Origin of spatial charge inhomogeneity in graphene

In an ideal graphene sheet, charge carriers behave as two-dimensional Dirac fermions(1). This has been confirmed by the discovery of a half-integer quantum Hall effect in graphene flakes placed on a SiO2 substrate. The Dirac fermions in graphene, however, are subject to microscopic perturbations that include topographic corrugations and electron-density inhomogeneities (that is, charge puddles). Such perturbations profoundly alter Dirac-fermion behaviour, with implications for their fundamental physics as well as for future graphene device applications. Here we report a new technique of Dirac-point mapping that we have used to determine the origin of charge inhomogeneities in graphene. We find that fluctuations in graphene charge density are caused not by topographical corrugations, but rather by charge-donating impurities below the graphene. These impurities induce surprising standing wave patterns due to unexpected backscattering of Dirac fermions. Such wave patterns can be continuously modulated by electric gating. Our observations provide new insight into impurity scattering of Dirac fermions and the microscopic mechanisms limiting electronic mobility in graphene.