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 <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\tilde{\xi}=\sqrt{\hbar D/\Delta}$</EquationSource> </InlineEquation>, instead of the BCS coherence length <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\xi_0$</EquationSource> </InlineEquation>. Moreover, in three dimensions, the algebraic prefactor scales as 1/r instead of 1/r <Superscript>2</Superscript>. The calculation involves the virtual diffusion probability of quasiparticles below the superconducting gap, in the normal and the anomalous channel. Copyright Springer-Verlag Berlin/Heidelberg 2003