Superconductivity, Charge Orderings and Phase Separations in Systems with Local Electron Pairing

We study two effective models developed for description of superconductors with short-coherence length: (i) the extended Hubbard model with on-site attraction and intersite repulsion, (ii) the model of hard-core charged bosons on a lattice. The analysis is concentrated on the problem of phase separations and competition between superconductivity (SS) and charge-density-wave (CDW) orderings. The phase diagrams of the systems are shown to consist of at least seven different states, including 3 types of phase separated (PS) states: CDW-SS (PS1), CDW-normal (PS2) and the state of electron droplets (PS3). By taking into account the PS states and the effects of longer-range density-density interactions (beyond nearest neighbors) our paper substantially generalizes and modifies the conclusions of previous papers concerning the models considered.