Magnetotransport of Dirac fermions in graphene in the presence of spin-orbit interactions

We study theoretically the quantum transport in graphene while accounting for spin-orbit interactions (SOIs). Our method is based on the Schwinger proper-time Green's function and a decomposition over Landau level poles and the Kubo formula. Analytical expressions for both the longitudinal and the Hall conductivities are derived and given explicitly. We find, when the Rashba SOI is taken into account, the Shubnikov-de Haas (SdH) oscillation peaks of the longitudinal conductivity versus the chemical potential are split, while the SdH oscillation of the longitudinal conductivity versus a external magnetic field exhibits a beating pattern. The temperature dependence of the longitudinal conductivity becomes non-monotonic for nonzero field away from half-filling. The Rashba SOI tends to suppress the quantum Hall effect in graphene.