Josephson Current in a Gapped Graphene Superconductor/Barrier/Superconductor Junction: Case of Massive Electrons

The Josephson effect in a gapped graphene-based superconductor/barrier/superconductor junction is studied. The superconductivity in gapped graphene may be achieved by depositing conventional superconductor on the top of the gapped graphene such as graphene grown on SiC substrate. In gapped graphene system, the carriers exhibit massive Dirac fermions. We focus on the effect of pseudo-Dirac-like mass on the supercurrent. In contrast to that in the gapless graphene superconductor/barrier/superconductor junction, we find that the supercurrent exhibits dependency of the Fermi energy. Also, the massive supercurrent anomalously oscillates as a function of the gate potential. This novel behavior is due to the effect of electrons acquiring mass in gapped graphene.