Nernst and magneto-thermal conductivity in a lattice model of Weyl fermions

TL;DR

This paper investigates the Nernst effect and thermal conductivity in Weyl semimetals using a lattice model, revealing an anomalous Nernst response and violations of the Wiedemann-Franz law due to Berry curvature and chiral anomaly.

Contribution

It demonstrates the existence of an anomalous Nernst response in TR-broken Weyl semimetals and analyzes thermal conductivity violations of Wiedemann-Franz law in a lattice model.

Findings

TR-broken Weyl semimetals exhibit an anomalous Nernst response.

Wiedemann-Franz law is violated in the parallel thermal and electrical conductivities.

Chiral anomaly influences thermal transport properties.

Abstract

Weyl semimetals (WSM) are topologically protected three dimensional materials whose low energy excitations are linearly dispersing massless Dirac fermions, possessing a non-trivial Berry curvature. Using semi-classical Boltzmann dynamics in the relaxation time approximation for a lattice model of time reversal (TR) symmetry broken WSM, we compute both magnetic field dependent and anomalous contributions to the Nernst coefficient. In addition to the magnetic field dependent Nernst response, which is present in both Dirac and Weyl semimetals, we show that, contrary to previous reports, the TR-broken WSM also has an anomalous Nernst response due to a non-vanishing Berry curvature. We also compute the thermal conductivities of a WSM in the Nernst (${\nabla T} \perp \mathbf{B}$) and the longitudinal (${\nabla T} \parallel \mathbf{B}$) set-up and confirm from our lattice model that in the parallel set-up, the Wiedemann-Franz law is violated between the longitudinal thermal and electrical conductivities due to chiral anomaly.