The superconductor-insulator transition in the presence of strong compensation was recently realized in La doped YBCO. Compensation of acceptors by donors makes it possible to change independently the concentration of holes n and the total concentration of charged impurities N. We propose a theory of the superconductor-insulator phase diagram in the (N, n) plane, which exhibits interesting new features in the case of strong coupling superconductivity, where Cooper pairs are compact, non-overlapping bosons. For compact Cooper pairs the transition occurs at a significantly higher density than in the case of spatially overlapping pairs. We establish the superconductor insulator phase diagram by studying how the potential of randomly positioned charged impurities is screened by by strongly bound Cooper pairs. The pairs are either delocalized or localized in the resulting self-consistent potential.
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