First-principles Theory of Nonlocal Screening in Graphene

Using the quasiparticle self-consistent \emph{GW} (QS\emph{GW}) and local-density (LD) approximations, we calculate the $q$-dependent static dielectric function, and derive an effective 2D dielectric function corresponding to screening of point charges. In the $q${}$\to$0 limit, the 2D dielectric constant is found to scale approximately as the square root of the macroscopic dielectric function. Its value is $\simeq$4, in agreement with the predictions of Dirac model. At the same time, in contrast with the Dirac model, the dielectric function is strongly dependent on $q$. The QS\emph{GW} approximation is shown to describe QP levels very well, with small systematic errors analogous to bulk $sp$ semiconductors. Local-field effects are rather more important in graphene than in bulk semiconductors.