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Register a new userChiral anomaly induced nonlinear Nernst and thermal Hall effects in Weyl semimetals
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Chiral anomaly or Adler-Bell-Jackiw anomaly in Weyl semimetals (WSMs) has a significant impact on the electron transport behaviors, leading to remarkable longitudinal or planar electrical and thermoelectric transport phenomena in the presence of electromagnetic gauge fields. These phenomena are consequences of the imbalanced chiral charge and energy induced by chiral anomaly in the presence of parallel electric ($mathbf{E}$) and magnetic ($mathbf{B}$) fields ($mathbf{E cdot B } eq 0$) or $(mathbf{B cdot abla }T eq 0)$ ($mathbf{ abla}T$ is the thermal gradient). We here propose another two fascinating transport properties, namely, the nonlinear planar Nernst effect and nonlinear planar thermal Hall effect induced by chiral anomaly in the presence of $mathbf{B cdot abla}T eq 0$ in WSMs. Using the semiclassical Boltzmann transport theory, we derive the analytical expressions for the chiral anomaly induced nonlinear Nernst and thermal Hall transport coefficients and also evaluate the fundamental mathematical relations among them in the nonlinear regime. The formulas we find in this current work are consistent with that predicted for the nonlinear anomalous electrical and thermoelectric effects induced by Berry curvature dipole recently. Additionally, in contrast to the recent work, by utilizing the lattice Weyl Hamiltonian with intrinsic chiral chemical potential, we find that the chiral anomaly induced nonlinear planar effects can exist even for a pair of oppositely tilted or non-tilted Weyl cones in both time reversal and inversion broken WSMs. The chiral anomaly induced nonlinear planar effects predicted here along with the related parameter dependencies are hence possible to be realized in realistic WSMs in experiment.
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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 anomaly induced linear Hall effect, the magnitude of CNHE decreases with the topological charge n. Interestingly, we find that unlike the case of n=1, the CNHE has different behaviors in different planes. Our prediction on the behavior of CNHE in mWSM can directly be checked in experiments.
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 nodes. Interestingly, the momentum shift is tightly correlated with the chirality of the node to produce a net anomalous Hall signal. Application of our proposal to the recently discovered TaAs family of Weyl semimetals leads to an order-of-magnitude estimate of the photoinduced Hall conductivity which is within the experimentally accessible range.
Weyl semimetals are intriguing topological states of matter that support various anomalous magneto-transport phenomena. One such phenomenon is a negative longitudinal ($mathbf{ abla} T parallel mathbf{B}$) magneto-thermal resistivity, which arises due to chiral magnetic effect (CME). In this paper we show that another fascinating effect induced by CME is the planar thermal Hall effect (PTHE), i.e., appearance of an in-plane transverse temperature gradient when the current due to $mathbf{ abla} T$ and the magnetic field $mathbf{B}$ are not aligned with each other. Using semiclassical Boltzmann transport formalism in the relaxation time approximation we compute both longitudinal magneto-thermal conductivity (LMTC) and planar thermal Hall conductivity (PTHC) for a time reversal symmetry breaking WSM. We find that both LMTC and PTHC are quadratic in B in type-I WSM whereas each follows a linear-B dependence in type-II WSM in a configuration where $mathbf{ abla} T$ and B are applied along the tilt direction. In addition, we investigate the Wiedemann-Franz law for an inversion symmetry broken WSM (e.g., WTe$_{2}$) and find that this law is violated in these systems due to both chiral anomaly and CME.
Weyl semimetals are well-known for hosting topologically protected linear band crossings, serving as the analog of the relativistic Weyl Fermions in the condensed matter context. Such analogy persists deeply, allowing the existence of the chiral anomaly under parallel electric and magnetic field in Weyl semimetals. Different from such picture, here we show that, a unique mechanism of the chiral anomaly exists in Weyl semimetals by injecting a spin current with parallel spin polarization and flow direction. The existence of such a chiral anomaly is protected by the topological feature that each Weyl cone can also be a source or drain of the spin field in the momentum space. It leads to measurable experimental signals, such as an electric charge current parallel with an applied magnetic field in the absence of the electric field, and a sharp peak at certain resonant frequency in the injection current in achiral Weyl semimetals through the circular photogalvanic effect. Our work shows that the topological implication of Weyl semimetals goes beyond the link with relativistic Weyl Fermions, and offers a promising scenario to examine the interplay between topology and spin.
The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin-orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. By using the tight-binding Hamiltonian combining with the nonequilibrium Greens function method, the three elements of the spin current in the transverse leads and then spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has the essential difference with the traditional one: The z direction spin currents is zero without the magnetic field while it appears under the magnetic field, and the x and y direction spin currents in the two transverse leads flows out or flows in together, in contrary to the traditional spin Nernst effect, in which the spin current is induced by the spin-orbit coupling and flows out from one lead and flows in on the other. So we call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have the center-reversal-type symmetry, the mirror-reversal-type symmetry and the electron-hole-type symmetry, which lead to the spin Nernst coefficients being odd function or even function of the Fermi energy, the magnetic field and the transverse terminals. Moreover, the spin Nernst effect in the Weyl semimetals are strongly anisotropic and its coefficients are strongly dependent on both the direction of thermal gradient and the direction of the transverse lead connection. Three non-equivalent connection modes (x-z, z-x and x-y modes) are studied in detail, and the spin Nernst coefficients for three different modes exhibit very different behaviors. These strongly anisotropic behaviors of the spin Nernst effect can be used as the characterization of magnetic Weyl semimetals.
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