Geodesic scattering by surface deformations of a topological insulator

TL;DR

This paper investigates how surface deformations on topological insulators cause electron scattering, affecting surface conductivity, with a focus on geodesic scattering mechanisms at high electron densities.

Contribution

It introduces a geodesic scattering model for surface electrons on topological insulators and derives the resulting conductivity behavior considering surface deformations.

Findings

Geodesic scattering dominates at high electron densities.

Conductivity scales as the square root of electron density.

Surface deformations significantly limit surface conductivity.

Abstract

We consider the classical ballistic dynamics of massless electrons on the conducting surface of a three-dimensional topological insulator, influenced by random variations of 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 {\sigma}, for arbitrary anisotropic dispersion relation. At large surface electron densities n this geodesic scattering mechanism (with {\sigma} propto sqrt{n}) is more effective at limiting the surface conductivity than electrostatic potential scattering.