Anisotropic conductivity in 2D massive Dirac Fermions: an effect of time reversal symmetry breaking in the surface states o a topological insulator

We calculate the conductivity tensor for massive Dirac Fermions within the semiclassical Boltzmann approach. We consider the effect of two different types of scattering mechanism, namely scalar and magnetic, that act incoherently and use the symmetries of the transition rate to exactly solve the Boltzmann equation. We prove that the conductivity can be anisotropic depending on the strength of the magnetic scatterers in each direction. In the particular situation of magnetic impurities polarised in the x-direction, the conductivity is three times larger in y-direction as compared with the conductivity in the x-direction, for white noise scattering correlation function. We compare the approach we apply with the most commonly used way of dealing with more than one source of scattering, namely with Matthiessen's rule, and show that the approach we applied is more general and suitable for anisotropic scattering.