Electron orderings and phase separation in extended Hubbard models: superconductivity and charge orderings

Abstract: In this lecture we present results for a class of extended Hubbard models. In first part we discuss the exact results for a lattice model of superconductor with pair hopping. We focus on properties of superconducting phase (including metastable phases) and an influence of the external paramagnetic field. Moreover we analyze the effects of intersite magnetic and density-density interactions on mutual relations and competition between superconductivity and other electron orderings: magnetic and charge-ordered phases. Our results are exact in the limit of infinite dimensions. We also discuss the exact and some approximate results for finite dimensions in the ground state. They show that superconductivity can coexists with charge orderings and magnetism in states with phase separation. In addition, effects of finite bandwidth in the model considered will be presented (results obtained by various approximate methods). In second part we show results for the extended Hubbard model with both (i) the effective on-site interaction U and (ii) the intersite density-density interactions W (nearest-neighbors and next-nearest neighbors). In the analysis of the phase diagrams and thermodynamic properties of this model we have adopted the approaches, which treat the on-site interaction term exactly and the intersite interactions within the mean- field approximation. For finite bandwidth the model have been studied using diagonalization method by Lanczos algorithm within the dynamical mean field theory. Our investigation of the general case show that, depending on values of the interaction parameters and electron concentration/chemical potential, the system can exhibit not only several homogeneous charge ordered metallic and insulating phases, but also various phase separated states.