Origin of spatial charge inhomogeneity in graphene

Abstract

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 Diracpoint 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. Topographic corrugations and charge puddles in graphene are two of the most significant types of disorder in this new material. Topographic corrugations 24 , for example, have been suggested as a cause for the suppression of anticipated antilocalization 5 . Electron and hole puddles 6 have similarly been blamed for obscuring universal conductivity in graphene 7 . These issues are part of a puzzle regarding the factors that limit graphene’s mobility 812 . In order for graphene to fulfil its promise as a next-generation nanodevice substrate it is important to understand the origin of the disorder and the influence it has on Dirac fermions. We have made new progress in this direction by using the techniques of scanning tunnelling microscopy (STM) and spectroscopy to simultaneously probe topographic and electronic disorder in graphene with an electron-density spatial resolution two orders of magnitude higher than previous scanning single-electron transistor microscopy measurements 6 . Figure 1a shows the STM topography of a typical 30 30nm 2 area of a graphene monolayer on SiO2. We observe random corrugations with lateral dimension of a few nanometres and a vertical dimension of1:5¯ (r.m.s.), probably due to roughness in the underlying SiO2 surface and/or intrinsic ripples of the graphene sheet 24,13 . STM imaging at the atomic scale clearly resolves the graphene honeycomb lattice on top of the broader surfacecorrugationalloverthesamplesurface(inset).