Superconducting spin filter

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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 the grounded lead 2; its magnitude depends on the competition between processes of Andreev and normal quasiparticle transmission from the lead 1 to the 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 the lead-2 is finite. 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).