Polarization Transport of Transverse Acoustic Waves: Berry Phase and Spin Hall Effect of Phonons

TL;DR

This paper analyzes the polarization and transport properties of transverse acoustic waves in inhomogeneous media, revealing a phonon spin Hall effect driven by Berry phase and spin-orbit interactions, analogous to electromagnetic phenomena.

Contribution

It introduces a semiclassical framework for phonon polarization, demonstrating the Berry phase's role and the spin Hall effect in acoustic wave transport.

Findings

Identification of Berry phase effects in phonon polarization

Prediction of transverse phonon transport due to spin Hall effect

Analysis of boundary reflection phenomena influenced by Berry curvature

Abstract

We carry out a detailed analysis of the short-wave (semiclassical) approximation for the linear equations of the elasticity in a smoothly inhomogeneous isotropic medium. It is shown that the polarization properties of the transverse waves are completely analogous to those of electromagnetic waves and can be considered as spin properties of optical phonons. In particular, the Hamiltonian of the transverse waves contains an additional term of the phonon spin-orbit interaction arising from the Berry gauge potential in the momentum space. This potential is diagonal in the basis of the circularly polarized waves and corresponds to the field of two `magnetic monopoles' of opposite signs for phonons of opposite helicities. This leads to the appearance of the Berry phase in the equation for the polarization evolution and an additional ``anomalous velocity'' term in the ray equations. The anomalous velocity has the form of the `Lorentz force' caused by the Berry gauge field in momentum space and gives rise to the transverse transport of waves of opposite helicities in opposite directions. This is a manifestation of the spin Hall effect of optical phonons. The effect directly relates to the conservation of total angular momentum of phonons and also influences reflection from a sharp boundary (acoustic analogue of the transverse Ferdorov--Imbert shift).