Ground-state of graphene in the presence of random charged impurities

We calculate quantum mechanically the carrier density dependent ground state properties of gated disordered graphene layers in the presence of random charged impurities in the substrate. Our theory includes the self-consistent effects of non-linear screening and many-body effects. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias (i.e. the average density), the impurity density, and the impurity location. At zero bias (i.e. for small average carrier density), we find that the graphene layer breaks up into inhomogeneous random puddles of electrons and holes characterized by a correlation length $\approx 10 d$, where $d$ is the separation of the impurities from the graphene layer. Many-body effects have only small quantitative effects on the calculated results.