Spontaneous symmetry breaking induced thermospin effect in superconducting tunnel junctions

We discuss the charge and the spin tunneling currents between two Bardeen-Cooper-Schrieffer (BCS) superconductors, where one density of states is spin-split by the proximity of a ferromagnetic insulator. In the presence of a large temperature bias across the junction, we predict the generation of a spin-polarized thermoelectric current. This thermospin effect is the result of a spontaneous particle-hole symmetry breaking in the absence of any polarizing tunnel barrier. The two spin components, which move in opposite directions, generate a spin current larger than the purely polarized case when the thermoactive component dominates over the dissipative one.