Theoretical study of superconducting proximity effect in single and multi-layered graphene

Theoretical analysis of superconducting current in graphite thin films (or graphene) in proximity to superconductors is presented, especially paying attention to the band structure. We derive the general formula to calculate the free energy of the superconductor-graphite film-superconductor junction, which enable us to calculate the critical current of the junction. We introduce two models for the band structures: (1) Fermi point type (characteristic to monolayer case) and (2) zero-gap semiconductor type (characteristic to bilayer case). Then we calculate the superconducting critical current as a function of junction length and temperature.