Andreev scattering and cotunneling between two superconductor-normal metal interfaces: the dirty limit

Crossed Andreev reflections and cotunneling occur between two neighbouring superconductor- normal metal or superconducting-ferromagnet interfaces. Previous works assumed a clean BCS superconductor. Here the calculation of the corresponding crossed conductance terms is generalized to a dirty superconductor. The range of the effect is shown to be the coherence length (ξ) over tilde = root(h) over barD/Delta, instead of the BCS coherence length xi(0). Moreover, in three dimensions, the algebraic prefactor scales as 1/r instead of 1/r(2). The calculation involves the virtual diffusion probability of quasiparticles below the superconducting gap, in the normal and the anomalous channel.