Strongly anharmonic current-phase relation in ballistic graphene Josephson junctions

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 superconductor-normal metal-superconductor (SNS) Josephson junctions within 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 S∣N 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 toward the harmonic result. In short junctions (L