  When graphene is close to charge neutrality, its energy landscape is highly
inhomogeneous, forming a sea of electron-like and hole-like puddles, which
determine the properties of graphene at low carrier density. However, the
details of the puddle formation have remained elusive. We demonstrate
numerically that in sharp contrast to monolayer graphene, the normalized
autocorrelation function for the puddle landscape in bilayer graphene depends
only on the distance between the graphene and the source of the long-ranged
impurity potential. By comparing with available experimental data, we find
quantitative evidence for the implied differences in scanning tunneling
microscopy measurements of electron and hole puddles for monolayer and bilayer
graphene in nominally the same disorder potential.
