Self-consistent solution for proximity effect and Josephson current in ballistic graphene SNS Josephson junctions

TL;DR

This paper employs a self-consistent tight-binding BdG approach to analyze proximity effects and Josephson currents in ballistic graphene SNS junctions, revealing enhanced critical currents and persistent superconductivity in long junctions.

Contribution

It introduces a self-consistent method for analyzing graphene SNS junctions, showing improved predictions of critical currents and superconductivity persistence compared to previous non-selfconsistent models.

Findings

Self-consistency does not significantly alter the current-phase relationship for short junctions.

Critical current is notably increased with junction length.

Superconductivity persists in long junctions without Fermi level mismatch.

Abstract

We use a tight-binding Bogoliubov-de Gennes (BdG) formalism to self-consistently calculate the proximity effect, Josephson current, and local density of states in ballistic graphene SNS Josephson junctions. Both short and long junctions, with respect to the superconducting coherence length, are considered, as well as different doping levels of the graphene. We show that self-consistency does not notably change the current-phase relationship derived earlier for short junctions using the non-selfconsistent Dirac-BdG formalism but predict a significantly increased critical current with a stronger junction length dependence. In addition, we show that in junctions with no Fermi level mismatch between the N and S regions superconductivity persists even in the longest junctions we can investigate, indicating a diverging Ginzburg-Landau superconducting coherence length in the normal region.