Josephson effect in ballistic graphene

TL;DR

This paper analyzes the Josephson effect in ballistic graphene SNS junctions by solving the Dirac-Bogoliubov-De-Gennes equations, revealing universal behaviors of supercurrent related to doping levels and junction geometry.

Contribution

It provides a theoretical solution for supercurrent in impurity-free graphene SNS junctions, highlighting the role of doping and junction aspect ratio in supercurrent behavior.

Findings

Supercurrent depends on superconducting gap and junction aspect ratio.

Universal product of critical current and resistance near the Dirac point.

Recovery of ballistic results away from the Dirac point.

Abstract

We solve the Dirac-Bogoliubov-De-Gennes equation in an impurity-free superconductor-normal-superconductor (SNS) junction, to determine the maximal supercurrent that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result is determined by the superconducting gap and by the aspect ratio of the junction (length L, small relative to the width W and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result in which the Fermi wave length takes over from L. The product of critical current and normal-state resistance retains its universal value (up to a numerical prefactor) on approaching the Dirac point.