Scattering in graphene associated with charged out-of-plane impurities

A charged impurity outside the plane of a graphene layer contributes to scattering of electrons (and holes) in the graphene. The interaction occurs through two distinct mechanisms associated with the charge: (1) the (screened) Coulomb potential, and (2) the electric field perpendicular to the graphene plane that causes a spatially varying Rashba spin-orbit interaction. Both types of scattering are examined, with the screened potential self-consistently calculated in nonlinear Thomas-Fermi approximation. Different selection rules for the two mechanisms lead to qualitative differences in the differential scattering cross-sections. Using accepted parameters for the Rashba interaction, the latter is found to make only a very small contribution to the scattering associated with a remote charge.