Superconductor-insulator transition in the presence of Coulomb disorder

Superconductor-insulator transition driven by the decreasing concentration of electrons n is studied in the case of the disorder potential created by randomly positioned charged impurities. Electrons and Cooper pairs (formed by a non-Coulomb attraction) nonlinearly screen the random potential of impurities. Both electrons and Cooper pairs can be delocalized or localized in the resulting self-consistent potential. The border separating the superconductor and insulator phases in the plane of the concentration of electrons and the length of the Cooper pair is found. For a strong disorder, the central segment of this border follows the Bose-Einstein-Condensation-BCS crossover line defined for a clean sample.