MICROSCOPIC THEORY OF JOSEPHSON MESOSCOPIC CONSTRICTIONS

We present a microscopic theory for the dc Josephson effect in model m esoscopic constrictions. Our method is based on a nonequilibrium Green function formalism which allows for a self-consistent determination o f the order parameter profile along the constriction. The various regi mes defined by the different length scales (Fern-Li wavelength lambda( F), coherence length xi0, and constriction length L(C)) can be analyze d, including the case where all these lengths are comparable. For lamb da(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 p hase-slip center inside the constriction can be found, in agreement wi th previous phenomenological theories.