Josephson super-current in graphene-superconductor junction

TL;DR

This paper calculates the Josephson super-current in a graphene-superconductor-graphene junction, revealing how inter-valley tunneling causes oscillations in the critical current and analyzing temperature effects.

Contribution

It introduces a tunneling Hamiltonian approach that separately considers intra- and inter-valley tunneling, highlighting the impact of inter-valley processes on the Josephson current in graphene.

Findings

Inter-valley tunneling causes oscillations in the critical current.

The temperature dependence of the critical current matches experimental data.

Separable contributions of intra- and inter-valley tunneling are demonstrated.

Abstract

Within the tunneling Hamiltonian formulation for the eight-component spinors,the Josephson critical super-current has been calculated in a planar superconductor-normal graphene-superconductor junction. Coupling between superconductor regions and graphene is taken into account by a tunneling Hamiltonian which contains two types of tunneling, intra-valley and inter-valley tunneling. Within the present tunneling approach, we find that the contributions of two kinds of tunneling to the critical super-current, are completely separable. Therefore, it is possible to consider the effect of the inter-valley tunnelings in the critical super-current. The incorporation of these type of processes into the tunneling Hamiltonian, exposes a special feature of the graphene Josephson junctions. The effect of inter-valley tunneling appears in the length dependence plot of critical current in the form of oscillations. We also present the results for temperature dependence of critical super-current and compare with experimental results and other theoretical calculations.