Gapless Weyl semimetals (WSMs) are a novel class of topological materials that host massless Weyl fermions as their low-energy excitations. When the Weyl cone is tilted, the Lorentz invariance is broken and the Lifshitz transition drives the system from type-I WSMs into type-II WSMs. Here, based on the lattice model, we perform a systematic numerical study of the effect of on-site disorder on the diagonal magnetoconductivity in tilted WSMs.We use the self-consistent Born approximation to calculate the disorder-induced self-energy and then apply the Kubo-Streda formula to calculate the diagonal magnetoconductivity. For the transverse magnetoconductivity σ_xx, the disorder is found to exhibit distinct effects in the quantum limit regime and in the quantum oscillation regime of type-I WSMs, which could be understood from Einstein's relationship.With strong disorder, σ_xx shows a linear relation with the inverse magnetic field 1/B , which exhibits certain robustness to both the Fermi energy and the Weyl cone tilting. For the longitudinal magnetoconductivity σ_zz , the strong disorder can break the positive magnetoconductivity as well as the Shubnikov-de Haas oscillations.By analyzing the spectral function, we find that the chiral anomaly is still preserved at strong disorder even when the Weyl cone is overtilted, as there is no gap opening around the Weyl nodes. The implications of our results for experiments are discussed.
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…
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…
Type-II Weyl semimetals are characterized by the tilted linear dispersion in the low-energy excitations, mimicking Weyl fermions but with manifest violation of the Lorentz invariance, which has intriguing quantum transport properties. The magnetoconductivity of type-II Weyl semimetals is investigated numerically based on lattice models in parallel electric and magnetic field. We show that in the high-field regime, the sign of the magnetoconductivity of an inversion-symmetry-breaking type-II Weyl semimetals depends on the direction of the magnetic field, whereas in the weak field regime, positi…
Weyl semimetals are three-dimensional topological states of matter, in a sense that they host paired monopoles and antimonopoles of Berry curvature in momentum space, leading to the chiral anomaly. The chiral anomaly has long been believed to give a positive magnetoconductivity or negative magnetoresistivity in strong and parallel fields. However, several recent experiments on both Weyl and Dirac topological semimetals show a negative magnetoconductivity in high fields. Here, we study the magnetoconductivity of Weyl and Dirac semimetals in the presence of short-range scattering potentials. In …
We study the transport of the fermions with a small mass in the presence of Coulomb impurities, which could be realized in slightly distorted Dirac semimetals. Using the semiclassical Boltzmann equation, we derive the relaxation times for two kinds of intra-cone transition process. One is due to the effect of mass, and the other is due to the excited states in Landau levels under the weaker magnetic field. Hence we derive the mass dependence and the magnetic field dependence of the longitudinal magnetoconductivity in the presence of parallel electric and magnetic fields.
Weyl semimetals (WSMs) host charged Weyl fermions as emergent quasiparticles. We develop a unified analytical theory for the anomalous positive longitudinal magnetoconductance (LMC) in a WSM, which bridges the gap between the classical and ultra-quantum approaches. More interestingly, the LMC is found to exhibit periodic-in-$1/B$ quantum oscillations, originating from the oscillations of the nonequilibrium chiral chemical potential. The quantum oscillations, superposed on the positive LMC, are a remarkable fingerprint of a WSM phase with chiral anomaly, whose observation is a valid criteria fo…
Recently, a class of Dirac semimetals, such as \textrm{Na}$_{\mathrm{3}}% $\textrm{Bi} and \textrm{Cd}$_{\mathrm{2}}$\textrm{As}$_{\mathrm{3}}$, are discovered to carry $\mathbb{Z}_{2}$ monopole charges. We present an experimental mechanism to realize the $\mathbb{Z}_{2}$ anomaly in regard to the $\mathbb{Z}_{2}$ topological charges, and propose to probe it by magnetotransport measurement. In analogy to the chiral anomaly in a Weyl semimetal, the acceleration of electrons by a spin bias along the magnetic field can create a $\mathbb{Z}_{2}$ charge imbalance between the Dirac points, the relaxa…
We study the positive longitudinal magnetoconductivity (LMC) and planar Hall effect as emergent effects of the chiral anomaly in Weyl semimetals, following a recent-developed theory by integrating the Landau quantization with Boltzmann equation. It is found that, in the weak magnetic field regime, the LMC and planar Hall conductivity (PHC) obey $\cos^{6}θ$ and $\cos^{5}θ\sin θ$ dependences on the angle $θ$ between the magnetic and electric fields. For higher magnetic fields, the LMC and PHC cross over to $\cos^{2}θ$ and $\cosθ\sinθ$ dependences, respectively. Interestingly, the PHC could exhib…
Using the Feynman diagram techniques, we derive the finite-temperature conductivity and magnetoconductivity formulas from the quantum interference and electron-electron interaction, for a three-dimensional disordered Weyl semimetal. For a single valley of Weyl fermions, we find that the magnetoconductivity is negative and proportional to the square root of magnetic field at low temperatures, as a result of the weak antilocalization. By including the contributions from the weak antilocalization, Berry curvature correction, and Lorentz force, we compare the calculated magnetoconductivity with a …
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 present the detailed analyses of magneto-conductivities in a Weyl semimetal within Born and self-consistent Born approximations. In the presence of the charged impurities, the linear magnetoresistance can happen when the charge carriers are mainly from the zeroth (n=0) Landau level. Interestingly, the linear magnetoresistance is very robust against the change of temperature, as long as the charge carriers mainly come from the zeroth Landau level. We denote this parameter regime as the high-field regime. On the other hand, the linear magnetoresistance disappears once the charge carriers from…
We investigate the effect of disorder on the Landau levels (LLs) in tilted three dimensional Weyl semimetals (WSMs) when a magnetic field is present. Based on the minimum lattice model and by using the exact diagonalization and Kubo's formula, we numerically calculate the Hall conductivity and the density of states (DOS), from which several striking signatures are found to distinguish type-I WSMs from type-II WSMs: the first is the response of the Hall conductivity to the Fermi energy around the band center in clean limit, the second is the performance of the Hall conductivity to disorder, whe…
Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and nega…
Weyl semimetal is a recently discovered state of quantum matter, which generally possesses tilted energy dispersion. Here, we investigate the electron tunneling through a Weyl semimetal p-n-p junction. The angular dependence of electron tunneling exhibits an anomalous profile such that perfect transmission angles are shifted along the direction of the tilt. Coupling of the tilted dispersion and electrical potential within the barrier region gives rise to a transverse momentum shift, which is analogous to the transverse Lorentz displacement induced by magnetic barriers.
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 propose the linear and nonlinear planar Hall effect (PHE) in tilted Weyl semimetals in the presence of an in-plane magnetic and electric field, where the field-induced Berry connection (FBC) plays a key role. We show that the PHE is ascribed to the quantum metric, distinct from the well-known chiral anomaly-induced PHE arising from the Berry curvature. Using a tilting vector to describe the model, we demonstrate the constrains on the linear and nonlinear PHE by the tilting directions. The linear PHE is intrinsic that is determined by the topological properties of energy bands, whereas the n…
Using first principles pseudopotential density functional theory calculations, we find that terminating zigzag graphene nanoribbons (ZGNR) with monovalent alkali atoms at a reduced concentration has a dramatic impact on their properties. In particular, using sodium atoms for the saturation of ZGNR edges at half the concentration of edge-carbon atoms make it a one dimensional, perfect semimetal, where the valance and conduction bands meet at only a single, Dirac-like point. Unlike pristine graphene, the Dirac-"cones" of Na-ZGNR is not symmetric with respect to wave vector, but rather it is tilt…
We investigate the tunneling conductance of Weyl semimetal with tilted energy dispersion by considering electron transmission through a p-n-p junction with one-dimensional electric and magnetic barrier. In the presence of both electric and magnetic barriers, we found that a large conductance gap can be produced by the aid of tilted energy dispersion without a band gap. The origin of this effect is the shift of the electrons wave-vector at barrier boundaries caused by i) the pseudo-magnetic field induced by electrical potential, i.e., a newly discovered feature that is only possible in the mate…
We study the effects of pseudo-magnetic fields on Weyl semimetals with over-tilted Weyl cones, or type II cones. We compare the phenomenology of the resulting pseudo-Landau levels in the type II Weyl semimetal to the known case of type I cones. We predict that due to the nature of the chiral Landau level resulting from a magnetic field, a pseudo-magnetic field, or their combination, the optical conductivity can be utilized to detect a type II phase and deduce the direction of the tilt. Finally, we discuss ways to engineer homogeneous and inhomogeneous type II semimetals via generalizations of …
The Onsager-Casimir reciprocal relations are a fundamental symmetry of nonequilibrium statistical systems. Here we study an unusual chirality-dependent Hall effect in a tilted Weyl semimetal Co$_3$Sn$_2$S$_2$ with broken time reversal symmetry. It is confirmed that the reciprocal relations are satisfied. Since two Berry curvature effects, an anomalous velocity and a chiral chemical potential, contribute to the observed Hall effect, the reciprocal relations suggest their intriguing connection.
We have generalized a quasiclassical model for Weyl semimetals with a tilted band in the presence of an externally applied magnetic field. This model is applicable to ballistic, moderately disordered, and samples containing a high density of nonmagnetic impurities. We employ this formalism and show that a self-biased supercurrent, creating a ϕ0-junction, can flow through a triplet channel in Weyl semimetals. Furthermore, our results demonstrate that multiple supercurrent reversals are accessible through varying junction thickness and parameters characterizing Weyl semimetals. We discuss the in…
We investigate the optical activity of tilted nodal loop semimetals. We calculate the full conductivity matrix for a band structure containing a nodal loop with possible tilt in the $x-y$ plane, which allows us to study the Kerr rotation and ellipticity both for a thin film and a bulk material. We find signatures in the Kerr signal that give direct information about the tilt velocity and direction, the radius of the nodal loop and the internal chemical potential of the system. These findings should serve as guide to understanding optical measurements of nodal loop semimetals and as an addition…
We study the conductivity of two-dimensional graphene-type materials with tilted cones as well as their three-dimensional Weyl counterparts and show that a covariant quantum Boltzmann equation is capable of providing an accurate description of these materials' transport properties. The validity of the covariant Boltzmann approach is corroborated by calculations within the Kubo formula. We find a strong anisotropy in the conductivities parallel and perpendicular to the tilt direction upon increase of the tilt parameter $η$, which can be interpreted as the boost parameter of a Lorentz transforma…
The Weyl semimetal is a new quantum state of topological semimetal, of which topological surface states -- the Fermi arcs exist. In this paper, the Fermi arcs in Weyl semimetals are classified into two classes -- class-1 and class-2. Based on a tight-binding model, the evolution and transport properties of class-1/2 Fermi arcs are studied via the tilting strength of the bulk Weyl cones. The (residual) anomalous Hall conductivity of topological surface states is a physical consequence of class-1 Fermi arc and thus class-1 Fermi arc becomes a nontrivial topological property for hybrid or type-II…
Although Lorentz invariance forbids the presence of a term that tilts the energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not forbidden and, in fact, generic for condensed matter realizations of Weyl semimetals. We here investigate the combined effect of such a tilted Weyl dispersion and the presence of potential disorder. In particular, we address the influence of a tilt on the disorder-induced phase transition between a quasi-ballistic phase at weak disorder, in which the disorder is an irrelevant perturbation, and a diffusive phase at strong disorder. Our main resul…
From the Kubo formula for transport in a tilted Weyl semimetal we calculate the absorptive part of the dynamic conductivity for both right and left handed circular polarized light. These depend on the real part of the longitudinal conductivity and the imaginary part of the transverse (Hall) conductivity. We include the effect of the chiral anomaly which pumps charge from negative to positive chirality node when the usual ${\bs E}\cdot{\bs B}$ term is included in the electrodynamics and obtain analytic expressions. To calculate the Hall angle we further provide expressions for the imaginary par…
We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorder-induced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to …
Tilting the Weyl cone breaks the Lorentz invariance and enriches the Weyl physics. Here, we report the observation of a magnetic-field-antisymmetric Seebeck effect in a tilted Weyl semimetal, Co$_3$Sn$_2$S$_2$. Moreover, it is found that the Seebeck effect and the Nernst effect are antisymmetric in both the in-plane magnetic field and the magnetization. We attribute these exotic effects to the one-dimensional chiral anomaly and phase space correction due to the Berry curvature. The observation is further reproduced by a theoretical calculation, taking into account the orbital magnetization.
Topological Weyl semimetals can host Weyl nodes with monopole charges in momentum space. How to detect the signature of the monopole charges in quantum transport remains a challenging topic. Here, we reveal the connection between the parity of monopole charge in topological semimetals and the quantum interference corrections to the conductivity. We show that the parity of monopole charge determines the sign of the quantum interference correction, with odd and even parity yielding the weak anti-localization and weak localization effects, respectively. This is attributed to the Berry phase diffe…
Electric, thermal, and thermoelectric magnetoconductivity for Weyl/multi-Weyl semimetals in planar Hall set-ups induced by the combined effects of topology and strain
Ruderman-Kittel-Kasuya-Yosida (RKKY) is an essential long range magnetic interaction between magnetic impurities or magnetic layered structures, the magnitude of which oscillates with the distance ($\mathrm{R}$) between them. We have investigated the RKKY interaction between two magnetic impurities in both time-reversal and inversion symmetry broken Weyl semimetals (WSMs) where the energy dispersion is tilted in momentum space and the momentum of the conduction electron is locked with the pseudo-spin. Two important features are revealed, firstly, at the small tilt limit, we show that the RKKY …
We study the dynamic chiral magnetic conductivity (DCMC) and natural optical activity in an inversion-broken tilted Weyl semimetal (WSM). Starting from the Kubo formula, we derive the analytical expressions for the DCMC for two different directions of the incident electromagnetic wave. We show that the angle of rotation of the plane of polarization of the transmitted wave exhibits remarkable anisotropic behavior and is larger along the tilt direction. This striking anisotropy of DCMC which results in anisotropic optical activity and rotary power, can be experimentally observed as a topological…
A new type of angular oscillations of the high-frequency conductivity for conductors with a band-contact line has been predicted. The effect is caused by groups of charge carriers near the self-intersection points of the Fermi surface, where the electron energy spectrum is near-linear and can be described by anisotropic Dirac cone model. The amplitude of the resonance peaks satisfies the simple sum rule. The ease in changing the degree of anisotropy of the Dirac cone due to the angle of inclination of the magnetic field makes the considered type of oscillations attractive for experimental obse…
We predict the existence of a novel long-lived gapless plasmon mode in a type-II Dirac semimetal (DSM). This gapless mode arises from the out-of-phase oscillations of the density fluctuations in the electron and the hole pockets of a type-II DSM. It originates beyond a critical wave-vector along the direction of the tilt axis, owing to the momentum separation of the electron and hole pockets. A similar out-of-phase plasmon mode arises in other multi-component charged fluids as well, but generally it is Landau damped and lies within the particle-hole continuum. In the case of a type-II DSM, the…
We calculate the A.C. optical response to circularly polarized light of a Weyl semimetal (WSM) with varying amounts of tilt of the Dirac cones. Both type-I and II (overtilted) WSM are considered in a continuum model with broken time reversal (TR) symmetry. The Weyl nodes appear in pairs of equal energies but of opposite momentum and chirality. For type-I the response of a particular node to right (RHP) and left (LHP) hand polarized light are distinct only in a limited range of photon energy $Ω$, $\frac{2}{1+C_{2}/v}<\fracΩμ<\frac{2}{1-C_{2}/v}$ with $μ$ the chemical potential and $C_{2}$ the t…
Spin lattice relaxation rate is investigated for 3D tilted cone Weyl semimetals (TCWSMs). The nuclear spin relaxation rate is presented as a function of temperature and tilt parameter. We find that the relaxation rate behaves as $(1-ζ^2)^{-α}$ with $α\approx 9$ where $0\le ζ< 1$ is the tilt parameter. We demonstrate that such a strong enhancement for $ζ\lesssim 1$ that gives rise to very fast relaxation rates, is contributed by the combined effect of a new hyperfine interactions arising from the tilt itself, and the anisotropy of the ellipsoidal Fermi surface. Extracting an effective density o…
The electronic and optical conductivities for anisotropic tilted Dirac semimetals are calculated using the Kubo formula. As in graphene, it is shown that the minimal conductivity is sensitive to the order in which the temperature, frequency and scattering limits are taken. Both intraband and interband scattering are found to be direction dependent. In the high frequency and low temperature limit, the conductivities do not depend on frequency and are weighted by the anisotropy in such a way that the geometrical mean $\sqrt{σ_{xx}σ_{yy}}$ of the conductivity is the same as in graphene. This resu…
We study the anomalous Nernst and thermal Hall effects in a linearized low-energy model of a tilted Weyl semimetal, with two Weyl nodes separated in momentum space. For inversion symmetric tilt, we give analytic expressions in two opposite limits: for a small tilt, corresponding to a type-I Weyl semimetal, the Nernst conductivity is finite and independent of the Fermi level, while for a large tilt, corresponding to a type-II Weyl semimetal, it acquires a contribution depending logarithmically on the Fermi energy. This result is in a sharp contrast to the nontilted case, where the Nernst respon…
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 investigate high-order harmonic generations (HHGs) under the comparison of Weyl cones in two types. Due to the hyperboloidal electron pocket structure, strong noncentrosymmetrical generations in high orders are observed around a single type-II Weyl point, especially at frequency zero. Such remarkable DC signal is proved to have attributions from the intraband transition after spectral decomposition. Under weak pulse electric field , the linear optical response of a non-tilted Weyl cone is consistent with the Kubo theory. With more numerical simulations, we conclude the non-zero chemical pot…
We analyze the effect of the tilt on the transverse thermoelectric coefficient of Weyl semimetals in the \emph{conformal} limit, i.e., zero temperature and zero chemical potential. Using the Kubo formalism, we find a nonmonotonic behavior of the thermoelectric conductivity as a function of the tilt perpendicular to the magnetic field, and a linear behavior when the tilt is aligned to the magnetic field. An ``axial Nernst" current (chiral currents counter propagating perpendicularly to the magnetic field and the temperature gradient) is generated in inversion symmetric Weyl materials when the t…
We suggest the possibility of a linear magnetochiral effect in time reversal breaking Weyl semimetals. Generically the magnetochiral effect consists in a simultaneous linear dependence of the magnetotransport coefficients with the magnetic field and a momentum vector. This simultaneous dependence is allowed by the Onsager reciprocity relations, being the separation vector between the Weyl nodes the vector that plays such role. As a side consequence, we find a non vanishing positive longitudinal magnetoconductivity at Fermi energies above the point where the chirality of the Weyl nodes is globa…
The recent discovery of magnetic Weyl semimetal Co3Sn2S2 opens up new avenues for research into the interactions between topological orders, magnetism, and electronic correlations. Motivated by the observations of large anomalous Hall effect because of large Berry curvature, we investigate another Berry curvature-induced phenomenon, the anomalous thermal Hall effect in Co3Sn2S2. We study it with and without strain, using a Wannier tight-binding Hamiltonian derived from first principles density functional theory calculations. We first identify this material as a tilted type-I Weyl semimetal bas…
We study the effective symmetry profiles of superconducting pair correlations and the flow of charge supercurrent in ballistic Weyl semimetal systems with a tilted dispersion relation. Utilizing a microscopic method in the ballistic regime and starting from both opposite-pseudospin and equal-pseudospin phonon-mediated opposite-spin electron-electron couplings, we calculate the anomalous Green's function to study various superconducting pair correlations that Weyl semimetal systems may develop. The momentum-space profile reveals that by properly manipulating the parameters of Weyl semimetal sys…
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…
