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.
The superconducting transition temperature (TC) in nanostructured Pb remains nearly constant as the particle size is reduced from 65 to 7nm, below which size the superconductivity is lost rather abruptly. In contrast, there is a large enhancement in
the upper critical field (HC2) in the same size regime. We explore the origin of the unusual robustness of the TC over such a large particle size range in nanostructured Pb, by measuring the temperature dependence of the superconducting energy gap in planar tunnel junctions of Al/Al2O3/nano-Pb. We show that below 22nm, the electron phonon coupling strength increases monotonically with decreasing particle size, and almost exactly compensates for the quantum size effect, which is expected to suppress TC.
