mediated magnetic proximity effect in topological insulator/magnetic insulator heterostructures

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

Li, Mingda; Song, Qichen; Zhao, Weiwei

The possible realization of dissipationless chiral edge current in a topological insulator/magnetic insulator heterostructure is based on the condition that the magnetic proximity exchange coupling at the interface is dominated by the Dirac surface states of the topological insulator. We report a polarized neutron reflectometry observation of Dirac-electron-mediated magnetic proximity effect in a bulk-insulating topological insulator (Bi 0.2Sb 0.8) 2Te 3/magnetic insulator EuS heterostructure. We are able to maximize the proximity-induced magnetism by applying an electrical back gate to tune the Fermi level of topological insulator to be close to the Dirac point. A phenomenological model based on diamagnetic screeningmore » is developed to explain the suppressed proximity-induced magnetism at high carrier density. Our work paves the way to utilize the magnetic proximity effect at the topological insulator/magnetic insulator heterointerface for low-power spintronic applications.« less

Dirac-electron-mediated magnetic proximity effect in topological insulator/magnetic insulator heterostructures

DOE PAGES

Li, Mingda; Song, Qichen; Zhao, Weiwei; ...

2017-11-01

The possible realization of dissipationless chiral edge current in a topological insulator/magnetic insulator heterostructure is based on the condition that the magnetic proximity exchange coupling at the interface is dominated by the Dirac surface states of the topological insulator. We report a polarized neutron reflectometry observation of Dirac-electron-mediated magnetic proximity effect in a bulk-insulating topological insulator (Bi 0.2Sb 0.8) 2Te 3/magnetic insulator EuS heterostructure. We are able to maximize the proximity-induced magnetism by applying an electrical back gate to tune the Fermi level of topological insulator to be close to the Dirac point. A phenomenological model based on diamagnetic screeningmore » is developed to explain the suppressed proximity-induced magnetism at high carrier density. Our work paves the way to utilize the magnetic proximity effect at the topological insulator/magnetic insulator heterointerface for low-power spintronic applications.« less

Dirac dispersion generates unusually large Nernst effect in Weyl semimetals

NASA Astrophysics Data System (ADS)

Watzman, Sarah J.; McCormick, Timothy M.; Shekhar, Chandra; Wu, Shu-Chun; Sun, Yan; Prakash, Arati; Felser, Claudia; Trivedi, Nandini; Heremans, Joseph P.

2018-04-01

Weyl semimetals contain linearly dispersing electronic states, offering interesting features in transport yet to be thoroughly explored thermally. Here we show how the Nernst effect, combining entropy with charge transport, gives a unique signature for the presence of Dirac bands and offers a diagnostic to determine if trivial pockets play a role in this transport. The Nernst thermopower of NbP exceeds its conventional thermopower by a 100-fold, and the temperature dependence of the Nernst effect has a pronounced maximum. The charge-neutrality condition dictates that the Fermi level shifts with increasing temperature toward the energy that has the minimum density of states (DOS). In NbP, the agreement of the Nernst and Seebeck data with a model that assumes this minimum DOS resides at the Dirac points is taken as strong experimental evidence that the trivial (non-Dirac) bands play no role in high-temperature transport.

Light-cone expansion of the Dirac sea in the presence of chiral and scalar potentials

NASA Astrophysics Data System (ADS)

Finster, Felix

2000-10-01

We study the Dirac sea in the presence of external chiral and scalar/pseudoscalar potentials. In preparation, a method is developed for calculating the advanced and retarded Green's functions in an expansion around the light cone. For this, we first expand all Feynman diagrams and then explicitly sum up the perturbation series. The light-cone expansion expresses the Green's functions as an infinite sum of line integrals over the external potential and its partial derivatives. The Dirac sea is decomposed into a causal and a noncausal contribution. The causal contribution has a light-cone expansion which is closely related to the light-cone expansion of the Green's functions; it describes the singular behavior of the Dirac sea in terms of nested line integrals along the light cone. The noncausal contribution, on the other hand, is, to every order in perturbation theory, a smooth function in position space.

Generalized virial theorem for massless electrons in graphene and other Dirac materials

NASA Astrophysics Data System (ADS)

Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

2016-05-01

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

Spin texture of the surface state of three-dimensional Dirac material Ca3PbO

NASA Astrophysics Data System (ADS)

Kariyado, Toshikaze

2015-04-01

The bulk and surface electronic structures of a candidate three-dimensional Dirac material Ca3PbO and its family are discussed especially focusing on the spin texture on the surface states. We first explain the basic features of the bulk band structure of Ca3PbO, such as emergence of Dirac fermions near the Fermi energy, and compare it with the other known three-dimensional Dirac semimetals. Then, the surface bands and spin-texture on them are investigated in detail. It is shown that the surface bands exhibit strong momentum-spin locking, which may be useful in some application for spin manipulation, induced by a combination of the inversion symmetry breaking at the surface and the strong spin-orbit coupling of Pb atoms. The surface band structure and the spin-textures are sensitive to the surface types.