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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.
Motivated by the recent proposals for unconventional emergent physics in twisted bilayers of nodal superconductors, we study the peculiarities of the Josephson effect at the twisted interface between $d$-wave superconductors. We demonstrate that for
A thin superconducting disk, with radius $R=4xi$ and height $H=xi$, is studied in the presence of an applied magnetic field parallel to its major axis. We study how the boundaries influence the decay of the order parameter near the edges for three-dimensional vortex states.
We propose a mechanism whereby spin supercurrents can be manipulated in superconductor/ferromagnet proximity systems via nonequilibrium spin injection. We find that if a spin supercurrent exists in equilibrium, a nonequilibrium spin accumulation will
The Andreev bound states and charge transport in a Josephson junction between two superconductors with intrinsic exchange fields are studied. We find that for a parallel configuration of the exchange fields in the superconductors the discrete spectru
Electron tunneling between superconductors and normal metals has been used for an efficient refrigeration of electrons in the latter. Such cooling is a non-linear effect and usually requires a large voltage. Here we study the electron cooling in hete