Proximity effect and Josephson current in clean strong/weak/strong superconducting trilayers

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 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 ${T}_{c}^{\ensuremath{'}}$, where ${T}_{c}>{T}_{c}^{\ensuremath{'}}$. The weak link $({N}^{\ensuremath{'}})$ 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 nonzero value for temperatures greater than ${T}_{c}^{\ensuremath{'}}$ 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 ${N}^{\ensuremath{'}}$ layer, we show that this can lead to an even larger effect on the Josephson critical current by effectively shortening the weak link.