Theory of the "universal" degradation of T c in high-temperature superconductors

The superconducting ${T}_{c}$ decreases similarly with disorder (as measured by resistivity $\ensuremath{\rho}$) for all systems with high ${T}_{c}$. We propose that this is a localization effect. For strong disorder, electron diffusion is slow and strongly scale dependent. This increases the effective Coulomb repulsion. Model calculations with realistic parameters describe well the experimental ${T}_{c}\ensuremath{-}\mathrm{vs}\ensuremath{-}\ensuremath{\rho}$ curves. Explanations are suggested for the relatively large critical conductance found.