Interference phenomena and long - range proximity effect in clean superconductor -- ferromagnet systems

TL;DR

This paper investigates how spatial and momentum variations of the exchange field in clean superconductor-ferromagnet systems lead to long-range proximity effects, explaining recent experimental observations.

Contribution

It reveals that small modulations and momentum dependence of the exchange field induce long-range superconducting correlations through interference effects.

Findings

Long-range supercurrent contributions due to exchange field modulation.

Momentum dependence from spin-orbit interaction causes extended superconducting correlations.

Explains recent experimental results on ferromagnetic nanowires.

Abstract

We study peculiarities of proximity effect in clean superconductor -- ferromagnet structures caused by either spatial or momentum dependence of the exchange field. Even a small modulation of the exchange field along the quasiparticle trajectories is shown to provide a long range contribution to the supercurrent due to the specific interference of particle- and hole- like wave functions. The momentum dependence of the exchange field caused by the spin -- orbit interaction results in the long -- range superconducting correlations even in the absence of ferromagnetic domain structure and can explain the recent experiments on ferromagnetic nanowires.