First-principles theory of nonlocal screening in graphene

Using the quasiparticle (QP) self-consistent GW (QSGW) and local-density approximations, we calculate the q-dependent static dielectric function of undoped graphene and derive an effective two-dimensional (2D) dielectric function corresponding to screening of point charges. In the q -> 0 limit, the 2D dielectric constant is found to scale approximately as the square root of the macroscopic dielectric function. Its value is similar or equal to 4, in agreement with the predictions of the Dirac model. At the same time, in contrast with the Dirac model, the dielectric function is strongly dependent on q. The QSGW 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.