Surface phonon propagation in topological insulators

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 renormalization of sound velocity and attenuation and its dependence on the 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.