Hexagonal Warping Effects on the Surface Transport in Topological Insulators

We investigate the charge conductivity and current-induced spin polarization on the surface state of a three-dimensional topological insulator by including the hexagonal warping effect of Fermi surface both in classical and quantum diffusion regimes. We present general expressions of conductivity and spin polarization, which are reduced to simple forms for usual scattering potential. Due to the hexagonal warping, the conductivity and spin polarization show an additional quadratic carrier density dependence both for Boltzmann contribution and quantum correction. In the presence of warping term, the surface states still reveal weak anti-localization. Moreover, the dielectric function in the random phase approximation is also explored, and we find that it may be momentum-angle-dependent.