# Spin-polarized multiple Andreev reflections in spin-split superconductors

## TL;DR

This paper investigates how spin-splitting fields affect multiple Andreev reflections and subharmonic gap structures in superconductors, revealing an even-odd effect and providing a method to determine Zeeman field parameters.

## Contribution

It introduces a detailed analysis of spin-dependent Andreev reflections in spin-split superconductors, highlighting an even-odd effect and linking bound state splitting to Zeeman field characteristics.

## Key findings

- Odd order multiple Andreev reflections split in non-collinear fields
- Subharmonic gap structure depends on spin-splitting amplitude and orientation
- Threshold energies for spin-polarized Andreev processes are identified

## Abstract

We study the transport properties of a voltage biased contact between two spin-split superconductors separated by an insulating barrier of arbitrary transparency. At low transparency, the contribution of multiple Andreev reflections leads to a subharmonic gap structure that crucially depends on the amplitude and relative angle of the spin-splitting fields of each superconductor. For non-collinear fields, we find an interesting even-odd effect on the bound states within the gap, where the odd order multiple Andreev reflections split, but the even order ones remain at their expected positions. By computing the current-voltage characteristics, we determine the transparency required for the emergence of a subharmonic gap structure and show that the splitting of the odd bound states is associated with different threshold energies of spin-polarized Andreev processes. Our findings provide a tool to experimentally determine the amplitude and orientation of Zeeman fields in spin-split superconductors.