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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 $I_c$ 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 increasing the ratio of the outer to inner radii of the Corbino disk ($R_2/R_1$), while in the limit of $R_2/R_1 \rightarrow 1$ it scales like a diffusive Corbino disk. The product of the critical current and the normal-state resistance $I_cR_N$ attains the same value for the planar structure at zero doping. These results reveals the pseudodiffusive behavior of the graphene Corbino Josephson junction similar to the planar structure.