Magnetotransport and thermoelectricity in Landau-quantized disordered graphene

We have studied the electric and thermal response of two-dimensional Dirac fermions in a quantizing magnetic field in the presence of localized disorder. The electric and heat current operators in the presence of magnetic field are derived. The self-energy due to impurities is calculated self-consistently and depends strongly on the frequency and field strength, resulting in asymmetric peaks in the density of states at the Landau level energies, and small islands connecting them. The Shubnikov-de Haas oscillations remain periodic in 1/B, in spite of the distinct quantization of quasiparticle orbits compared to normal metals. The Seebeck coefficient depends strongly on the field strength and orientation. For finite field and chemical potential, the Wiedemann-Franz law can be violated.