Geodesic scattering by surface deformations of a topological insulator

Abstract

We consider the classical ballistic dynamics of massless electrons on the conducting surface of a three-dimensional topological insulator, influenced by random variations in the surface height. By solving the geodesic equation and the Boltzmann equation in the limit of shallow deformations, we obtain the scattering cross section and the conductivity σ, for arbitrary anisotropic dispersion relation. At large surface electron densities n this geodesic scattering mechanism (with σ∝√n) is more effective at limiting the surface conductivity than electrostatic potential scattering. © 2010 The American Physical Society.