00:00 11-03-2008

In many cases inhomogeneities are known to exist near the metal (or superconductor) - insulator transition even for a nominally homogenous material. This follows from either well-known domain-wall arguments or from an analysis of the Harris criterion. 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 than a metallic, state indeed appears. As an application, we will show that the various quite universal correlations, observed for high-Tc and many ordinary superconductors between the low-temperature superfluid density Ns and Tc, follow very simply from the inhomogeneous picture. These correlations include the Uemura and the Homes' ones. Both follow from our model for higher and lower resistance respectively. Finally, we shall discuss the question why many high-Tc materials conform to the dirty limit while their parameters put them in the clean limit.

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