Phonon-assisted phase separation in strongly correlated systems

We relate the phase separation observed in many crystals with pronounced electron correlations to the regions of negative electron compressibility. They were found in several models describing strong electron correlations. At low temperatures, these regions arise near chemical potentials corresponding to the change of the ground state in the site Hamiltonian. The negative electron compressibility leads to the separation of the system into electron-rich and electron-poor domains. The energy released in the course of this separation is absorbed by phonons. Another role of phonons is to give a definite form -- stripes or checkerboards -- to lattice distortions and domains of different electron concentrations. The shape, direction, and periodicity of such textures are determined by wave vectors of lattice distortions, which most strongly scatter electrons.