Non-local Andreev reflection in superconducting quantum dots

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Abstract
With the aid of the Keldysh technique, we develop a microscopic theory of non-local electron transport in three-terminal normal metal–superconductor–normal metal (NSN) structures consisting of a chaotic superconducting quantum dot attached to one superconducting and two normal electrodes. Our theory fully accounts for nonequilibrium effects and disorder in a superconducting terminal. We go beyond the perturbation theory in tunneling and derive a general expression for the system conductance matrix, which remains valid in both weak and strong tunneling limits. We demonstrate that the proximity effect yields a decrease of the crossed Andreev reflection (CAR). Beyond the weak tunneling limit, the contribution of CAR to the non-local conductance does not cancel that of the direct electron transfer between two normal terminals. We argue that the temperature dependence of the non-local resistance of NSN devices is determined by the two competing processes—Andreev reflection and charge imbalance—and it has a pronounced peak occurring at the crossover between these two processes. This behavior is in a good agreement with recent experimental observations.
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