Andreev bound states for superconducting-ferromagnetic box

TL;DR

This paper derives an exact quantization condition and a semi-classical density of states formula for Andreev bound states in ferromagnetic-superconducting boxes, showing their agreement across various exchange field strengths.

Contribution

It introduces a new exact quantization condition and semi-classical approximation for Andreev bound states in ferromagnetic-superconducting hybrid systems with box geometry.

Findings

Semi-classical formula agrees with exact results for large exchange fields.

The formulas are valid when the exchange field is small compared to the Fermi energy.

The work extends understanding of bound states in hybrid superconducting-ferromagnetic systems.

Abstract

Within the microscopic Bogoliubov--de Gennes (BdG) formalism an exact quantization condition for Andreev bound states of the ferromagnetic-superconducting hybrid systems of box geometry is derived and a semi-classical formula for the density of states is obtained. The semi-classical formula is shown to agree with the exact result, even when the exchange field $h$, is much larger than the superconductor order parameter, provided $h$ is small compared with the Fermi energy.