Planar Thermal Hall Effect in Weyl Semimetals

TL;DR

This paper predicts and analyzes the planar thermal Hall effect in Weyl semimetals, revealing how chiral magnetic effects induce in-plane transverse temperature gradients and examining their dependence on magnetic field and symmetry properties.

Contribution

It introduces the concept of the planar thermal Hall effect in Weyl semimetals and computes its behavior using semiclassical Boltzmann formalism, highlighting differences between type-I and type-II systems.

Findings

LMTC and PTHC are quadratic in B for type-I WSM.

LMTC and PTHC are linear in B for type-II WSM.

Wiedemann-Franz law is violated in inversion symmetry broken WSMs.

Abstract

Weyl semimetals are intriguing topological states of matter that support various anomalous magneto-transport phenomena. One such phenomenon is a negative longitudinal ($\mathbf{\nabla} T \parallel \mathbf{B}$) 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 $\mathbf{\nabla} T$ 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 $\mathbf{\nabla} T$ 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.