Fate of global superconductivity in arrays of long SNS junctions

TL;DR

This study investigates how the Berezinskii-Kosterlitz-Thouless transition temperature in arrays of mesoscopic superconducting islands on normal metal films depends on island spacing and size, revealing a $1/d^2$ relation and deviations due to mesoscopic effects.

Contribution

It demonstrates the $T_{BKT}$ dependence on island spacing and size, highlighting the role of Thouless energy and mesoscopic island effects in global superconductivity.

Findings

$T_{BKT}$ scales as $1/d^2$ with island spacing

Island height influences $T_{BKT}$ due to mesoscopic effects

Wide spacing leads to a metallic, non-superconducting transition

Abstract

Normal-metal films overlaid with arrays of superconducting islands undergo Berezinskii-Kosterlitz-Thouless (BKT) superconducting transitions at a temperature $T_{BKT}$. We present measurements of T$_{BKT}$ for arrays of mesoscopic Nb islands patterned on Au films for a range of island spacings $d$. We show that $T_{BKT} \sim 1/d^2$, and explain this dependence in terms of the quasiclassical prediction that the Thouless energy, rather than the superconducting gap, governs the inter-island coupling. We also find two deviations from the quasiclassical theory: (i) $T_{BKT}$ is sensitive to island height, because the islands are mesoscopic; and (ii) for widely spaced islands the transition appears to lead, not to a superconducting state, but to a finite-resistance "metallic" one.