We formulate a microscopic theory of non-local electron transport in three-terminal diffusive normal-superconducting-normal (NSN) structures with arbitrary interface transmissions. At low energies $\varepsilon$ we predict strong enhancement of non-local spectral conductance $g_{ 12} \propto 1/\varepsilon$ due to quantum interference of electrons in disordered N-terminals. In contrast, non-local resistance $R_{ 12}$ remains smooth at small $\varepsilon$ and, furthermore, is found to depend neither on parameters of NS 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.
Categories: cond-mat.supr-con cond-mat.mes-hall