Josephson current and multiple Andreev reflections in graphene SNS junctions

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 gate dependence of the proximity induced subgap features (multiple Andreev reflections) and of the supercurrent to theoretical predictions, we find that the diffusive junction model yields close quantitative agreement with the results. By contrast, predictions of the ballistic SGS model are inconsistent with the data. We show that all SGS devices reported so far, our own as well as those of other groups, fall in the diffusive junction category. This is attributed to substrate induced potential fluctuations due to trapped charges and to the invasiveness of the metallic leads.