Correlated charged impurity scattering in graphene

Abstract: Understanding disorder in graphene is essential for electronic applications; in contrast to conventional materials, the extraordinarily low electron-phonon scattering1, 2 in graphene implies that disorder3-7 dominates its resistivity even at room temperature. Charged impurities5, 8-10 have been identified as an important disorder type in graphene on SiO2 substrates11, 12, giving a nearly linear carrier-density-dependent conductivity {\sigma}(n), and producing electron and hole puddles13-15 which determine the magnitude of graphene's minimum conductivity {\sigma}min10. Correlations of charged impurities are known to be essential in achieving the highest mobilities in remotely-doped semiconductor heterostructures16-18, and are present to some degree in any impurity system at finite temperature. Here we show that even modest correlations in the position of charged impurities, realized by annealing potassium on graphene, can increase the mobility by more than a factor of four. The results are well understood theoretically19 considering an impurity correlation length which is temperature dependent but independent of impurity density. Impurity correlations also naturally explain the sub-linear {\sigma}(n) commonly observed in substrate-bound graphene devices2, 11, 12, 20.