Strongly anharmonic current-phase relation in ballistic graphene Josephson junctions

TL;DR

This paper investigates the temperature-dependent current-phase relation in ballistic graphene SNS Josephson junctions, emphasizing the roles of proximity effect and depairing, and compares self-consistent and standard modeling approaches.

Contribution

It introduces a self-consistent BdG formalism to study the CPR in graphene junctions, highlighting the importance of proximity effect and depairing effects, which are often neglected.

Findings

Proximity effect reduces CPR skewness with temperature.

Current depairing influences the critical phase, making it less than π/2.

Self-consistent modeling captures effects missed by rigid boundary assumptions.

Abstract

Motivated by a recent experiment directly measuring the current-phase relation (CPR) in graphene under the influence of a superconducting proximity effect, we here study the temperature dependence of the CPR in ballistic graphene SNS Josephson junctions within the the self-consistent tight-binding Bogoliubov-de Gennes (BdG) formalism. By comparing these results with the standard Dirac-BdG method, where rigid boundary conditions are assumed at the SN interfaces, we show on a crucial importance of both proximity effect and depairing by current for the CPR. The proximity effect grows with temperature and reduces the skewness of the CPR towards the harmonic result. In short junctions ($L<\xi$) current depairing is also important and gives rise to a critical phase $\phi_c<\pi/2$ over a wide range of temperatures and doping levels.