Josephson effect in graphene Corbino disks

TL;DR

This paper explores the Josephson effect in graphene Corbino disks, revealing a transition from standard tunneling to ballistic Josephson effects influenced by electrochemical potential and barrier shape, supported by numerical simulations.

Contribution

It extends the analysis of Josephson effects to graphene Corbino disks, identifying conditions for different tunneling regimes and their robustness against barrier shape variations.

Findings

Standard Josephson tunneling occurs near the Dirac point with rectangular barriers.

Graphene-specific multimode Dirac-Josephson tunneling is robust across barrier shapes.

Ballistic Josephson effect is restored in unipolar regimes with smooth barriers.

Abstract

Peculiar features of the Josephson effect in graphene were described theoretically by Titov and Beenakker [Phys. Rev. B 74, 041401(R) (2006)], who solved the Dirac-Bogoliubov-de-Gennes equation for a superconductor-graphene-superconductor junction with rectangular geometry. Here, we adopt the analysis for graphene Corbino disks, finding out that -- for the outer to inner radii ratio $r_2/r_1\gtrsim{}5$ -- such systems may demonstrate, when varying the electrochemical potential and the spatial profile of the electrostatic barrier, crossover from standard Josephson tunneling (SJT), via graphene-specific multimode Dirac-Josephson tunneling (MDJT), towards the ballistic Josephson effect (BJE). Signatures of SJT appear only near the Dirac point when the barrier shape is close to rectangular, MDJT appears in the tripolar range and is very robust against varying the barrier shape, and BJE is restored in the unipolar range when smoothing the barrier shape. A comparison with the results of a numerical simulation of quantum transport on the honeycomb lattice is also given.