We theoretically investigate the spin Hall conductivity (SHC) in topological Dirac semimetals (TDSMs) whose Dirac points are protected by rotational symmetry. On the basis of a general phase diagram of the system with time-reversal, inversion and four-fold rotational symmetries, we reveal that the SHC is sensitive to the phase to which the system belong. The phase and the SHC are characterized by the mirror Chern numbers and the presence or absence of gapless bulk Dirac points. It is also found that the representative TDSM Cd$_3$As$_2$ supports a large and negative SHC $σ_{xy}^z\sim -10^4 (\hbar/e) (Ω.\textrm{m})^{-1}$. The principle behind the dependency of SHC on the phase diagram is also explained.
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 investigate the magneto-optical response of double Weyl semimetals whose energy dispersion is intrinsically anisotropic. We find that in the presence of a magnetic field, the most salient feature of the optical conductivity is a series of resonant peaks with the corresponding frequencies scaling linearly with the strength of the magnetic field. In addition, the optical conductivity is found to be anisotropic, with two of the three longitudinal components residing at a linear background and the remaining one at a constant background. The effects of chemical potential, temperature, impurity s…
Weyl semimetals are a topological phase of matter that have drawn recent interest and have been suggested as a possible phase of the pyrochlore irridates, among other materials. Here, we compute the magneto-optical response of an isolated Weyl point. We find that the conductivity is a series of asymmetric peaks lying on top of a linear background. We find additional features in the conductivity that are explained by the underlying Landau level structure. We show that weak disorder tends to blur out the peaks, but they still show up as measurable oscillations on a linear background.
We calculate the surface dc conductivity of Weyl semimetals and show that it contains an anomalous contribution in addition to a Drude contribution from the Fermi arc. The anomalous part is independent of the surface scattering time, and appears at nonzero temperature and doping (away from the Weyl nodes), increasing quadratically with both with a universal ratio of coefficients. Microscopically, it results from the contribution of the gapless bulk to the surface conductivity. We argue that this can be interpreted as the conductivity of an effective interacting surface fluid that coexists with…
We investigate the dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi. In the semimetal, the band structure holds point nodes at the $Γ$ and R points in the Brillouin zone and more than three bands touch at the nodes. Around the nodes, electronic states are predicted to be described as the multifold chiral fermion, a new class of fermion. We show that the dynamical conductivity exhibits a characteristic spectrum corresponding to the band structure and the chiral fermionic states. The dynamical conductivity of CoSi is calculated as a function of photon energy by using the …
A multifold Hopf semimetal is a topological point node semimetal possessing an anisotropy in the internal electronic structure, e.g., the dipole structure of the Berry curvature. In this paper, the unique features of threefold Hopf semimetals in terms of the optical conductivity are theoretically investigated with a minimal theoretical model by using linear response theory for a linearly polarized photon. The frequency spectrum of the optical conductivity shows an anisotropic dependence on the polarization angle of the incident photon even if the electronic band structure is completely isotrop…
We study the transport properties in nodal line semimetals with short-ranged impurity potentials at zero temperature. By computing the Drude conductivity and the corrections from the interference of particle and hole trajectories, we find that the electrons are localized in directions both parallel and perpendicular to the plane of nodal ring. We further calculate the conductivity in a weak magnetic field, and find that the perpendicular magnetic field totally destroys the weak localization gives a positive quantum interference correction, which is similar to the result in Weyl semimetals. But…
We propose an unconventional type of Hall effect in a topological Dirac semimetal with ferromagnetic electrodes. The topological Dirac semimetal itself has time-reversal symmetry, whereas attached ferromagnetic electrodes break it, causing the large Hall response. This induced Hall effect is a characteristic of the helical surface/edge states that arise in topological materials, such as topological Dirac semimetals or quantum spin Hall insulators. We compute the Hall conductance/resistance and the Hall angle by using a lattice model with four-terminal geometry. For topological Dirac semimetals…
In this paper, we numerically study the magnetic transport properties of disordered Weyl semimetals (WSM) in the ultra-quantum limit. We find a positive magnetic conductivity for the long-range disorder, although the system tends to have negative magnetic conductivity for the weak short-range disorder. Remarkably, for long-range disorder, such a positive magnetic conductivity cannot be described by the semiclassical Boltzmann transport theory even in the weak disorder limit, and the back-scattering assisted by the high Landau levels is always important. Our results have significant implication…
In addition to the well known chiral anomaly, Dirac semimetals have been argued to exhibit mirror anomaly, close analogue to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular step-like anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized theory), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the li…
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 physics of massless relativistic quantum particles has recently arisen in the electronic properties of solids following the discovery of graphene. Around the accidental crossing of two energy bands, the electronic excitations are described by a Weyl equation initially derived for ultra-relativistic particles. Similar three and four band semimetals have recently been discovered in two and three dimensions. Among the remarkable features of graphene are the characterization of the band crossings by a topological Berry winding, leading to an anomalous quantum Hall effect, and a finite minimal …
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 study the frequency-dependent conductivity of nodal line semimetals (NLSMs), focusing on the effects of carrier density and energy dispersion on the nodal line. We find that the low-frequency conductivity has a rich spectral structure which can be understood using scaling rules derived from the geometry of their Dupin cyclide Fermi surfaces. We identify different frequency regimes, find scaling rules for the optical conductivity in each, and demonstrate them with numerical calculations of the inter- and intraband contributions to the optical conductivity using a low-energy model for a gener…
Magneto-optical studies of Weyl semimetals have been proposed as a versatile tool for observing low-energy Weyl fermions in candidate materials including the chiral Landau level. However, previous theoretical results have been restricted to the linearized regime around the Weyl node and are at odds with experimental findings. Here, we derive a closed form expression for the magneto-optical conductivity of generic Weyl semimetals in the presence of an external magnetic field aligned with the tilt of the spectrum. The systems are taken to have linear dispersion in two directions, while the tilti…
We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its bandstructure. This particular type of Weyl semimetal has a finite anomalous Hall conductivity, chiral edge states, and occurs as an intermediate phase b…
Motivated by recent transport experiments, we theoretically study the quantum Hall effect in topological semimetal films. Owing to the confinement effect, the bulk subbands originating from the chiral Landau levels establish energy gaps that have quantized Hall conductance and can be observed in relatively thick films. We find that the quantum Hall state is strongly anisotropic for different confinement directions not only due to the presence of the surface states but also because of the bulk chiral Landau levels. As a result, we re-examine the quantum Hall effect from the surface Fermi arcs a…
Typical Weyl semimetals host chiral surface states and hence show an anomalous Hall response. Although a Weyl semimetal phase is known to be robust against weak disorder, the influence of disorder on chiral states is not fully clarified so far. We study the behavior of such chiral states in the presence of disorder and its consequences on an anomalous Hall response, focusing on a thin slab of Weyl semimetal with chiral surface states along its edge. It is shown that weak disorder does not disrupt chiral edge states but crucially affects them owing to the renormalization of a mass parameter: th…
We investigate the topological phase derived by time-reversal breaking fields in a nonsymmorphic symmetry-protected two-dimensional Dirac semimetal. When the nonsymmorphic symmetry is preserved even in the presence of the field, the two-dimensional electronic states change into two distinct topological phases with the insulating gap. One phase is well-known as quantum Hall states with chiral edge modes accompanying the Hall current, but the other one is an unconventional topological phase with helical edge modes in the absence of time-reversal symmetry.
We theoretically study the circularly polarized light-induced Floquet state in line-node semimetals with time-reversal symmetry and inversion symmetry. It is found that the Floquet state can show the photovoltaic anomalous Hall effect when an applied circularly polarized light gaps out the line node in the bulk and leave Weyl point nodes. The Hall conductivity is sensitive to the location of Fermi level: When the Fermi level locates at the node, the Hall conductivity depends on the radius of line node and is nearly independent of the intensity of light. Away from the line node, the Hall conduc…
Weyl semimetals are known to host massless surface states called Fermi arcs. These Fermi arcs are the manifestation of the bulk-edge correspondence in topological matter and thus are analogous to the topological chiral surface states of topological insulators. It has been shown that the latter, depending on the smoothness of the surface, host massive Volkov-Pankratov(VP) states that coexist with the chiral ones. Here, we investigate these VP states in the framework of Weyl semimetals, namely their density of states and magneto-optical response. We find the selection rules corresponding to opti…
Among different topological and related phases of condensed matter, nodal semimetals occupy a special place - the electronic band topology in these materials is related to three-dimensional bulk, rather than to surface, states. A great variety of different realizations of electronic band crossings (the nodes) leads to a plethora of different electronic properties, ranging from the chiral anomaly to solid-state realizations of a black-hole horizon. The different nodal phases have similar low-energy band structure and quasiparticle dynamics, which both can be accessed experimentally by a number …
In this work, we propose a ferromagnetic Bi$_2$Se$_3$ as a candidate to hold the coexistence of Weyl- and nodal-line semimetal phases, which breaks the time reversal symmetry. We demonstrate that the type-I Weyl semimetal phase, type-I-, type-II- and their hybrid nodal-line semimetal phases can arise by tuning the Zeeman exchange field strength and the Fermi velocity. Their topological responses under U(1) gauge field are also discussed. Our results raise a new way for realizing Weyl and nodal-line semimetals and will be helpful in understanding the topological transport phenomena in three-dim…
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…
The interband optical response of a three-dimensional Dirac cone is linear in photon energy ($Ω$). Here, we study the evolution of the interband response within a model Hamiltonian which contains Dirac, Weyl and gapped semimetal phases. In the pure Dirac case, a single linear dependence is observed, while in the Weyl phase, we find two quasilinear regions with different slopes. These regions are also distinct from the large-$Ω$ dependence. As the boundary between the Weyl (WSM) and gapped phases is approached, the slope of the low-$Ω$ response increases, while the photon-energy range over whic…
We experimentally investigate a non-linear Hall effect for three-dimensional WTe$_2$ and Cd$_3$As$_2$ single crystals, representing Weyl and Dirac semimetals, respectively. We observe finite second-harmonic Hall voltage, which depends quadratically on the longitudinal current in zero magnetic field. Despite this observation well corresponds to the theoretical predictions, only magnetic field dependence allows to distinguish the non-linear Hall effect from a thermoelectric response. We demonstrate that second-harmonic Hall voltage shows odd-type dependence on the direction of the magnetic field…
We investigate the 3D quantum Hall effect in Weyl semimetals and elucidate a global picture of the edge states. The edge states hosting 3D quantum Hall effect are combinations of Fermi arcs and chiral bulk Landau levels parallel to the magnetic field. The Hall conductance, $σ_{xz}^H$, shows quantized plateaus at Weyl nodes while tuning the magnetic field. However, the chiral Landau levels manipulate the quantization of Weyl orbits, especially under a tilted magnetic field, and the resulting edge states lead to distinctive Hall transport phenomena. A tilted magnetic field contributes an intrins…
The quantum-limit Hall effect at $ν= nh/eB\sim O(1)$ that hosts a variety of exotic quantum phenomena requires demanding strong magnetic field $B$ and low carrier density $n$. We propose to realize quantum-limit Hall effect even in the presence of large carrier density residues $n_e$ and $n_h$ relative to the magnetic field $B$ in topological semimetals, where a single Fermi surface contour allow both electron-type and hole-type carriers and approaches charge neutrality as $n_e\sim n_h$. The underlying filling factor $ν= |n_e-n_h|h/eB$ explicitly violates the Onsager's relation for quantum osc…
We show that an electric field applied to a strained topological Dirac semimetal, such as Na3Bi and Cd3As2, induces a spin Hall current that is quadratic in the electric field. By regarding the strain as an effective "axial magnetic field" for the Dirac electrons, we investigate the electron and spin transport semiclassically in terms of the chiral kinetic theory. The nonlinear spin Hall effect arises as the cross effect between the regular Hall effect driven by the axial magnetic field and the anomalous Hall effect coming from the momentum-space topology. It provides an efficient way to gener…
We generalize a semiclassical theory and use the argument of angular momentum conservation to examine the ballistic transport in lightly-doped Weyl semimetals, taking into account various phase-space Berry curvatures. We predict universal transverse shifts of the wave-packet center in transmission and reflection, perpendicular to the direction in which the Fermi energy or velocities change adiabatically. The anomalous shifts are opposite for electrons with different chirality, and can be made imbalanced by breaking inversion symmetry. We discuss how to utilize local gates, strain effects, and …
After the experimental realization, the Berry curvature dipole (BCD) induced nonlinear Hall effect (NLHE) has attracted tremendous interest to the condensed matter community. Here, we investigate another family of Hall effect, namely, chiral anomaly induced nonlinear Hall effect (CNHE) in multi-Weyl semimetal (mWSM). In contrast to the BCD induced NLHE, CNHE appears because of the combination of both chiral anomaly and anomalous velocity due to non-trivial Berry curvature. Using the semiclassical Boltzmann theory within the relaxation time approximation, we show that, in contrast to the chiral…
Fermi arc surface states, a hallmark of topological Dirac semimetals, can host carriers that exhibit unusual dynamics distinct from that of their parent bulk. Here we find that Fermi arc carriers in intrinsic Dirac semimetals possess a strong and anisotropic light matter interaction. This is characterized by a large Fermi arc optical conductivity when light is polarized transverse to the Fermi arc; when light is polarized along the Fermi arc, Fermi arc optical conductivity is significantly muted. The large surface spectral weight is locked to the wide separation between Dirac nodes and persist…
The Weyl semimetal is characterized by three-dimensional linear band touching points called Weyl nodes. These nodes come in pairs with opposite chiralities. We show that the coupling of circularly polarized photons with these chiral electrons generates a Hall conductivity without any applied magnetic field in the plane orthogonal to the light propagation. This phenomenon comes about because with all three Pauli matrices exhausted to form the three-dimensional linear dispersion, the Weyl nodes cannot be gapped. Rather, the net influence of chiral photons is to shift the positions of the Weyl no…
Intrinsic spin Hall conductivities are calculated for strong spin-orbit Bi$_{1-x}$Sb$_x$ semimetals, from the Kubo formula and using Berry curvatures evaluated throughout the Brillouin zone from a tight-binding Hamiltonian. Nearly-crossing bands with strong spin-orbit interaction generate giant spin Hall conductivities in these materials, ranging from 474 ($\hbar$/e)($Ω$cm)$^{-1}$ for bismuth to 96 ($\hbar$/e)($Ω$cm)$^{-1}$ for antimony; the value for bismuth is more than twice that of platinum. The large spin Hall conductivities persist for alloy compositions corresponding to a three-dimensio…
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 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…
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…
Magnus Hall effect (MHE) is a non-linear Hall effect requiring no external magnetic field, which can be observed when an in-built electric field couples to the Berry curvature of the bandstructure, producing a current in the transverse direction. In this paper, we explore MHE in the context of various three-dimensional semimetals, incorporating various features like tilt, anisotropy, and multi-fold degeneracy. We numerically calculate the Magnus Hall conductivity tensors and transport coefficients, within the framework of the Boltzmann transport theory. Although MHE was originally predicted fo…
ZrSiS is one of the strong candidates for realistic nodal-line semimetal. We theoretically investigate the dynamical conductivity in ZrSiS by using a multi-orbital theoretical model based on the first-principles band calculation. We find that the dynamical conductivity in the clean limit is actually not frequency independent unlike the ideal Dirac model, while nearly flat dependence is achieved by introducing the energy broadening possibly induced by the disorder. The results can be applied to other compounds with the similar crystal structure, such as ZrSiSe, ZrSiTe, and HfSiS.
Anisotropic magnetoresistance is the change tendency of resistance of a material on the mutual orientation of the electric current and the external magnetic field. Here, we report experimental observations in the Dirac semimetal Cd3As2 of giant anisotropic magnetoresistance and its transverse version, called the planar Hall effect. The relative anisotropic magnetoresistance is negative and up to -68% at 2 K and 10 T. The high anisotropy and the minus sign in this isotropic and nonmagnetic material are attributed to a field-dependent current along the magnetic field, which may be induced by the…
We present a theory of magnetotransport phenomena related to the chiral anomaly in Weyl semimetals. We show that conductivity, thermal conductivity, thermoelectric and the sound absorption coefficients exhibit strong and anisotropic magnetic field dependences. We also discuss properties of magneto-plasmons and magneto-polaritons, whose existence is entirely determined by the chiral anomaly. Finally, we discuss the conditions of applicability of the quasi-classical description of electron transport phenomena related to the chiral anomaly.
We investigate an unconventional topological phase transition that occurs in quantum spin Hall (QSH) systems when applying an external in-plane magnetic field. We show that this transition between QSH and trivial insulator phases is separated by a stable topological gapless phase, which is protected by the combination of particle-hole and reflection symmetries, and thus, we dub it as crystalline Weyl semimetal. We explore the stability of this new phase when particle-hole symmetry breaking terms are present. Especially, we predict a robust unconventional topological phase transition to be visi…
We numerically study the three-dimensional (3D) quantum Hall effect (QHE) and magnetothermoelectric transport of Weyl semimetals in the presence of disorder. We obtain a bulk picture that the exotic 3D QHE emerges in a finite range of Fermi energy near the Weyl points determined by the gap between the $n=-1$ and $n=1$ Landau levels (LLs). The quantized Hall conductivity is attributable to the chiral zeroth LLs traversing the gap, and is robust against disorder scattering for an intermediate number of layers in the direction of the magnetic field. Moreover, we predict several interesting charac…
We investigate the influence of surface states on the nonlinear Hall response of non-centrosymmetric time-reversal invariant Weyl semimetals. To do so, we perform a tomography of the Berry curvature dipole in a slab system using a minimal two-band model. We find that in the type-I phase, the nonlinear Hall response is not particularly sensitive to the presence of Fermi arcs or other trivial surface states. However, in the type-II phase, we find that these surface states contribute substantially to the Berry curvature dipole, leading to a strong thickness dependence of the nonlinear Hall respon…
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 g…
Weyl semimetals harbor topological Fermi-arc surface states which determine the nontrivial charge current response to external fields. We here study the quasiparticle decay rate of Fermi arc states arising from their coupling to acoustic phonons, as well as the phonon-limited conductivity tensor for a clean Weyl semimetal slab. Using the phonon modes for an isotropic elastic continuum with a deformation potential coupling to electrons, we determine the temperature dependence of the quasiparticle decay rate, both near and far away from the arc termination points. By solving the coupled Boltzman…
