Microscopic Theory of Josephson Mesoscopic Constrictions

Abstract

We present a microscopic theory for the d.c. Josephson effect in model mesoscopic constrictions. Our method is based on a non-equilibrium 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 (Fermi wavelength ${\lambda }_F$, coherence length ${\xi }_0$ and constriction length $L_C$) can be analyzed, including the case where all these lengths are comparable. For the case ${\lambda }_F\widetilde{<}(L_C,{\xi }_0)$ phase oscillations with spatial period ${\lambda }_F/2$ can be observed. In the case of $L_C>{\xi }_0$ solutions with a phase-slip center inside the constriction can be found, in agreement with previous phenomenological theories.

4 pages (RevTex 3.0), 3 postscript figures available upon request, 312456-CG

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