# Colloquium: Nonequilibrium effects in superconductors with a spin-splitting field

## TL;DR

This paper reviews recent advances in understanding non-equilibrium phenomena in spin-split superconductors, highlighting their transport properties and potential applications in thermoelectricity and spintronics.

## Contribution

It provides a comprehensive theoretical framework based on quantum kinetic equations to describe non-equilibrium charge, spin, and energy distributions in hybrid superconducting structures.

## Key findings

- Large thermoelectric effects observed in spin-split superconductors
- Transport measurements reveal properties of non-equilibrium modes
- Spin injection and diffusion are extensively characterized

## Abstract

We review the recent progress in understanding the properties of spin-split superconductors under non-equilibrium conditions. Recent experiments and theories demonstrate a rich variety of transport phenomena occurring in devices based on such materials that suggest direct applications in thermoelectricity, low-dissipative spintronics, radiation detection and sensing. We discuss different experimental situations and present a theoretical framework based on quantum kinetic equations. Within this framework we provide an accurate description of the non-equilibrium distribution of charge, spin and energy, which are the relevant non-equilibrium modes, in different hybrid structures. We also review experiments on spin-split superconductors and show how transport measurements reveal the properties of the non-equilibrium modes and their mutual coupling. We discuss in detail spin injection and diffusion and very large thermoelectric effects in spin-split superconductors.