Theory of quantum conduction of supercurrent through a constriction

Abstract

The dc Josephson current through a constriction in a two-dimensional superconductor-semiconductor-superconductor junction is calculated. It is shown that when the Fermi wavelength is comparable with the width of the constriction, the critical current shows a steplike variation as a function of the width of the constriction; this is reminiscent of the quantization of the normal-state conductance of point contacts in a two-dimensional electron gas.