Absence of charge backscattering in the nonequilibrium current of normal - superconductor structures

We study the nonequilibrium transport properties of a normal-superconductor-normal structure, focussing on the effect of adding an impurity in the superconducting region. Current conservation requires the su-perfluid velocity to be nonzero, causing a distortion of the quasiparticle dispersion relation within the superconductor. For weakly reflecting interfaces we find a regime of intermediate voltages in which Andreev transmission is the only permitted mechanism for quasiparticles to enter the superconductor. Impurities in the superconductor can only cause Andreev reflection of these quasiparticles and thus cannot degrade the current. At higher voltages, a state of gapless superconductivity develops which is sensitive to the presence of impurities. 1 During the last few years, considerable progress has been made in the understanding of transport in mesoscopic structures with superconducting elements. 1 The possibility of phase-coherent Andreev reflection 2 provides a rich variety of situations with novel transport anomalies. 3 It has been pointed out 4,5 that a limitation of conventional descriptions of An-dreev reflection is that, by assuming a uniform phase in the superconducting region, they implicitly contain a violation of current conservation. While this shortcoming may be unimportant in the regime of low current densities, it certainly cannot be overlooked in situations where the superconductor supports current densities that are comparable to its equilibrium critical value. This may easily be the case in transmissive structures with applied voltages V ∼ ∆ 0 /e, where ∆ 0 is the zero current superconducting gap. It has been shown 4,5 that the introduction of a nonuniform superconducting phase to ensure self-consistency (and, with it,