Proximity effect in clean strong/weak/strong superconducting tri-layers

TL;DR

This paper investigates the proximity effect in superconducting tri-layers, revealing an unexpectedly large Josephson current at temperatures above the weak link's critical temperature, using BdG equations for different pairing symmetries.

Contribution

It models the proximity effect in superconductor/weak superconductor/superconductor trilayers with BdG equations, highlighting enhanced currents due to superconducting correlations in the weak link.

Findings

Large Josephson current persists above the weak link's $T_c$.

Proximity effect is stronger with s-wave or d-wave symmetry.

Superconducting pockets in the weak link further increase the effect.

Abstract

Recent measurements of the Josephson critical current through LSCO/LCO/LSCO thin films showed an unusually large proximity effect. Using the Bogoliubov-de Gennes (BdG) equations for a tight binding Hamiltonian we describe the proximity effect in weak links between a superconductor with critical temperature $T_c$ and one with critical temperature $T_c$', where $T_c>T_c$'. The weak link (N') is therefore a superconductor above its own critical temperature and the superconducting regions are considered to have either s-wave or d-wave symmetry. We note that the proximity effect is enhanced due to the presence of superconducting correlations in the weak link. The dc Josephson current is calculated, and we obtain a non-zero value for temperatures greater than $T_c$' for sizes of the weak links that can be almost an order of magnitude greater than the conventional coherence length. Considering pockets of superconductivity in the N' layer, we show that this can lead to an even larger effect on the Josephson critical current by effectively shortening the weak link.