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First-principles Theory of Nonlocal Screening in Graphene

Using the quasiparticle self-consistent GW (QSGW) 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 function is found to scale approximately as the square root of the macroscopic dielectric function. Its value is ~4, a factor approximately 1.5 larger than predictions of Dirac model. Both kinds of dielectric functions depend strongly on q, in contrast with the Dirac model. 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.