  The Josephson Effect and Superconducting Proximity Effect were observed in
Superconductor -Graphene-Superconductor (SGS) Josephson junctions with
coherence lengths comparable to the distance between the superconducting leads.
By comparing the measured temperature and doping dependence of the supercurrent
and the proximity induced sub-gap features (multiple Andreev reflections) to
theoretical predictions we find that, contrary to expectations, the ballistic
transport model fails to describe the SGS junctions. In contrast, the diffusive
junction model yields close quantitative agreement with the results. This
conclusion is consistent with transport measurements in the normal state, which
yield mean free paths in the graphene link that are much shorter than the
junction length. We show that all devices fabricated on SiO2 substrates so far
(our own as well as those reported by other groups) fall in the diffusive
junction category.
