What is the value of the superconducting gap of a F/S/F trilayer ?

TL;DR

This paper investigates how exchange fields, disorder, and finite thickness influence the superconducting gap in atomic-thickness F/S/F trilayers, revealing a reentrant gap and the dominance of pair-breaking effects under certain conditions.

Contribution

It provides a detailed analysis of the interplay between pair-breaking and proximity effects in F/S/F trilayers with atomic thickness, considering various physical parameters.

Findings

Reentrant superconducting gap in weak ferromagnets for parallel alignment.

Disorder reduces effective hopping parameters, affecting the gap.

Superconducting gap in antiparallel alignment exceeds that in parallel with finite thickness.

Abstract

Based on the model of F/S/F trilayer with atomic thickness [A. Buzdin and M. Daumens, cond-mat/0305320] we discuss the relative roles of pair-breaking and proximity effects, as a function of the exchange field, of disorder and of a finite thickness in the superconducting layer. The exchange field can be small (weak ferromagnets) or large (strong ferromagnets) compared to the superconducting gap. With weak ferromagnets we show the existence of a reentrant superconducting gap for the F/S/F trilayer with atomic thickness in the parallel alignment (equivalent to the F/S bilayer). Qualitatively small disorder is equivalent to reducing the value of the hopping parameters. In the presence of a finite thickness in the superconducting layer the superconducting gap in the antiparallel alignment is larger than in the parallel alignment, meaning that pair breaking dominates over the proximity effect.