Josephson effect in graphene SBS junctions

We study Josephson effect in graphene superconductorbarriersuperconductor 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.