  Image potential states (IPSs) are electronic states localized in front of a
surface in a potential well formed by the surface projected bulk band gap on
one side and the image potential barrier on the other. In the limit of a
two-dimensional solid a double Rydberg series of IPSs has been predicted which
is in contrast to a single series present in three-dimensional solids. Here, we
confirm this prediction experimentally for mono- and bilayer graphene. The IPSs
of epitaxial graphene on SiC are measured by scanning tunnelling spectroscopy
and the results are compared to ab-initio band structure calculations. Despite
the presence of the substrate, both calculations and experimental measurements
show that the first pair of the double series of IPSs survives, and eventually
evolves into a single series for graphite. Thus, IPSs provide an elegant
quantum probe of the interfacial coupling in graphene systems.
