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

Abstract

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 ${V}_{0}$ 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 ${V}_{0}$. We also demonstrate that in the thin barrier limit, where ${V}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ and $d\ensuremath{\rightarrow}0$ keeping ${V}_{0}d$ finite, such an oscillatory behavior can be understood in terms of transmission resonance of Dirac\char21{}Bogoliubov\char21{}de Gennes quasiparticles in superconducting graphene. We discuss experimental relevance of our work.