Broken Lorentz symmetry and violation of the Wiedemann-Franz law in topological insulators

TL;DR

This paper investigates how a non-uniform gravitational field affects two-dimensional topological insulators, revealing violations of the Wiedemann-Franz law due to boundary thermal currents and modifications in quantum anomalous behavior.

Contribution

It introduces a systematic method to analyze edge state contributions to thermal transport in topological insulators under gravitational fields, highlighting the impact of a Newtonian mass term.

Findings

Bulk thermal current appears, violating Wiedemann-Franz law.

A non-zero boundary thermal current modifies thermal Hall conductivity.

The approach can be extended to other topological models.

Abstract

We study a two-dimensional topological insulator in the presence of a static non-uniform gravitational field, which mimics the variations in the temperature distribution. We derive an effective boundary free energy functional for the gravitational field and show that, in contrast to the case of massive Dirac fermions, the addition of a Newtonian mass term significantly modifies the quantum anomalous behavior of the system. A non-zero bulk thermal current appears, which violates the Wiedemann-Franz law. The systematic approach we develop to calculate the contribution of edge states to thermal Hall conductivity and energy magnetization can easily be extended to other models.