Superconducting proximity effect in graphene nanostructures

The superconducting proximity effect is studied theoretically for graphene(G)-superconductor(S) hybrid structures. Especially S-G-S junction is considered and the critical current is argued focusing on its temperature and junction-length dependences. The free energy of the total system is calculated by use of the tunneling approximation and the critical current is estimated from it. It is reported that the critical current can oscillate as a function of temperature and junction-length in bi-layer junctions. Some detailed comparison with ordinary S-normal metal-S junction is also given and both monolayer and bilayer junctions show some characteristic deviations.