Elastic scattering theory and transport in graphene

Abstract

Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the massless limit is relevant for pristine graphene, keeping finite mass allows for generalizations onto situations with broken symmetry between the two sublattices and provides a link to the scattering theory of electrons in a parabolic band. We demonstrate that the Dirac theory requires short-distance regularization for potentials which are more singular than $1∕r$. The formalism is then applied to scattering off a smooth short-ranged potential. Next, we consider the Coulomb potential scattering, where the Dirac theory is consistent for a point scatterer only for the effective impurity strength below $1∕2$. From the scattering phase shifts we obtain the exact Coulomb transport cross section in terms of the impurity strength. The results are relevant for transport in graphene in the presence of impurities that do not induce scattering between the Dirac points in the Brillouin zone.