Ab-initio band structure of doped graphene

We present an emph{ab-initio} study of the graphene quasi-particle band structure as function of the doping in G_0 W_0 approximation. We show that the LDA Fermi velocity is substantially renormalized and this renormalization rapidly decreases as function of the doping. We found, in agreement with previous papers, that close to the Dirac point the linear dispersion of the bands is broken but this behaviour disappears with a small doping. We discuss our results in the light of recent experiments on graphene and intercalate graphite.