Thermoelectric Transport Coefficients of a Dirac Electron Gas in High Magnetic Fields

We study the massive Dirac Hamiltonian in high magnetic fields focusing on the effects of the mass term and we show the main differences that arise compared to massless Dirac fermions. We calculate the thermoelectric transport coefficients based on the formalism developed by Luttinger, and study the transverse components of the electric conductivity, Seebeck, and heat conductivity tensors in high magnetic fields. We prove that the Mott formula and the Wiedemann-Franz law are valid at low temperatures.
The magnetic field dependence of measurable quantities strongly depend on the magnetic field dependence of the scattering rate, thus our result relies on the proper treatment of the impurities. We include impurities through the first Born approximation using screened charged impurities as impurity potential.
We recovered analytically the experimentally measured linear magnetoresistance in the massless case. The effect of the mass term becomes relevant at high magnetic fields in the quantum limit. We show that in the high field limit the electric conductivity does not change qualitatively in the case of finite mass term. On the other hand we find that the mass term causes significantly different behavior in the Seebeck tensor.