Surface charge conductivity of topological insulator in a magnetic field: effect of hexagonal warping

We investigate the influence of the hexagonal warping on the transport properties of the topological insulators. We study the charge conductivity within Kubo formalism in the first Born approximation using low energy expansion of the Hamiltonian near the Dirac point. The effects of disorder, magnetic field and chemical potential value are analyzed in details. We found that the presence of the hexagonal warping effects significantly the conductivity of the topological insulator. In particular, it gives rise to the growth of the longitudinal conductivity with the increase of the disorder and anisotropic anomalous in-plane magnetoresistance. The hexagonal warping also affects the quantum anomalous Hall effect and anomalous out-of-plane magnetoresistance. The obtained results are consistent with the experimental data.