MICROSCOPIC THEORY OF JOSEPHSON MESOSCOPIC CONSTRICTIONS

We present a microscopic theory for the dc Josephson effect in model mesoscopic constrictions. Our method is based on a nonequilibrium Green function formalism which allows for a self-consistent determination of the order parameter profile along the constriction. The various regimes defined by the different length scales (Fern-Li wavelength lambda(F), coherence length xi0, and constriction length L(C)) can be analyzed, including the case where all these lengths are comparable. For lambda(F) less than or similar (L(C), xi0) phase oscillations with spatial period lambda(F)/2 can be observed. For L(C) > xi0 solutions with a phase-slip center inside the constriction can be found, in agreement with previous phenomenological theories.