# Josephson Current in Ballistic Graphene Corbino Disk

## TL;DR

This paper investigates the Josephson current in a graphene Corbino disk junction, revealing nonzero critical current at the Dirac point and pseudodiffusive behavior influenced by the system's geometry.

## Contribution

It provides an analytical solution for the Josephson current in a graphene Corbino disk, highlighting geometry-dependent effects and pseudodiffusive characteristics at zero doping.

## Key findings

- Nonzero critical current at Dirac point.
- Critical current decreases with increasing R2/R1 ratio.
- Critical current times normal resistance matches planar structure at zero doping.

## Abstract

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.