Josephson coupling between superconducting islands on single and bilayer graphene

TL;DR

This paper investigates how Josephson coupling between superconducting islands on single and bilayer graphene depends on various parameters, revealing the influence of gate voltage and providing insights into conditions for granular superconductivity.

Contribution

It introduces a Green function approach to analyze Josephson coupling in graphene-based systems, highlighting the effects of gate voltage and layer structure on superconducting properties.

Findings

Gate voltage significantly affects Josephson coupling decay in bilayer graphene.

The study predicts a strong field dependence of the BKT transition temperature.

Comparison with existing literature for single-layer graphene is provided.

Abstract

We study the Josephson coupling of superconducting (SC) islands through the surface of single-layer (SLG) and bilayer (BLG) graphene, as a function of distance between the grains, temperature, chemical potential and external (transverse) gate-voltage. For SLG, we provide a comparison with existing literature. The proximity effect is analyzed through a Matsubara Green function approach. This represents the first step in a discussion of the conditions for the onset of a granular superconductivity within the film, made possible by Josephson currents flowing between superconductors. To ensure phase coherence over the 2D sample, a random spatial distribution can be assumed for the SC islands on the SLG sheet (or intercalating the BLG sheets). The tunable gate-voltage-induced band gap of BLG affects the asymptotic decay of the Josephson coupling-distance characteristic for each pair of SC islands in the sample, which results in the end in a qualitatively strong field-dependence of the relation between Berezinskii-Kosterlitz-Thouless transition critical temperature and gate-voltage.