Transport on the surface of a topological insulator

We study theoretically dc and ac transport on the surface of a three-dimensional topological insulator when its time-reversal symmetry is broken. Starting with a Kubo formula, we derive an explicit expression for the dc Hall conductivity, valid for finite temperatures. At zero temperature this expression gives the dc half-quantum Hall conductivity, provided the Fermi level lies in the gap. Corrections when the Fermi level is outside the gap and scattering by impurities are quantified. The longitudinal conductivity is also examined. At finite frequencies, we find a modified Drude term in sigma(xx)(omega) and logarithmic, frequency-dependent corrections in sigma(yx)(omega). The ac Hall conductivity exhibits a robust logarithmic singularity for excitation energies equal to the gapwidth. For these energies, we also find that the power spectrum, which is pertinent to optical experiments, exhibits drastic increase. The Hall conductivity remains almost unaffected for temperatures up to approximately 300 K. (C) 2014 AIP Publishing LLC.