Phonon Hall thermal conductivity from Green-Kubo formula

TL;DR

This paper derives a formula for phonon Hall thermal conductivity, revealing that off-diagonal elements are finite, antisymmetric, and depend on symmetry breaking, without relying on perturbative assumptions.

Contribution

It provides a non-perturbative derivation of the phonon Hall conductivity tensor, highlighting symmetry conditions for non-zero off-diagonal elements.

Findings

Diagonal conductivity diverges to infinity

Off-diagonal conductivity is finite and antisymmetric

Non-zero off-diagonal elements require mirror symmetry breaking

Abstract

We derive a formula for the thermal conductivity tensor of a ballistic phonon Hall model. It is found that, although the diagonal elements of the conductivity tensor diverge to infinite, the off-diagonal elements are finite,antisymmetric, and odd in magnetic field. The off-diagonal elements are non-zero only if the dynamic matrix of the phonon system breaks mirror reflection symmetry. The results are obtained without perturbative assumptions about the spin-phonon interactions.