Crossed Andreev reflection and spin-resolved non-local electron transport

The phenomenon of crossed Andreev reflection (CAR) is known to play a key role in non-local electron transport across three-terminal normal-superconducting-normal (NSN) devices. Here we review our general theory of non-local charge transport in three-terminal disordered ferromagnet-superconductor-ferromagnet (FSF) structures. We demonstrate that CAR is highly sensitive to electron spins and yields a rich variety of properties of non-local conductance which we describe non-perturbatively at arbitrary voltages, temperature, degree of disorder, spin-dependent interface transmissions and their polarizations. We demonstrate that magnetic effects have different implications: While strong exchange field suppresses disorder-induced electron interference in ferromagnetic electrodes, spin-sensitive electron scattering at SF interfaces can drive the total non-local conductance negative at sufficiently low energies. At higher energies magnetic effects become less important and the non-local resistance behaves similarly to the non-magnetic case. Our results can be applied to multi-terminal hybrid structures with normal, ferromagnetic and half-metallic electrodes and can be directly tested in future experiments.