Superconductivity in a dilute array of sites with strong onsite electron attraction

Superconductivity in a conducting material with a dilute array negative-$U$ sites with strong electron–electron attraction is studied. It is shown that at the attraction exceeding a certain threshold value, Cooper pairs arise at the sites. At low temperatures, a global coherent superconducting state emerges due to the intersite Andreev scattering. The dependences of the superconducting transition temperature and of the second critical magnetic field on the magnitude of attraction are calculated.