  We present a theoretical approach to describe the 2D transport properties of
the surfaces of three dimensional topological insulators (3DTIs) including
disorder and phonon scattering effects. The method that we present is able to
take into account the effects of the strong disorder-induced carrier density
inhomogeneities that characterize the ground state of the surface of 3DTIs,
especially at low doping, as recently shown experimentally. Due to the
inhomogeneous nature of the carrier density landscape, standard theoretical
techniques based on ensemble averaging over disorder assuming a spatially
uniform average carrier density are inadequate. Moreover the presence of strong
spatial potential and density fluctuations greatly enhance the effect of
thermally activated processes on the transport properties. The theory presented
is able to take into account all the effects due to the disorder-induced
inhomogeneities, momentum scattering by disorder, and the effect of
electron-phonon scattering processes. As a result the developed theory is able
to accurately describe the transport properties of the surfaces of 3DTIs both
at zero and finite temperature.
