Surface phonon propagation in topological insulators

TL;DR

This paper investigates how helical Dirac states in topological insulators influence surface phonons, revealing effects like sound velocity renormalization, attenuation, and a Kohn anomaly caused by intraband transitions.

Contribution

It introduces a continuum model coupling surface phonons with Dirac electrons, predicting phonon renormalization and a wave vector-dependent Kohn anomaly specific to topological insulators.

Findings

Renormalization of sound velocity and attenuation depends on chemical potential and wave vector.

A Kohn anomaly appears at wave vectors less than 2k_F due to intraband transitions.

The wave vector and chemical potential influence the anomaly's characteristics.

Abstract

The effect of helical Dirac states on surface phonons in a topological insulators is investigated. Their coupling is derived in the continuum limit by assuming displacement dependent Dirac cones. The resulting renormalisation of sound velocity and attenuation and its dependence on chemical potential and wave vector is calculated. At finite wave vectors a Kohn anomaly in the renormalized phonon frequency is caused by intraband-transitions. It appears at wave vectors q<2k_F due to a lack of backscattering for helical Dirac electrons. The wave vector and chemical potential dependence of this anomaly is calculated.