# Berry phase of phonons and thermal Hall effect in nonmagnetic insulators

## TL;DR

This paper demonstrates that nonmagnetic insulators can exhibit a phonon Hall effect due to Berry curvature induced by an external magnetic field, leading to finite thermal Hall conductivity without magnetic order.

## Contribution

It reveals a new mechanism for phonon Hall effect in nonmagnetic insulators via Berry curvature induced by magnetic fields, independent of magnetic moments or spin-orbit coupling.

## Key findings

- Finite thermal Hall conductivity estimated at 1.0×10^{-5} W/K·m under 10 T and 150 K.
- Berry curvature of acoustic phonons is induced by magnetic field, affecting thermal transport.
- Nonmagnetic insulators can exhibit phonon Hall effect without magnetic order.

## Abstract

A mechanism for phonon Hall effect (PHE) in non-magnetic insulators under an external magnetic field is theoretically studied. PHE is known in (para)magnetic compounds, where the magnetic moments and spin-orbit interaction play an essential role. In sharp contrast, we here show that a non-zero Berry curvature of acoustic phonons is induced by an external magnetic field due to the correction to the adiabatic Born-Oppenheimer approximation. This results in the finite thermal Hall conductivity $\kappa_H$ in nonmagnetic band insulators. Our estimate of $\kappa_H$ for a simple model gives $\kappa_H \sim 1.0\times 10^{-5} $[W/Km] at $ B=10 $[T] and $ T=150 $[K].