Open accessJournal Article

# Weyl, Dirac and high-fold chiral fermions in topological quantum materials.

Abstract: Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin-orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk-boundary correspondence giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and of Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss some of the exotic optical and magnetic responses observed in these materials, as well as the progress in developing some of the related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family of crystals as a prime example. Lastly, we discuss recent advances in Weyl-line phases in magnetic topological materials. With this Review, we aim to provide an introduction to the basic concepts underlying Weyl physics in condensed matter, and to representative materials and their electronic structures and topology as revealed by spectroscopic studies. We hope this work serves as a guide for future theoretical and experimental explorations of chiral fermions and related topological quantum systems with potentially enhanced functionalities.

Topics: Fermion (60%),
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Journal Article
Rinkle Juneja1, S. Thébaud1, Tribhuwan Pandey1, Tribhuwan Pandey2  +8 moreInstitutions (2)
Abstract: Quasiparticle physics underlies our understanding of the microscopic dynamical behaviors of materials that govern a vast array of properties, including structural stability, excited states and interactions, dynamical structure factors, and electron and phonon conductivities. Thus, understanding band structures and quasiparticle interactions is foundational to the study of condensed matter. Here we advance a ‘twist’ dynamical description of quasiparticles (including phonons and Bloch electrons) in non-symmorphic chiral and achiral materials. Such materials often have structural complexity, strong thermal resistance, and efficient thermoelectric performance for waste heat capture and clean refrigeration technologies. The twist dynamics presented here provides a novel perspective of quasiparticle behaviors in such complex materials, in particular highlighting how non-symmorphic symmetries determine band crossings and anti-crossings, topological behaviors, quasiparticle interactions that govern transport, and observables in scattering experiments. We provide specific context via neutron scattering measurements and first-principles calculations of phonons and electrons in chiral tellurium dioxide. Building twist symmetries into the quasiparticle dynamics of non-symmorphic materials offers intuition into quasiparticle behaviors, materials properties, and guides improved experimental designs to probe them. More specifically, insights into the phonon and electron quasiparticle physics presented here will enable materials design strategies to control interactions and transport for enhanced thermoelectric and thermal management applications.

Topics: Quasiparticle (60%), Phonon (52%)

2 Citations

Open accessJournal Article
Grigory Volovik1, Grigory Volovik2Institutions (2)
Abstract: The boundary between the type I and type II Weyl semimetals serves as the event horizon for the "relativistic" fermions. The interior of the black hole is represented by the type II Weyl semimetal, where the Fermi surface is formed. The process of the filling of the Fermi surface by electrons results in the relaxation inside the horizon. This leads to the Hawking radiation and to the reconstruction of the interior vacuum state. After the Fermi surface is fully occupied, the interior region reaches the equilibrium state, for which the Hawking radiation is absent. If this scenario is applicable to the real black hole, then the final state of the black hole will be the dark energy star with the event horizon. Inside the event horizon one would have de Sitter space time, which is separated from the event horizon by the shell of the Planck length width. Both the de Sitter part and the shell are made of the vacuum fields without matter. This is distinct from the gravastar, in which the matter shell is outside the "horizon", and which we call the type I gravastar. But this is similar to the other type of the vacuum black hole, where the shell is inside the event horizon, and which we call the type II gravastar. We suggest to study the vacuum structure of the type II gravastar using the $q$-theory, where the vacuum variable is the 4-form field introduced for the phenomenological description of the quantum vacuum.

Topics: Gravastar (71%), Event horizon (67%), Dark-energy star (61%) ... show more

Open accessJournal Article
29 Sep 2021-Physical Review B
Abstract: We identify an effect of chirality in the electrical conduction along magnetic vortices in a Weyl superconductor. The conductance depends on whether the magnetic field is parallel or antiparallel to the vector in the Brillouin zone that separates Weyl points of opposite chirality.

Topics: Magnetic field (53%), Superconductivity (53%), Brillouin zone (52%)

Open accessJournal Article
Grigory Volovik1, Grigory Volovik2Institutions (2)
01 Aug 2021-Jetp Letters
Abstract: The boundary between the type I and type II Weyl semimetals serves as the event horizon for the “relativistic” fermions. The interior of the black hole is represented by the type II Weyl semimetal, where the Fermi surface is formed. The process of the filling of the Fermi surface by electrons results in the relaxation inside the horizon. This leads to the Hawking radiation and to the reconstruction of the interior vacuum state. After the Fermi surface is fully occupied, the interior region reaches the equilibrium state, for which the Hawking radiation is absent. If this scenario is applicable to the real black hole, then the final state of the black hole will be the dark energy star with the event horizon. Inside the event horizon one would have de Sitter spacetime, which is separated from the event horizon by the shell of the Planck length width. Both the de Sitter part and the shell are made of the vacuum fields without matter. This is distinct from the gravastar, in which the matter shell is outside the “horizon,” and which we call the type I gravastar. However, this is similar to the other type of the vacuum black hole, where the shell is inside the event horizon, and which we call the type II gravastar. We suggest to study the vacuum structure of the type II gravastar using the q-theory, where the vacuum variable is the 4-form field introduced for the phenomenological description of the quantum vacuum.

Topics: Gravastar (71%), Event horizon (67%), Dark-energy star (61%) ... show more

Open accessJournal Article
Angus Huang1, Chin-Hsuan Chen1, Ching-Hao Chang2, Horng-Tay Jeng1  +1 moreInstitutions (3)
04 Aug 2021-Nanomaterials
Abstract: Magnetic two-dimensional (2D) van der Waals materials have attracted tremendous attention because of their high potential in spintronics. In particular, the quantum anomalous Hall (QAH) effect in magnetic 2D layers shows a very promising prospect for hosting Majorana zero modes at the topologically protected edge states in proximity to superconductors. However, the QAH effect has not yet been experimentally realized in monolayer systems to date. In this work, we study the electronic structures and topological properties of the 2D ferromagnetic transition-metal dichalcogenides (TMD) monolayer 1T-VSe2 by first-principles calculations with the Heyd-Scuseria-Ernzerhof (HSE) functional. We find that the spin-orbit coupling (SOC) opens a continuous band gap at the magnetic Weyl-like crossing point hosting the quantum anomalous Hall effect with Chern number C=2. Moreover, we demonstrate the topologically protected edge states and intrinsic (spin) Hall conductivity in this magnetic 2D TMD system. Our results indicate that 1T-VSe2 monolayer serves as a stoichiometric quantum anomalous Hall material.

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205 results found

Open accessJournal Article
Abstract: This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

18,972 Citations

Open accessJournal Article
Xiao-Liang Qi1, Shou-Cheng Zhang2Institutions (2)
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

9,145 Citations

Open accessJournal Article
02 May 2011-Physical Review B
Abstract: We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, and argue that it may be realized in a class of pyrochlore iridates (such as ${\mathrm{Y}}_{2}$Ir${}_{2}$O${}_{7}$) based on calculations using the $\text{LDA}+U$ method. This state is a three-dimensional analog of graphene with linearly dispersing excitations and provides a condensed-matter realization of Weyl fermions that obeys a two-component Dirac equation. It also exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which are impossible to realize in purely two-dimensional band structures. For intermediate correlation strengths, we find this to be the ground state of the pyrochlore iridates, coexisting with noncollinear magnetic order. A narrow window of magnetic axion'' insulator may also be present. An applied magnetic field is found to induce a metallic ground state.

Topics: Weyl semimetal (58%), Fermi point (52%), Ground state (51%) ... show more

3,230 Citations

Journal Article
25 Jan 1969-Physical Review
Abstract: Working within the framework of perturbation theory, we show that the axial-vector vertex in spinor electrodynamics has anomalous properties which disagree with those found by the formal manipulation of field equations. Specifically, because of the presence of closed-loop "triangle diagrams," the divergence of axial-vector current is not the usual expression calculated from the field equations, and the axial-vector current does not satisfy the usual Ward identity. One consequence is that, even after the external-line wave-function renormalizations are made, the axial-vector vertex is still divergent in fourth- (and higher-) order perturbation theory. A corollary is that the radiative corrections to ${\ensuremath{ u}}_{l}l$ elastic scattering in the local current-current theory diverge in fourth (and higher) order. A second consequence is that, in massless electrodynamics, despite the fact that the theory is invariant under ${\ensuremath{\gamma}}_{5}$ tranformations, the axial-vector current is not conserved. In an Appendix we demonstrate the uniqueness of the triangle diagrams, and discuss a possible connection between our results and the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decays. In particular, we argue that as a result of triangle diagrams, the equations expressing partial conservation of axial-vector current (PCAC) for the neutral members of the axial-vector-current octet must be modified in a well-defined manner, which completely alters the PCAC predictions for the ${\ensuremath{\pi}}^{0}$ and the $\ensuremath{\eta}$ two-photon decays.

Topics: Vertex function (68%), Order (ring theory) (65%),

2,952 Citations

Open accessJournal Article
Di Xiao1, Ming Che Chang2, Qian Niu3Institutions (3)
Abstract: Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

Topics: , Geometric phase (57%),

2,671 Citations

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