Cooper-pair propagation and superconducting correlations in graphene

TL;DR

This paper explores how superconducting correlations propagate in graphene, revealing how doping levels influence supercurrent decay and identifying a temperature scale that affects Cooper pair stability over long distances.

Contribution

It provides a detailed analysis of the distance-dependent decay of supercurrents in graphene and how doping modifies this behavior, highlighting conditions for observing long-range supercurrents.

Findings

Supercurrent decay in undoped graphene scales as W^2/L^3.

Doping changes decay to a 1/L^2 behavior, enabling supercurrents over micron scales.

A crossover temperature T ~ v_F/k_B L determines the onset of strong supercurrent decay.

Abstract

We investigate the Cooper-pair propagation and the proximity effect in graphene under conditions in which the distance L between superconducting electrodes is much larger than the width W of the contacts. In the case of undoped graphene, supercurrents may exist with a spatial decay proportional to W^2/L^3. This changes upon doping into a 1/L^2 behavior, opening the possibility to observe a supercurrent over length scales above 1 micron at suitable doping levels. We also show that there is in general a crossover temperature T ~ v_F/k_B L that marks the onset of the strong decay of the supercurrent, and that corresponds to the scale below which the Cooper pairs are not disrupted by thermal effects during their propagation.