Current-Phase Relationship in Short Superconducting Weak Leans

Abstract

We propose a one-dimensional model of a superconducting link which is "weak" only insofar as it has a lower critical current than the superconductors on either side. According to appropriate solutions of the Ginzburg-Landau equations, the supercurrent $J$ is a single-valued, odd function of the phase change $\varphi$ across the link, which goes to zero at $\varphi =0\mathrm{}$ and $\varphi =\pi$ and tends to the Josephson relation $J\propto sin\varphi$ in the limit of a very weak link.