Josephson Current through a Planar Junction of Graphene

TL;DR

This paper models the Josephson effect in planar graphene junctions using a tunneling Hamiltonian and quasiclassical Green's functions, revealing temperature and chemical potential dependencies of the critical current in monolayer and bilayer graphene.

Contribution

It introduces a comprehensive model for Josephson junctions in graphene, capturing proximity effects and differentiating monolayer and bilayer behaviors.

Findings

Critical current is a concave function of temperature at strong coupling.

Crossover to convex temperature dependence occurs with decreasing coupling.

Distinct chemical potential dependencies are observed in monolayer and bilayer graphene.

Abstract

Josephson effect in a planar graphene junction is studied by assuming that the coupling of a graphene sheet and two superconductors deposited on its top is described by a tunneling Hamiltonian. This model properly takes account of the proximity effect characteristic to a planar junction, and allows us to treat monolayer and bilayer cases in a parallel manner. Applying a quasiclassical Green's function approach to it we analyze the Josephson critical current $I_{\rm c}$ in a short-junction limit. As a characteristic feature of the planar junction we find that $I_{\rm c}$ is a concave function of temperature at the strong coupling limit while it crosses over to a convex function with decreasing the coupling strength. We also find different chemical-potential dependences of $I_{\rm c}$ in the monolayer and bilayer cases.