Current carrying Andreev bound states in a Superconductor-Ferromagnet proximity system

TL;DR

This paper investigates the ground state of a superconductor-ferromagnet heterostructure, revealing a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) like state with spontaneous currents caused by Andreev bound states, influenced by disorder and interface transparency.

Contribution

It demonstrates the realization of an FFLO-like state with spontaneous currents in a ferromagnet-superconductor system using self-consistent quasiclassical theory.

Findings

FFLO-like state with oscillating pairing amplitude

Spontaneous current generated by Andreev bound states

Effects of disorder and interface transparency on the state

Abstract

We study the ground state properties of a ferromagnet-superconductor heterostructure on the basis of a quasiclassical theory. We have solved the Eilenberger equations together with Maxwell's equation fully self-consistently and found that due to the proximity effect a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) like state is realized in such system. Moreover this state has oscillations of the pairing amplitude in either one or two directions, depending on the exchange splitting and thickness of the ferromagnet. In particular, using semiclassical arguments (Bohr-Sommerfeld quantization rule) we show that owing to the presence of the Andreev bound states in the ferromagnet, a spontaneous current in the ground state is generated as a hallmark of the FFLO state in the direction parallel to the interface. We also discuss the effects of the the elastic disorder and finite transparency of the interface on the properties of the $FFLO$ state in the system.