Inherited Berry curvature of phonons in Dirac materials with time-reversal symmetry

TL;DR

This paper demonstrates how phonons in Dirac materials with time-reversal symmetry can acquire Berry curvature through electron-phonon coupling, linking phononic properties to electronic topological characteristics.

Contribution

It introduces a model showing phonons gain Berry curvature via coupling to electrons in Dirac materials with time-reversal symmetry, exemplified by BaMnSb2.

Findings

Phonons can acquire Berry curvature through electron coupling.

The phonon Berry curvature is proportional to the electronic valley Chern number.

Application to BaMnSb2 illustrates the theoretical model.

Abstract

The Berry curvature of phonons is an active subject of research in condensed matter physics. Here, we present a model in which phonons acquire a Berry curvature through their coupling to electrons in crystals with time-reversal symmetry. We illustrate this effect for BaMnSb$_2$, a quasi two-dimensional Dirac insulator, whose low-energy massive Dirac fermions generate a phonon Berry curvature that is proportional to the electronic valley Chern number.