# Proximity effect in a ferromagnetic semiconductor with spin-orbit interactions

## TL;DR

This paper theoretically investigates how spin-orbit interactions influence the proximity effect and Cooper pair symmetry in ferromagnetic semiconductors, revealing disorder-dependent dominant pairing states and effects on Josephson current.

## Contribution

It provides a theoretical analysis of the proximity effect in ferromagnetic semiconductors with Rashba spin-orbit coupling, highlighting disorder-dependent Cooper pair symmetries and their impact on Josephson effects.

## Key findings

- In clean limits, spin-singlet pairs dominate due to spin-momentum locking.
- In dirty limits, equal-spin-triplet pairs dominate because of impurity effects.
- Spin-orbit interaction significantly influences the Josephson current behavior.

## Abstract

We study theoretically the proximity effect in a ferromagnetic semiconductor with Rashba spin-orbit interaction. The exchange potential generates opposite-spin-triplet Cooper pairs which are transformed into equal-spin-triplet pairs by the spin-orbit interaction. In the limit of strong spin-orbit interaction, symmetry of the dominant Cooper pair depends on the degree of disorder in a ferromagnet. In the clean limit, spin-singlet $s$-wave Cooper pairs are the most dominant because the spin-momentum locking stabilizes a Cooper pair consisting of a time-reversal partner. In the dirty limit, on the other hand, equal-spin-triplet $s$-wave pairs are dominant because random impurity potentials release the locking. We also discuss the effects of the spin-orbit interaction on the Josephson current.