Crossed Andreev Reflection and Charge Imbalance in Diffusive Normal-Superconducting-Normal Structures

We formulate a microscopic theory of nonlocal electron transport in three-terminal diffusive normal-superconducting-normal (NSN) structures with arbitrary interface transmissions. At low energies epsilon, we predict strong enhancement of nonlocal spectral conductance g(12)proportional to 1/epsilon due to quantum interference of electrons in disordered N terminals. In contrast, nonlocal resistance R(12) remains smooth at small epsilon and, furthermore, is found to depend neither on parameters of normal-superconducting interfaces nor on those of N terminals. At higher temperatures, R(12) exhibits a peak caused by the trade-off between charge imbalance and Andreev reflection. Our results are in a good agreement with recent experimental observations and can be used for quantitative analysis of future experiments.