Anomalous Thermal Hall Effect in a Disordered Weyl Ferromagnet

TL;DR

This paper develops a theoretical framework to analyze the anomalous thermal Hall effect in disordered Weyl ferromagnets, incorporating disorder effects and going beyond traditional laws like Wiedemann-Franz.

Contribution

It introduces a unified approach using Keldysh formalism in curved spacetime to calculate thermal Hall conductivity considering disorder and intrinsic effects.

Findings

Reproduces Wiedemann-Franz law for specific contributions

Calculates anomalous thermal Hall conductivity without Wiedemann-Franz law

Incorporates nonmagnetic impurities via self-consistent T-matrix approximation

Abstract

We investigate the electric and thermal transport properties in a disordered Weyl ferromagnet on an equal footing by using the Keldysh formalism in curved spacetime. In particular, we calculate the anomalous thermal Hall conductivity, which consists of the Kubo formula and the heat magnetization, without relying on the Wiedemann-Franz law. We take nonmagnetic impurities into account within the self-consistent $T$-matrix approximation and reproduce the Wiedemann-Franz law for the extrinsic Fermi-surface and intrinsic Fermi-sea terms, respectively. This is the first step towards a unified theory of the anomalous Hall effect at finite temperature, where we should take into account both disorder and interactions.