Abstract
A model of superconductivity is proposed taking into account repulsive particle interaction, mesoscopic phase separation and softening of the crystalline lattice. These features are typical of many high-temperature superconductors. The main results obtained for the model are: (1) phase separation is possible only if repulsive forces play a significant role; (2) the critical temperature as a function of the superconducting phase fraction can have non-monotonic behaviour; (3) superconductivity is possible in heterophase systems even when it would be forbidden in pure samples. These results are in agreement with experiments.
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