The recent discovery of the quantum nonlinear Hall effect has revived the field of nonlinear transport. Here, we predict magnetic field-induced nonlinear Hall effect in time-reversal symmetric Weyl semimetal. We show that the interplay of the band geometric quantities, such as the Berry curvature, and the magnetic part of the Lorentz force can give rise to finite nonlinear Hall conductivity that is linear in the magnetic field. Such nonlinear Hall conductivity can manifest through nonlinear transport measurement as well as nonlinear optical phenomena like photocurrent and the second harmonic generation.
We theoretically study the band structure and the electronic transport in the Weyl semimetal nanowires in magnetic fields, and demonstrate that the interplay of the Fermi-arc surface states and the bulk Landau levels plays a crucial role in the magnetotransport. We show that a magnetic field perpendicular to the surface immediately hybridizes the counter-propagating surface modes into a series of dispersionless 0th Landau levels, and it leads to a significant reduction of the traveling modes and a rapid decay of the conductance. On the contrary, a magnetic field parallel to the wire adds linea…
We theoretically investigate the transport and magnetotransport properties of three-dimensional Weyl semimetals. Using the RPA-Boltzmann transport scattering theory for electrons scattering off randomly distributed charged impurities, together with an effective medium theory to average over the resulting spatially inhomogeneous carrier density, we smoothly connect our results for the minimum conductivity near the Weyl point with known results for the conductivity at high carrier density. In the presence of a non-quantizing magnetic field, we predict that for both high and low carrier densities…
We study magnetotransport in a disordered Weyl semimetal taking into account localization effects exactly. In the vicinity of a Weyl node, a single chiral Landau level coexists with a number of conventional non-chiral levels. Disorder scattering mixes these topologically different modes leading to peculiar localization effects. We derive the average conductance as well as the full distribution function of transmission probabilities along the field direction. Remarkably, we find that localization of the non-chiral modes is greatly enhanced in a strong magnetic field with the typical localizatio…
Magnetotransport such as the giant magnetoresistance and Hall effect lies at the heart of fundamental physics and technologies. Recently, some experiments have clearly demonstrated linear magnetotransport (LMT) proportional to magnetic field but the underlying physical mechanism is still unclear. In this work, we show that Berry curvature effect is a new mechanism dominating the LMT. The Berry-curvature-induced LMT widely exists in 66 out of 122 magnetic point groups. For typical magnetic Weyl semimetals Co$_3$Sn$_2$S$_2$ and ferromagnetic MnBi$_2$Te$_4$, Berry curvature induces LMT conductivi…
We study electric field and temperature gradient driven magnetoconductivity of a Weyl semimetal system. To analyze the responses, we utilize the kinetic equation with semiclassical equations of motion modified by the Berry curvature and orbital magnetization of the wave-packet. Apart from known positive quadratic magnetoconductivity, we show that due to chiral anomaly, the magnetconductivity can become non-analytic function of the magnetic field, proportional to 3/2 power of the magnetic field at finite temperatures. We also show that time-reversal symmetry breaking tilt of the Dirac cones res…
We study the density of states and magnetotransport properties of disordered Weyl semimetals, focusing on the case of a strong long-range disorder. To calculate the disorder-averaged density of states close to nodal points, we treat exactly the long-range random potential fluctuations produced by charged impurities, while the short-range component of disorder potential is included systematically and controllably with the help of a diagram technique. We find that for energies close to the degeneracy point, long-range potential fluctuations lead to a finite density of states. In the context of t…
We present a microscopic theory of diffusive magnetotransport in Weyl metals and clarify its relation to chiral anomaly. We derive coupled diffusion equations for the total and axial charge densities and show that chiral anomaly manifests as a magnetic-field-induced coupling between them. We demonstrate that a universal experimentally-observable consequence of this coupling in magnetotransport in Weyl metals is a quadratic negative magnetoresistance, which will dominate all other contributions to magnetoresistance under certain conditions.
We theoretically study the anisotropic magnetotransport in Dirac-Weyl magnetic junctions where a doped ferromagnetic Weyl semimetal is sandwiched between doped Dirac semimetals. We calculate the conductance using the Landauer formula and find that the system exhibits extraordinarily large anisotropic magnetoresistance (AMR). The AMR depends on the ratio of the Fermi energy and the strength of the exchange interaction. The origin of the AMR is the shift of the Fermi surface in the Weyl semimetal and the mechanism is completely different from the conventional AMR originating from the spin depend…
Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work, we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as …
We theoretically study the magnetoconductivity of the Weyl semimetal having a surface boundary under $E$ || $B$ geometry and demonstrate that the topological surface state plays an essential role in the magnetotransport. In the long-range disorder limit where the scattering between the two Weyl nodes vanishes, the conductivity diverges in the bulk model (i.e., periodic boundary condition) as usually expected, since the direct inter-node relaxation is absent. In the presence of the surface, however, the inter-node relaxation always takes place through the mediation by the surface states, and th…
Either in bulk form, or when exfoliated into atomically thin crystals, layered transition metal dichalcogenides are continuously leading to the discovery of new phenomena. The latest example is provided by 1T'-WTe$_2$, a semimetal recently found to exhibit the largest known magnetoresistance in bulk crystals, and predicted to become a two-dimensional topological insulator in strained monolayers. Here, we show that reducing the thickness through facile exfoliation provides an effective experimental knob to tune the electronic properties of WTe$_2$, which allows us to identify the microscopic me…
In topological semimetals and insulators, negative longitudinal magnetoresistance and angle-dependent planar Hall effect have been reported arising from the Berry curvature. Using the Boltzmann transport theory, we present a closed-form expression for the nonequilibrium distribution function which includes both the effects of the Berry curvature and Lorentz force. Using this formulation, we obtain analytical expressions for conductivity and resistivity tensors in Weyl semimetals demonstrating a non-monotonic field dependence arising from the competition between the two effects.
Weyl semimetals (WSM) exhibit chiral anomaly in their magnetotransport due to broken conservation laws. Here, we analyze the magnetotransport of WSM in the presence of the time-reversal symmetry-breaking tilt parameter. The analytical expression for the magnetoconductivity is derived in the small tilt limit using the semiclassical Boltzmann equation. We predict a planar Hall current which flows transverse to the electric field and in the plane containing magnetic and electric fields and scales linearly with the tilt parameter. A tilt-induced transverse conductivity is also present in the case …
We consider effects of spatial dispersion in noncentrosymmetric time-reversal invariant Weyl metals in the presence of a static magnetic field. In particular, we study currents that are linear in both the spatial derivatives of an applied electric field, and the static magnetic field, which are responsible for the phenomenon of gyrotropic birefringence. We show that the chiral anomaly and the chiral magnetic effect make the leading contribution to this class of phenomena in metals. We apply the obtained results to the problem of electromagnetic wave transmission through a thin slab of a Weyl s…
The recent explosion of research interest in Weyl semimetals has led to many proposed Weyl semimetal candidates and a few experimental observations of a Weyl semimetal in real materials. Through this experience, we have come to appreciate that typical Weyl semimetals host many Weyl points. For instance, the first Weyl semimetal observed in experiment, TaAs, hosts 24 Weyl points. Similarly, the Mo$_x$W$_{1-x}$Te$_2$ series, recently under study as the first Type II Weyl semimetal, has eight Weyl points. However, it is well-understood that for a Weyl semimetal without inversion symmetry but with…
A relativistic spinor with spin 3/2 is historically called Rarita-Schwinger spinor. The right- and left-handed chiral degrees of freedom for the massless Rarita-Schwinger spinor are independent and are thought of as the left- and right-Weyl fermion with helicity \pm3/2. We study three orbital spin-1/2 Weyl semimetals in the strong spin-orbital coupling limit with time reversal symmetry breaking. We find that in this limit the systems can be a J_{eff}=1/2 Weyl semimetal or a J_{eff}=3/2 semimetal, depending on the Fermi level position. The latter near Weyl points includes both degrees of freedo…
Kramers Weyl semimetals are Weyl semimetals that have Weyl points pinned at the time reversal invariant momenta. Recently it has been discovered that all chiral crystals host Weyl points at time reversal invariant momenta, so metals with chiral lattice symmetry all belong to the category of Kramers Weyl semimetals. In this work, we show that due to the chiral lattice symmetry, Kramers Weyl semimetals have the unique longitudinal magnetoelectric effect in which the charge current induced spin and orbital magnetization is parallel to the direction of the current. This feature allows Kramers Weyl…
Magnetotransport and magneto-optics experiments offer a very powerful probe for studying the physical properties of materials. Here, we investigate the second-order nonlinear magnetoconductivity of tilted type-I Weyl and multi-Weyl semimetal. In contrast to the presence of chiral anomaly in the linear response regime, we show that Weyl semimetal do not host chiral charge pumping in the nonlinear transport regime. We predict that an inversion symmetry broken and tilted Weyl semimetal can support finite longitudinal nonlinear magnetoconductivity, which is otherwise absent in untilted Weyl semime…
Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation betw…
We present a new switching mechanism that utilizes the proximity coupling between the surface spin texture of a Weyl semimetal and a superconductor, in a Weyl semimetal/superconductor/Weyl semimetal trilayer heterostructure. We show that the superconductivity in the middle layer can be fully suppressed by the surface spin texture of the Weyl semimetals in the presence of an external magnetic field, but it can be recovered again by only changing the field direction. The restoration of the middle-layer superconductivity indicates a sharp transition to a low-resistance state. This sharp switching…
Multi-band touchings such as 3-band, 6-band and 8-band touchings together with the emergence of high pseudospin fermions were predicted recently at high-symmetry points in three-dimensional space. In this paper, we propose a simple cubic model whose unit cell contains three atoms. There are 6 bands in the system due to the spin degrees of freedom. The 4-band and 2-band touchings are realized at high-symmetry points, where we derive low-energy theories, demonstrating the emergence of pseudospin-3/2 fermions and Weyl fermions, respectively. Away from the high-symmetry points, we find critical We…
We study a general phase transition between spinless topological nodal-line semimetal and Weyl semimetal phases. We classify topological nodal lines into two types based on their positions and shapes, and their phase transitions depends on their types. We show that the topological nodal-line semimetal becomes the Weyl semimetal by breaking time-reversal symmetry when the nodal lines enclose time-reversal invariant momenta (type-A nodal lines). We also discuss an effect of crystallographic symmetries determining the band structure of the topological nodal-line semimetals. Thanks to protection b…
Weyl semimetals possess low energy excitations which act as monopoles of Berry curvature in momentum space. These emergent monopoles are at the heart of the extensive novel transport properties that Weyl semimetals exhibit. The singular nature of the Berry curvature around the nodal points in Weyl semimetals allows for the possibility of large anomalous transport coefficients in zero applied magnetic field. Recently a new class, termed type-II Weyl semimetals, has been demonstrated in a variety of materials, where the Weyl nodes are tilted. We present here a study of anomalous transport in thi…
The separation of the Weyl nodes in a broken time-reversal symmetric Weyl semimetal leads to helical quasi-particle excitations at the Weyl nodes, which, when coupled with overall spin conservation allows only inter-nodal transport at the junction of the Weyl semimetal with a superconductor. This leads to an unusual periodic oscillation in the Josephson current as a function of $k_0L$, where $L$ is the length of the Weyl semimetal and $2k_0$ is the inter-nodal distance. This oscillation is robust and should be experimentally measurable, providing a direct path to confirming the existence of ch…
Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work, we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quant…
Weyl semimetals are emerging to become a new class of quantum-material platform for various novel phenomena. Especially, the Weyl orbit made from surface Fermi arcs and bulk relativistic states is expected to play a key role in magnetotransport, leading even to a three-dimensional quantum Hall effect (QHE). It is experimentally and theoretically important although yet unclear whether it bears essentially the same phenomenon as the conventional two-dimensional QHE. We discover an unconventional fully three-dimensional anisotropy in the quantum transport under magnetic field. Strong suppression …
Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phenomena. Based on first-principles calculations, we report that the chalcopyrites CuTlSe2, AgTlTe2, AuTlTe2 and ZnPbAs2 are ideal Weyl semimetals, having largely separated Weyl points (~ 0.05/A) and uncovered Fermi arcs that are amenable to experimental detections. We also construct a minimal effective model to capture the low-energy physics of this class of Weyl semimetals. Our discovery is a major step toward a perfect playground of intriguing Weyl semimetals and potential applications for low-powe…
We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have non-trivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated Doubling Theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that…
Multi-Weyl semimetals are new types of Weyl semimetals which have anisotropic non-linear energy dispersion and a topological charge larger than one, thus exhibiting a unique quantum response. Using a unified lattice model, we calculate the optical conductivity numerically in the multi-Weyl semimetal phase and in its neighboring gapped states, and obtain the characteristic frequency dependence of each phase analytically using a low-energy continuum model. The frequency dependence of longitudinal and transverse optical conductivities obeys scaling relations that are derived from the winding numb…
We experimentally compare two types of interface structures with magnetic and non-magnetic Weyl semimetals. They are the junctions between a gold normal layer and magnetic Weyl semimetal Ti$_2$MnAl, and a ferromagnetic nickel layer and non-magnetic Weyl semimetal WTe$_2$, respectively. Due to the ferromagnetic side of the junction, we investigate spin-polarized transport through the Weyl semimetal surface. For both structures, we demonstrate similar current-voltage characteristics, with hysteresis at low currents and sharp peaks in differential resistance at high ones. Despite this behavior re…
The term Weyl semimetal originates from the fact that its energy dispersion obeys a Weyl equation. However, a Weyl equation itself cannot fully describe the electron states in an actual bounded geometry. For example, the appearance of chiral surface states, which is a characteristic feature of a Weyl semimetal, cannot be captured with a Weyl equation. This indicates that some degree of freedom is lost when a Weyl equation is derived from a microscopic model of a Weyl semimetal. To overcome this difficulty, we present a framework consisting of a Weyl equation and a supplementary equation, which…
We investigate multilayer systems of a normal insulator and a Weyl semimetal. We calculate the bulk band structure and determine phase diagrams by changing the thickness of the normal insulator and that of the Weyl semimetal layer using two models; one is from the effective model for a Weyl semimetal, and the other is the lattice model. We compare the results between the two models, and found that they agree well. As a result, we find that the multilayer system shows a qualitatively different behavior depending on the stacking direction relative to the displacement vector connecting between tw…
We report the electrical transport properties for Weyl semimetal TaAs in an intense magnetic field. Series of anomalies occur in the longitudinal magnetoresistance and Hall signals at ultra-low temperatures when the Weyl electrons are confined into the lowest Landau level. These strongly temperature-dependent anomalies are ascribed to the electron-hole pairing instability. Our measurements show that the Weyl semimetal TaAs in the ultraquantum regime provides a good platform for studying electron-electron interaction in topological nontrivial semimetals.
We theoretically study the axial current $\bm{j}_5$ (defined as the difference between the charge current with opposite chirality) in doped Weyl semimetal using a Green's function technique. We show that the axial current is controlled by the magnetization dynamics in a magnetic insulator attached to a Weyl semimetal. We find that the induced axial current can be detected by using ferromagnetic resonance or the inverse spin Hall effect and can be converted into charge current with no accompanying energy loss. These properties make Weyl semimetal advantageous for application to low-consumption …
The propagation of light in Weyl semimetal films is analyzed. The magnetic family of these materials is known by anomalous Hall effect, which, being enhanced by the large Berry curvature, allows one to create strong gyrotropic and nonreciprocity effects without external magnetic field. The existence of nonreciprocal waveguide electromagnetic modes in ferromagnetic Weyl semimetal films in the Voigt configuration is predicted. Thanks to the strong dielectric response caused by the gapless Weyl spectrum and the large Berry curvature, ferromagnetic Weyl semimetals combine the best waveguide proper…
We generalize the concept of three-dimensional topological Weyl semimetal to a class of five dimensional (5D) gapless solids, where Weyl points are generalized to Weyl surfaces which are two-dimensional closed manifolds in the momentum space. Each Weyl surface is characterized by a U(1) second Chern number $C_2$ defined on a four-dimensional manifold enclosing the Weyl surface, which is equal to its topological linking number with other Weyl surfaces in 5D. In analogy to the Weyl semimetals, the surface states of the 5D metal take the form of topologically protected Weyl fermion arcs, which co…
Physicists have discovered a novel topological semimetal, the Weyl semimetal, whose surface features a non-closed Fermi surface while the low energy quasiparticles in the bulk emerge as Weyl fermions. Here they share a brief review of the development and present perspectives on the next step forward.
Isolated Weyl cones in a disordered environment do not show the phenomenon of Anderson localization due to the abscence of backscattering processes. However, besides the conventional three dimensional diffusive metal, an additional semimetallic phase can form. In this paper we study the effect of tilt on the physics of disorder in isolated Weyl cones. Our main finding is that while the semimetallic phase remains a stable phase, tilt decreases the size of the semimetallic region. Conversely, disorder increases the effective tilt of the quasiparticle excitations.
We study two Weyl semimetal generalizations in five dimensions (5d) which have Yang monopoles and linked Weyl surfaces in the Brillouin zone, respectively, and carry the second Chern number as a topological number. In particular, we show a Yang monopole naturally reduces to a Hopf link of two Weyl surfaces when the $\mathbf{TP}$ (time-reversal combined with space-inversion) symmetry is broken. We then examine the phase transition between insulators with different topological numbers in 5d. In analogy to the 3d case, 5d Weyl semimetals emerge as intermediate phases during the topological phase …
We investigate the tunneling of the quasiparticles arising in multi-Weyl semimetals through a barrier consisting of both electrostatic and vector potentials, existing uniformly in a finite region along the transmission axis. The dispersion of a multi-Weyl semimetal is linear in one direction (say, $k_z$), and proportional to $k_\perp^J$ in the plane perpendicular to it (where $k_\perp =\sqrt{k_x^2+k_y^2}$). Hence, we study the cases when the barrier is perpendicular to $k_z$ and $k_x$, respectively. For comparison, we also state the corresponding results for the Weyl semimetal.
In this work we introduce a thermal magnetotorsional effect (TME) as a novel topological response in magnetic Weyl semimetals. We predict that magnetization gradients perpendicular to the Weyl node separation give rise to temperature gradients depending only on the local positions of the Weyl nodes. The TME is a consequence of magnetization-induced effective torsional spacetime geometry and the finite temperature Nieh-Yan anomaly. Similarly to anomalous Hall effect and chiral anomaly, the TME has a universal material-independent form. We predict that the TME can be observed in magnetic Weyl se…
We consider a Weyl semimetal with two nodes and derive the scattering Hamiltonian in the presence of a boundary at $z=0$. We compute the photoemission spectrum and demonstrate the presence of the Fermi arcs which connect the two nodes. In the presence of an electric field parallel to the scattering surface we observe the one dimensional chiral anomaly.
The equality between the spectral, directional emittance and absorptance of an object under local thermal equilibrium is known as Kirchhoff's law of radiation. The breakdown of Kirchhoff's law of radiation is physically allowed by breaking time reversal symmetry and can open opportunities for nonreciprocal light emitters and absorbers. Large anomalous Hall conductivity and angle recently observed in topological Weyl semimetals, particularly type-I magnetic Weyl semimetals and type-II Weyl semimetals, are expected to create large nonreciprocal electromagnetic wave propagation. In this work, we …
Searching for the signature of the violation of chiral charge conservation in solids has inspired a growing passion on the magneto-transport in topological semimetals. One of the open questions is how the conductivity depends on magnetic fields in a semimetal phase when the Fermi energy crosses the Weyl nodes. Here, we study both the longitudinal and transverse magnetoconductivity of a topological Weyl semimetal near the Weyl nodes with the help of a two-node model that includes all the topological semimetal properties. In the semimetal phase, the Fermi energy crosses only the 0th Landau bands…
The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature. Such a topological semimetal features a novel type of anomalous surface state, the Fermi arc, which connects a pair of Weyl nodes through the boundary of the crystal. Here, we present theoretical calculations of the quasi-particle interference (QPI) patterns that arise from the surface states including the topological Fermi arcs in the Weyl semimetals TaAs and NbP. Most importantly, we discover that the QPI exhibits termination-points that are fingerprints of the Weyl nodes in t…
We identify a Weyl semimetal state in an inversion breaking, stoichiometric compound strontium silicide, SrSi$_2$, with many new and novel properties that are distinct from the TaAs family. We theoretically show that SrSi$_2$ is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral topological charge of 2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror s…
Weyl semimetals host linear energy dispersions around Weyl nodes, as well as monopoles of Berry curvature in momentum space around these points. These features give rise to unique transport signatures in a Weyl semimetal, such as transverse transport without an applied magnetic field, known as anomalous transport. The type-II Weyl semimetal, recently experimentally demonstrated in several materials, is classified by a tilting of the Weyl nodes. This paper provides a theoretical study on thermoelectric transport in time-reversal breaking type-II Weyl semimetals. Our results examine the balance …
We study the current-induced torques in asymmetric magnetic tunnel junctions containing a conventional ferromagnet and a magnetic Weyl semimetal contact. The Weyl semimetal hosts chiral bulk states and topologically protected Fermi arc surface states which were found to govern the voltage behavior and efficiency of current-induced torques. We report how bulk chirality dictates the sign of the non-equilibrium torques acting on the ferromagnet and discuss the existence of large field-like torques acting on the magnetic Weyl semimetal which exceeds the theoretical maximum of conventional magnetic…
