We grow epitaxial graphene monolayers on Ru(0001) that cover uniformly the substrate over lateral distances larger than several microns. The weakly coupled graphene monolayer is periodically rippled and it shows charge inhomogeneities in the charge distribution. Real space measurements by scanning tunneling spectroscopy reveal the existence of electron pockets at the higher parts of the ripples, as predicted by a simple theoretical model. We also visualize the geometric and electronic structure of edges of graphene nanoislands.

Scanning-tunneling microscopy observation of Pb nanocrystals grown on Cu(111) indicates that in the equilibrium distribution of island heights some heights appear much more frequently than others. The simultaneous, local spectroscopic characterization allows us to relate this finding to the confinement of electrons within the islands: the “magic,” preferred heights correspond to islands having a quantum well state far from the Fermi energy, while the “forbidden” heights turn out to be those that would have a quantum well state close to the Fermi level. The “magic” and “forbidden” heights can be predicted from the Fermi-surface geometry of bulk Pb.