Josephson effect in graphene superconductor/barrier/superconductor junctions: Oscillatory behavior of the Josephson current

We study Josephson effect in graphene superconductor/barrier/superconductor junctions with short and wide barriers of thickness d and width L, which can be created by applying a gate voltage V₀ across the barrier region. We show that Josephson current in such graphene junctions, in complete contrast to their conventional counterparts, is an oscillatory function of both the barrier width d and the applied gate voltage V₀. We also demonstrate that in the thin barrier limit, where V₀→∞ and d→0 keeping V₀d finite, such an oscillatory behavior can be understood in terms of transmission resonance of Dirac--Bogoliubov--de Gennes quasiparticles in superconducting graphene. We discuss experimental relevance of our work.