Topological Nature of the Phonon Hall Effect

TL;DR

This paper offers a topological perspective on the phonon Hall effect in dielectrics, linking it to Berry curvature and band topology changes, including phase transitions marked by Chern number shifts.

Contribution

It introduces a topological framework for understanding phonon Hall conductivity, connecting band topology changes to observable effects in phonon transport.

Findings

Phonon Hall conductivity exhibits nonmonotonic behavior with magnetic field.

A phase transition in phonon Hall effect is identified, linked to band topology change.

Band touching and splitting cause shifts in Chern numbers, affecting phonon transport.

Abstract

We provide a topological understanding on phonon Hall effect in dielectrics with Raman spinphonon coupling. A general expression for phonon Hall conductivity is obtained in terms of the Berry curvature of band structures. We find a nonmonotonic behavior of phonon Hall conductivity as a function of magnetic field. Moreover, we observe a phase transition in phonon Hall effect, which corresponds to the sudden change of band topology, characterized by the altering of integer Chern numbers. This can be explained by touching and splitting of phonon bands.