# Proximity Effect in Superconducting Heterostructures with Strong Spin-Orbit Coupling and Spin Splitting

## TL;DR

This paper investigates how strong spin-orbit coupling and exchange fields in superconducting heterostructures influence the proximity effect, revealing conditions under which long-range proximity effects are suppressed or enhanced.

## Contribution

It develops a generalized quasiclassical theory for systems with large SOC and exchange fields, clarifying the conditions affecting the long-range proximity effect in such materials.

## Key findings

- No long-range proximity effect when SOC energy is comparable to exchange field.
- Impurities with strong SOC and exchange fields induce spin-flip scattering, suppressing the proximity effect.
- Increasing SOC or exchange field can extend the decay length of superconducting correlations.

## Abstract

It has been shown that singlet Cooper pairs can be converted into triplet ones and diffuse into a ferromagnet over a long distance in a phenomenon known as the long-range proximity effect (LRPE). This happens in materials with inhomogeneous magnetism or spin-orbit coupling (SOC). Most of the previous studies focus on the cases with small SOC and exchange field. However, the physics was not clear when SOC and exchange field strength are both much greater than the disorder strength. In this work, we consider a two dimensional system with a large Rashba-type SOC and exchange field in the case where only one band is partially occupied. We develop a generalized quasiclassical theory by projecting the Green function onto the partially occupied band (POB). We find that when the SOC energy scale is comparable with the exchange field, there is no LRPE. The reason is that the nonmagnetic impurities together with the large SOC and exchange field can effectively generate spin-flip scattering, which suppresses the proximity effect. We also show that when increasing either SOC or exchange field, the decay length of superconducting correlations can be significantly increased due to an approximately restored time reversal symmetry or spin rotation symmetry around the $z$ (out-of-plane) axis.