A constrained theory of non-BCS type superconductivity in gapped Graphene

We show that gapped Graphene, with a local constraint that current arising from the two valley fermions are exactly equal, shows a non-BCS type superconductivity. Unlike the conventional mechanisms, this superconductivity phenomenon does not require any pairing. We estimate the critical temperature for superconducting-to-normal transition via Berezinskii-Kosterlitz-Thouless mechanism, and find that it is proportional to the gap.