The surface Fermi arc states in $Z_2$ Weyl semimetals $A_3 Bi$ (A=Na, K, Rb) are studied by employing a continuum low-energy effective model. It is shown that the surface Fermi arc states can be classified with respect to the ud-parity symmetry. Because of the symmetry, the arcs come in mirror symmetric pairs. The effects of symmetry breaking terms on the structure of the Fermi arcs are also studied. Among other results, we find at least two qualitatively different types of the surface Fermi arcs. The arcs of the first type link disconnected sheets of the bulk Fermi surface, while arcs of the second type link different points of the same bulk Fermi surface sheet.
Heavy fermion semimetals represent a promising setting to explore topological metals driven by strong correlations. In this paper, we i) summarize the theoretical results in a Weyl-Kondo semimetal phase for a strongly correlated model with inversion-symmetry-breaking and time-reversal invariance, and the concurrent work that has experimentally discovered this phase in the non-magnetic non-centrosymmetric heavy fermion system Ce$_3$Bi$_4$Pd$_3$; and ii) describe what is expected theoretically when the time-reversal symmetry is also broken.
We present a theory of charge density wave (CDW) states in Weyl semimetals and their interplay with the chiral anomaly. In particular, we demonstrate a special nature of the shortest-period CDW state, which is obtained when the separation between the Weyl nodes equals exactly half a primitive reciprocal lattice vector. Its topological properties are shown to be distinct from all other Weyl CDW states. We make a connection between this observation and the three-dimensional fractional quantum Hall state, which was recently proposed to exist in magnetic Weyl semimetals.
Weyl semimetals are phases of matter with excitations effectively described by massless Dirac fermions. Their critical nature makes unclear the persistence of such phase in presence of disorder. We present a theorem ensuring the stability of the semimetallic phase in presence of weak quasiperiodic disorder. The proof relies on the subtle interplay of the relativistic Quantum Field Theory description combined with number theoretical properties used in KAM theory.
Weyl semimetals, featuring massless linearly dispersing chiral fermions in three dimensions, provide an excellent platform for studying the interplay of electronic interactions and topology, and exploring new correlated states of matter. Here, we examine the effect of a local repulsive interaction on an inversion-symmetry breaking Weyl semimetal model, using cluster dynamical mean field theory and variational cluster approximation methods. Our analysis reveals a continuous transition from the gapless Weyl semimetal phase to a gapped spin density wave ordered phase at a critical value of the in…
The effective low energy description of interacting Dirac and Weyl semimetals is that of massless quantum electrodynamics with several Lorentz breaking material parameters. We perform a renormalization group analysis of Coulomb interaction in anisotropic Dirac and Weyl semimetals and show that the anisotropy persists in the material systems at the infrared fixed point. In addition, a tilt of the fermion cones breaking inversion symmetry induces a magnetoelectric term in the electrodynamics of the material whose magnitude runs to match that of the electronic tilt at the fixed point.
We study a holographic model which exhibits a quantum phase transition from the strongly interacting Weyl semimetal phase to an insulating phase. In the holographic insulating phase there is a hard gap in the real part of frequency dependent diagonal conductivities. However, the anomalous Hall conductivity is nonzero at zero frequency, indicting that it is a Chern insulator. This holographic quantum phase transition is always of first order, signified by a discontinuous anomalous Hall conductivity at the phase transition, in contrast to the very continuous holographic Weyl semimetal/trivial se…
Motivated by the proposal of a Weyl-semimetal phase in pyrochlore iridates, we consider a Hubbard-type model on the pyrochlore lattice. To shed light on the question as to why such a state has not been observed experimentally, its robustness is analyzed. On the one hand, we study the possible phases when the system is doped. Magnetic frustration favors several phases with magnetic and charge order that do not occur at half filling, including additional Weyl-semimetal states close to quarter filling. On the other hand, we search for density waves that break translational symmetry and destroy th…
We study the effects of momentum relaxation on the holographic Weyl semimetal which exhibits a topological quantum phase transition between the Weyl semimetal phase and a topological trivial phase. The conservation of momentum in the field theory is broken by the axion fields in holography. The topological Weyl semimetal phase is characterized by a nontrivial anomalous Hall conductivity. We find that the critical value of the phase transition decreases when we increase the momentum relaxation strength up to a special value, above which it goes to zero. This indicates that the Weyl semimetal ph…
We show that hybrid Dirac and Weyl semimetals can be realized in a three-dimensional Luttinger semimetal with quadratic band touching (QBT). We illustrate this using periodic kicking scheme. In particular, we focus on a momentum-dependent drivings (nonuniform driving) and demonstrate the realization of various hybrid Dirac and Weyl semimetals. We identify a unique hybrid dispersion Dirac semimetal with two nodes, where one of the nodes is linear while the other is dispersed quadraticlly. Next, we show that by tilting QBT via periodic driving and in the presence of an external magnetic field, o…
Taking into account the interplay between the disorder and Coulomb interaction, the phase diagram of three-dimensional anisotropic Weyl semimetal is studied by renormalization group theory. Weak disorder is irrelevant in anisotropic Weyl semimetal, while the disorder becomes relevant and drives a quantum phase transition from semimetal to compressible diffusive metal phases if the disorder strength is larger than a critical value. The long-range Coulomb interaction is irrelevant in clean anisotropic Weyl semimetal. However, interestingly, we find that the long-range Coulomb interaction exerts …
Weyl semimetals have been classified into type-I and type-II with respect to the geometry of their Fermi surfaces at the Weyl points. Here, we propose a new class of Weyl semimetal, whose unique Fermi surface contains two electron or two hole pockets touching at a multi-Weyl point, dubbed as type-III Weyl semimetal. Based on first-principles calculations, we first show that quasi-one-dimensional compound (TaSe4)2I is a type-III Weyl semimetal with larger chiral charges. (TaSe4)2I can support four-fold helicoidal surface states with remarkably long Fermi arcs on the (001) surface. Angle-resolve…
We study the magnetic field effects on the quantum critical point (QCP) in the holographic Weyl semimetal model. We show that it increases quadratically with the magnetic field for weak field and linear with the magnetic field for strong field. Our findings are compatible with previous results in the literature from other approaches.
It is generally believed that non-Hermiticity can transform Weyl semimetals into Weyl-exceptional-ring semimetals. However, this belief is from the systems without skin effect. We investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart. It is found in both the static and periodically driven cases that the skin effect makes this general belief no longer valid. We discover that exotic non-Hermitian topological matters, e.g., a composite phase of Weyl semimetal and topologica…
We construct an exactly solvable lattice model of a fractional Weyl semimetal (FWS). The low energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect (CPGE) and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function they provide strong experimental signatures for this exotic gapless state of matter.
The surface of a Weyl semimetal famously hosts an exotic topological metal that contains open Fermi arcs rather than closed Fermi surfaces. In this work, we show that the surface is also endowed with a feature normally associated with strongly interacting systems, namely, Luttinger arcs, defined as zeros of the electron Green's function. The Luttinger arcs connect surface projections of Weyl nodes of opposite chirality and form closed loops with the Fermi arcs when the Weyl nodes are undoped. Upon doping, the ends of the Fermi and Luttinger arcs separate and the intervening regions get filled …
Classification of topological insulators and superconductors is manifested in terms of spin cobordism groups for lower dimensions. It is discussed that the periodic table of topological insulators is a result of the possible choices of spin structures on Brillouin zones of relevant topological materials. This framework is extended to the case of Weyl semimetals. It is shown that the classification of Weyl semimetals can be managed in terms of spin$^c$ cobordism groups via the extension of spin structures to spin$^c$ structures. Topological invariants of Weyl semimetals are connected to the top…
We introduce a simple model to describe the formation of heavy Weyl semimetals in non-centrosymmetric heavy fermion compounds under the influence of a parity-mixing, onsite hybridization. A key aspect of interaction-driven heavy Weyl semimetals is the development of surface Kondo breakdown, which is expected to give rise to a temperature-dependent re-configuration of the Fermi arcs and the Weyl cyclotron orbits which connect them via the chiral bulk states. Our theory predicts a strong temperature dependent transformation in the quantum oscillations at low temperatures. In addition to the effe…
We study the interaction between elliptically polarized light and a three-dimensional Luttinger semimetal with quadratic band touching using Floquet theory. In the absence of light, the touching bands can have the same or the opposite signs of the curvature; in each case, we show that simply tuning the light parameters allows us to create a zoo of Weyl semimetallic phases. In particular, we find that double and single Weyl points can coexist at different energies, and they can be tuned to be type I or type II. We also find an unusual phase transition, in which a pair of Weyl nodes form at fini…
Disorder in Weyl semimetals and superconductors is surprisingly subtle, attracting attention and competing theories in recent years. In this brief review, we discuss the current theoretical understanding of the effects of short-ranged, quenched disorder on the low energy-properties of three-dimensional, topological Weyl semimetals and superconductors. We focus on the role of non-perturbative rare region effects on destabilizing the semimetal phase and rounding the expected semimetal-to-diffusive metal transition into a cross over. Furthermore, the consequences of disorder on the resulting natu…
We explore the stability of three-dimensional Weyl and Dirac semimetals subject to quasiperiodic potentials. We present numerical evidence that the semimetal is stable for weak quasiperiodic potentials, despite being unstable for weak random potentials. As the quasiperiodic potential strength increases, the semimetal transitions to a metal, then to an "inverted" semimetal, and then finally to a metal again. The semimetal and metal are distinguished by the density of states at the Weyl point, as well as by level statistics, transport, and the momentum-space structure of eigenstates near the Wey…
