  We explore the spatial variations of the unoccupied electronic states of
graphene epitaxially grown on Ru(0001) and observed three unexpected features:
the first graphene image state is split in energy, unlike all other image
states, the split state does not follow the local work function modulation, and
a new interfacial state at +3 eV appears on some areas of the surface. These
results show the system behaves as a self-organized periodic array of quantum
dots.
