Diffusion at the surface of topological insulators

We consider the dc transport properties of topological insulator surface states in the presence of uncorrelated point-like disorder, both in the classical and quantum regimes. The dc conductivity of those two-dimensional surface states depends strongly on the amplitude of the hexagonal warping of their Fermi surface. A perturbative analysis of the warping is shown to fail to describe the transport in Bi2Se3 over a broad range of experimentally available Fermi energies, and in Bi2Te3 for the higher Fermi energies. Hence we develop a fully non-perturbative description of these effects. In particular, we find that the dependence of the warping amplitude on the Fermi energy manifests itself in a strong dependence of the diffusion constant on this Fermi energy, leading to several important experimental consequences. Moreover, the combination of a strong warping with an in-plane Zeeman effect leads to an attenuation of conductance fluctuations in contrast to the situation of unwarped Dirac surface states.