Superconducting spin filter

Consider two normal leads coupled to a superconductor; the first lead is biased while the second one and the superconductor are grounded. In general, a finite current I₂(V₁, 0) is induced in grounded lead 2; its magnitude depends on the competition between processes of Andreev and normal quasiparticle transmission from lead 1 to lead 2. It is known that, in the tunneling limit, when normal leads are weakly coupled to the superconductor, I₂(V₁, 0)=0 if |V₁|<Δ, and the system is in the clean limit. In other words, Andreev and normal tunneling processes compensate each other. We consider the general case: the voltages are below the gap, the system is either dirty or clean. It is shown that I₂(V₁, 0)=0 for general configuration of the normal leads; if the first lead injects spin-polarized current then I₂=0, but spin current in lead 2 is finite. A XISIN structure, where X is a source of the spin-polarized current, could be applied as a filter separating spin current from charge current. We do an analytical progress calculating I₁(V₁, V₂), I₂(V₁, V₂).