  We consider the transport properties of topological insulators surface states
in the presence of uncorrelated point-like disorder, both in the classical and
quantum regimes. The transport properties of those two-dimensional surface
states depend strongly on the amplitude of the hexagonal warping of their Fermi
surface. It is shown that a perturbative analysis of the warping fails to
describe the transport in experimentally available topological insulators, such
as Bi2Se3 and Bi2Te3. 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.

Mesoscale and Nanoscale Physics