Observation of electron-hole puddles in graphene using a scanning single-electron transistor

The electronic structure of graphene causes its charge carriers to behave like relativistic particles. For a perfect graphene sheet free from impurities and disorder, the Fermi energy lies at the so-called 'Dirac point', where the density of electronic states vanishes. But in the inevitable presence of disorder, theory predicts that equally probable regions of electron-rich and hole-rich puddles will arise. These puddles could explain graphene's anomalous non-zero minimal conductivity at zero average carrier density. Here, we use a scanning single-electron transistor to map the local density of states and the carrier density landscape in the vicinity of the neutrality point. Our results confirm the existence of electron-hole puddles, and rule out extrinsic substrate effects as explanations for their emergence and topology. Moreover, we find that, unlike non-relativistic particles the density of states can be quantitatively accounted for by considering non-interacting electrons and holes.