The superfluid density - Tc correlations in inhomogenous superconductors

Following a short discussion of the granular model for an inhomogenous superconductor, we review the Uemura and Homes correlations. We show how both follow in two appropriate limits of a simple granular superconductor model. Definite expressions are given for the almost universal coefficients appearing in

these relationships in terms of known constants. The picture is in a semiquantitative agreement with a large number of experimental results on both high- T_c and disordered conventional superconductors. A physical understanding will be given to how these inhomogeneities often arise.