Effects of the structure of charged impurities and dielectric environment on conductivity of graphene

Abstract: We investigate the conductivity of doped graphene in the semiclassical Boltzmann limit, as well as the conductivity minimum within the self-consistent transport theory. Using the hard-disk model for a two-dimensional distribution of impurities gives rise to both strong increase in the slope of conductivity at low charge carrier densities in graphene and a strongly sub-linear behavior of the conductivity at high charge carrier densities when the correlation distance between the impurities is large. On the other hand, we find that a super-linear dependence of the conductivity on charge carrier density in heavily doped graphene may arise from increasing the distance of impurities from graphene or allowing their clustering, whereas the existence of a electric dipole impurities may give rise to an electron-hole asymmetry in the conductivity. We show that finite thickness of a dielectric layer in the top gating configuration, as well as the existence of non-zero air gap(s) between graphene and the dielectric(s) exert strong influences on the conductivity and its minimum. While a decrease in the dielectric thickness is shown to increase the conductivity in doped graphene and even gives rise to finite conductivity in neutral graphene for a 2D distribution of impurities. We find that an increase in the dielectric thickness gives rise to a super-linear behavior of the conductivity when impurities are homogeneously distributed throughout the dielectric. Moreover, the dependence of graphene's mobility on its charge carrier density is surprisingly strongly affected, quantitatively and qualitatively, by the graphene-dielectric gap(s) when combined with the precise position of a 2D distribution of charged impurities. Finally, we show the changes in the conductivity minimum in neutral graphene as the correlation distance between the impurities and the dielectric thickness is altered.