The circular photogalvanic effect (CPGE) is the photocurrent generated in an optically active material in response to an applied ac electric field, and it changes sign depending on the chirality of the incident circularly polarized light. It is a non-linear dc current as it is second-order in the applied electric field, and for a certain range of low frequencies, takes on a quantized value proportional to the topological charge for a system which is a source of nonzero Berry flux. We show that for a non-interacting double-Weyl node, the CPGE is proportional to two quanta of Berry flux. On examining the effect of short-ranged Hubbard interactions upto first-order corrections, we find that this quantization is destroyed. This implies that unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in topological semimetals is not protected.
We investigate polarization-dependent ultrafast photocurrents in the Weyl semimetal TaAs using terahertz (THz) emission spectroscopy. Our results reveal that highly directional, transient photocurrents are generated along the non-centrosymmetric c-axis regardless of incident light polarization, while helicity-dependent photocurrents are excited within the ab-plane. This is consistent with earlier static photocurrent experiments, and demonstrates on the basis of both the physical constraints imposed by symmetry and the temporal dynamics intrinsic to current generation and decay that optically i…
The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum $e^3/h^2$ for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbard interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are…
Weyl semimetals are one kind of three-dimensional gapless semimetal with nontrivial topology in the momentum space. The chiral anomaly in Weyl semimetals manifests as a charge imbalance between the Weyl nodes of opposite chiralities induced by parallel electric and magnetic fields. We investigate the chiral anomaly effect on the plasmon mode in both intrinsic and doped Weyl semimetals within the random phase approximation. We prove that the chiral anomaly gives rise to a different plasmon mode in intrinsic Weyl semimetals. We also find the chiral anomaly leads to some exotic properties in the …
Weyl semimetals are a new class of Dirac material that posses bulk energy nodes in three dimensions. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We derive expressions for the density of states, electronic specific heat, and the quantum oscillations of the magnetization, DC conductivity, and thermal conductivity. We find phase shifts in the quantum oscillations that distinguish the Weyl semimetal from conventional three dimensional Schrödinger Fermions.
We examine the magneto-optical response of chiral multifold fermions. Specifically, we show that they are ideal candidates for observing the Helical Magnetic Effect (HME) previously predicted for simple Weyl fermions. Unlike Weyl fermions, the HME is present in multifold fermions even in the simplest case where the low-energy dispersion is linear and spherically symmetric. In this ideal case, we derive an analytical expression for the HME and find it is proportional to the circular photogalvanic effect; for realistic parameters and accounting for the geometry of the setup, the HME photocurrent…
We discuss the possibility of realizing Weyl semimetal phase in the magnetically doped topological band insulators. When the magnetic moments are ferromagnetically polarized, we show that there are three phases in the system upon the competition between topological mass and magnetic mass: topological band insulator phase, Weyl semimetal phase, and trivial phase. We explicitly derive the low energy theory of Weyl points from the general continuum Hamiltonian of topological insulators near the Dirac point, e.g. ${\bf k} \cdot {\bf p}$ theory near $Γ$ point for Bi_{2}Se_{3}. Furthermore, we intro…
We consider theoretically surface plasmon polaritons in Weyl semimetals. These materials contain pairs of band touching points - Weyl nodes - with a chiral topological charge, which induces an optical anisotropy and anomalous transport through the chiral anomaly. We show that these effects, which are not present in ordinary metals, have a direct fundamental manifestation in the surface plasmon dispersion. The retarded Weyl surface plasmon dispersion depends on the separation of the Weyl nodes in energy and momentum space. For Weyl semimetals with broken time-reversal symmetry, the distance bet…
We theoretically propose that giant magnetochiral anisotropy is achieved in Weyl semimetals in noncentrosymmetric crystals as a consequence of the chiral anomaly. The magnetochiral anisotropy is the nonlinearity of the resistivity $ρ$ that depends on the current $\boldsymbol{I}$ and the magnetic field $\boldsymbol{B}$ as $ρ=ρ_0 (1 + γ\boldsymbol{I} \cdot \boldsymbol{B})$, and can be applied to rectifier devices controlled by $\boldsymbol{B}$. We derive the formula for the coefficient $γ$ in noncentrosymmetric Weyl semimetals. The obtained formula for $γ$ shows that the magnetochiral anisotropy…
When a Dirac semimetal is subject to a circularly polarized laser, it is predicted that the Dirac cone splits into two Weyl nodes and a nonequilibrium transient state called the Floquet Weyl semimetal is realized. We focus on the previously unexplored low-frequency regime, where the upper and lower Dirac bands resonantly couple with each other through multi-photon processes, which is a realistic situation in solid state ultrafast pump-probe experiments. We find a series of new Weyl nodes emerging in pairs when the Floquet replica bands hybridize with each other. The nature of the Floquet Weyl …
Using first-principles calculations, we investigate the photogalvanic effect in the Weyl semimetal material TaAs. We find colossal photocurrents caused by the Weyl points in the band structuure in a wide range of laser frequency. Our calculations reveal that the photocurrent is predominantly contributed by the three-band transition from the occupied Weyl band to the empty Weyl band via an intermediate band away from the Weyl cone, for excitations both by linearly and circularly polarized lights. Therefore, it is significant to sum over all three-band transitions by considering a full set of Bl…
We study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk materials of Weyl semimetals. In particular, the helical spin textures of Weyl semimetals manifest the spin-momentum locking of Weyl fermions in a visible manner. The spin-wave fluctuations of the helical order carry electric charge density; therefore, the spin textures can be electrically controlled in a simple and predictable manner.
We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory we show that in the presence of sufficiently weak randomness (i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. Mean density of states at zero energy serves as the order parameter and displays sing…
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…
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…
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…
Weyl fermions, which are fermions with definite chiralities, can give rise to anomalous breaking of the symmetry of the physical system which they are a part of. In their (3+1)-dimensional realizations in condensed matter systems, i.e., the so-called Weyl semimetals, this anomaly gives rise to topological electromagnetic response of magnetic fluctuations, which takes the form of non-local interaction between magnetic fluctuations and electromagnetic fields. We study the physical consequences of this non-local interaction, including electric field assisted magnetization dynamics, an extra gaple…
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.
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measure…
Type II Weyl semimetal, a three dimensional gapless topological phase, has drawn enormous interest recently. These topological semimetals enjoy overtilted dispersion and Weyl nodes that separate the particle and hole pocket. Using perturbation renormalization group, we identify possible renormalization of the interaction vertices, which show a tendency toward instability. We further adopt a self-consistent mean-field approach to study possible instability of the type II Weyl semimetals under short-range electron-electron interaction. It is found that the instabilities are much easier to form i…
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…
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…
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…
It is shown that the Weyl semimetal TaAs can have a significant polar vector contribution to its optical activity. This is quantified by ab initio calculations of the resonant x-ray diffraction at the Ta L1 edge. For the Bragg vector (400), this polar vector contribution to the circular intensity differential between left and right polarized x-rays is predicted to be comparable to that arising from linear dichroism. Implications this result has in regards to optical effects predicted for topological Weyl semimetals are discussed.
The interplay of electronic band structures and electron-electron interactions is known to brew new phases in condensed matter. In this paper, we investigate thermodynamic phases and corresponding electronic structures of the Weyl semimetal in the strong onsite Coulomb interaction limit. Based on a minimum model of the Weyl semimetal with two linear Weyl nodes, it is shown that generically the Weyl semimetal becomes magnetic in the presence of interactions. In particular, it is shown that the Dzyaloshinskii-Moriya exchange interaction is generally induced so that the A-type antiferromagnetic (…
Weyl fermions play a major role in quantum field theory but have been quite elusive as fundamental particles. Materials based on quasi two-dimensional bismuth layers were recently designed and provide an arena for the study of the interplay between anisotropic Dirac fermions, magnetism and structural changes, allowing the formation of Weyl fermions in condensed matter. Here, we perform an optical investigation of YbMnBi$_2$, a representative type II Weyl semimetal, and contrast its excitation spectrum with the optical response of the more conventional semimetal EuMnBi$_2$. Our comparative stud…
Weyl points with monopole charge $\pm 1$ have been extensively studied, however, real materials of multi-Weyl points, whose monopole charges are higher than $1$, have yet to be found. In this Rapid Communication, we show that nodal-line semimetals with nontrivial line connectivity provide natural platforms for realizing Floquet multi-Weyl points. In particular, we show that driving crossing nodal lines by circularly polarized light generates double-Weyl points. Furthermore, we show that monopole combination and annihilation can be observed in crossing-nodal-line semimetals and nodal-chain semi…
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 propose to realize Weyl semimetals in a cubic optical lattice. We find that there exist three distinct Weyl semimetal phases in the cubic optical lattice for different parameter ranges. One of them has two pairs of Weyl points and the other two have one pair of Weyl points in the Brillouin zone. For a slab geometry with (010) surfaces, the Fermi arcs connecting the projections of Weyl points with opposite topological charges on the surface Brillouin zone is presented. By adjusting the parameters, the Weyl points can move in the Brillouin zone. Interestingly, for two pairs of Weyl points, as…
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 …
We study the AC electrical conductivity at zero temperature in a holographic model for a Weyl semimetal. At small frequencies we observe a linear dependence in the frequency. The model shows a quantum phase transition between a topological semimetal (Weyl semimetal phase) with a non vanishing anomalous Hall conductivity and a trivial semimetal. The AC conductivity has an intermediate scaling due to the presence of a quantum critical region in the phase diagram of the system. The phase diagram is reconstructed using the scaling properties of the conductivity. We compare with the experimental da…
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.
We study the electromagnetic properties of Weyl semimetals with strong interactions. Focusing on a single Weyl cone in the band structure, we induce strong interactions by coupling the Weyl fermion with a tunable coupling constant $g_f$ to a quantum critical system. The critical fluctuations are described by a conformal field theory containing fermionic operators with scaling dimension $Δ$. Employing the methods of the holographic correspondence, we then derive the effective theory of the Weyl fermion in the presence of external electric and magnetic fields. In particular, we determine the fre…
We performed a series of high-pressure synchrotron X-ray diffraction (XRD) and resistance measurements on the Weyl semimetal NbAs. The crystal structure remains stable up to 26 GPa according to the powder XRD data. The resistance of NbAs single crystal increases monotonically with pressure at low temperature. Up to 20 GPa, no superconducting transition is observed down to 0.3 K. These results show that the Weyl semimetal phase is robust in NbAs, and applying pressure is not a good way to get a topological superconductor from a Weyl semimetal.
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 demonstrate that the physical reason for the nontrivial topological properties of Dirac semimetals $A_3 Bi$ (A=Na,K,Rb) is connected with a discrete symmetry of the low-energy effective Hamiltonian. By making use of this discrete symmetry, we argue that all electron states can be split into two separate sectors of the theory. Each sector describes a Weyl semimetal with a pair of Weyl nodes and broken time-reversal symmetry. The latter symmetry is not broken in the complete theory because the time-reversal transformation interchanges states from different sectors. Our findings are supported …
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…
