F/S interfaces: point contact versus atomic thickness geometries

TL;DR

This paper compares perturbative approaches to ferromagnet/superconductor interfaces in point contact and atomic thickness geometries, revealing differences and similarities in their breakdowns and regimes of strong and weak ferromagnetism.

Contribution

It introduces a comparative analysis of perturbation theories for different interface geometries, highlighting the unique weak ferromagnet regime in atomic thickness configurations.

Findings

Perturbation theories differ between geometries but both break down at fourth order in tunnel amplitude.

Strong ferromagnet regimes are qualitatively similar in both geometries.

Weak ferromagnet regime appears only in atomic thickness geometry, linked to Andreev bound states.

Abstract

We contrast perturbative expansions of ferromagnet / superconductor interfaces in two geometries: (i) a point contact geometry where a single weak link connects a 3D ferromagnet to a 3D superconductor and (ii) an atomic thickness geometry with an infinite planar interface connecting a quasi-2D ferromagnet to a quasi-2D superconductor. Perturbation theories are rather different in the two approaches but they both break down at order $t^4$ ($t$ is the tunnel amplitude). The regimes of strong ferromagnets are in a qualitative agreement in both geometries. The regime of weak ferromagnets exists only for the atomic thickness geometry and is related to Andreev bound states due to lateral confinement in the superconductor.