Oscillation of the Critical Temperature in Proximity Systems Involving Graphite

We study properties of superconducting-graphite proximity systems as a function of graphite thickness. Size quantization effects become prominent for semi-metallic thin films and lead to oscillations of normal and superconducting properties. In particular, we discuss the oscillation of the density of states and of $T_c$ and compare to existing experimental data.\footnote{T.~Kubo {\it et al.} Physica C {\bf 420}, 78 (2005), {\it ibid.} {\bf 460-462}, 1013 (2007)} We also discuss the increase of the critical temperature in graphite/Nb thin films with respect to the observed value in a single Nb thin film. The result is analyzed in terms of additional pairing contributions and possible intrinsic superconductivity in graphite. We also address the situation when graphite is replaced by a graphene multilayer.