Clustered impurities and carrier transport in supported graphene

We investigate the effects of charged impurity distributions and carrier-carrier interactions on electronic transport in graphene on ${\mathrm{SiO}}_{2}$ by employing a self-consistent coupled simulation of carrier transport and electrodynamics. We show that impurity clusters of characteristic width 40--50 nm generate electron-hole puddles of experimentally observed sizes. The residual conductivity and the linear-region slope of the conductivity versus carrier density dependence are determined by the impurity distribution, and the measured slope can be used to estimate the impurity density in experiment. Furthermore, we show that the high-density sublinearity in the conductivity stems from carrier-carrier interactions.