Microscopic theory of the dc Josephson effect in clean superconductor/insulator and superconductor/semiconductor multilayers

We have constructed a fully microscopic self-consistent theory of the dc Josephson effect in clean periodic superconducting multilayers with realistic finite-size repulsive barriers, at arbitrary temperatures. We have derived an explicit analytical expression for the critical Josephson current jc as a function of the superconductor-layer thickness a. In the limit a<ξ0, we have found fundamental differences with the Ambegaokar-Baratoff relation: a strong reduction of jc and an unusual temperature dependence. In this limit, we also predict an exponential decrease of the critical temperature and the gap parameter due to the depairing effect of the Josephson current. copyright 1997 The American Physical Society