An Inhomogeneous Josephson Phase Near the (Super) Conductor-Insulator Transition

In many cases inhomogeneities are known to exist near the metal (or superconductor)- insulator transition, as follows from well-known domain-wall arguments. If the conducting regions are large enough, and if they have superconducting correlations, it becomes energetically favorable for the system to go into a Josephson- coupled zero-resistance state before (i.e. at higher resistance than) the material becomes a real metal. We show that this is plausible by a simple comparison of the relevant coupling constants. We also illustrate using data in the literature on oxide materials as well as ultra-thin films, that when this proposed Josephson state is quenched by a magnetic field, an insulating, rather then a metallic, state indeed appears.