Longitudinal conductivity of a three-dimensional Dirac electron gas in magnetic field

We discuss a conductivity of a three-dimensional gas of Dirac electrons in the direction of magnetic field in high magnetic fields. Analytical expressions for the zero temperature conductivity are calculated in the linear response theory using the basis of relativistic Landau levels. The impurity scattering is treated in the self-consistent Born approximation which gives Landau level broadening increasing linearly in magnetic field. We demonstrate that in the special case of zero-gap Dirac semimetal this leads to the magnetic field and temperature independent conductivity in high magnetic field limit.