Berry Curvature and Phonon Hall Effect

TL;DR

This paper derives a general formula for phonon Hall conductivity in magnetic solids, linking it to phonon Berry curvature and dispersions, and predicts temperature-dependent behaviors for topological and ordinary phonon systems.

Contribution

It introduces a comprehensive theoretical framework incorporating Berry curvature into phonon dynamics, enabling the definition of topological phonon systems and predicting their thermal Hall responses.

Findings

Phonon Hall conductivity is proportional to T^3 at low temperatures for ordinary systems.

Topological phonon systems exhibit a linear T dependence with quantized coefficients.

A general formula for intrinsic phonon Hall conductivity is derived using corrected Kubo formula.

Abstract

We establish the general phonon dynamics of magnetic solids by incorporating the Mead-Truhlar correction in the Born-Oppenheimer approximation. The effective magnetic-field acting on the phonons naturally emerges, giving rise to the phonon Hall effect. A general formula of the intrinsic phonon Hall conductivity is obtained by using the corrected Kubo formula with the energy magnetization contribution incorporated properly. The resulting phonon Hall conductivity is fully determined by the phonon Berry curvature and the dispersions. Based on the formula, the topological phonon system could be rigorously defined. In the low temperature regime, we predict that the phonon Hall conductivity is proportional to $T^{3}$ for the ordinary phonon systems, while that for the topological phonon systems has the linear $T$ dependence with the quantized temperature coefficient.