Josephson current in ballistic graphene Corbino disk

We solve Dirac-Bogoliubov-De-Gennes (DBdG) equation in a superconductor-normal graphene-superconductor (SGS) junction with Corbino disk structure to investigate the Josephson current through this junction. We find that the critical current Ic has a nonzero value at Dirac point in which the concentration of the carriers is zero. We show this nonzero critical current depends on the system geometry and it decreases monotonically to zero by decreasing the ratio of the inner to outer radii of the Corbino disk (R1/R2), while in the limit of R1/R2→1 it scales like a diffusive Corbino disk. The product of the critical current and the normal-state resistance IcRN increases by increasing R1/R2 and attains the same value for the wide and short rectangular structure at the limit of R1/R2→1 at zero doping. These results reveals the pseudodiffusive behavior of the graphene Corbino Josephson junction similar to the rectangular structure at the zero doping.