Inhomogeneous phases in the Falicov-Kimball model: Dynamical mean-field approximation

An inhomogeneous dynamical mean-field approximation is proposed to investigate inhomogeneous phases of strongly correlated electron systems. The approximation is based on the dynamical mean-field theory and the direct lattice space representation. Within the approximation the self-energy although is a local function of frequency, but it still depends on the lattice site. Applied the inhomogeneous dynamical mean-field approximation to the Falicov-Kimball model on a square lattice, various inhomogeneous phases are obtained. For intermediate couplings these phases are characterized by charge ordered clusters embedding in an almost homogeneous surrounding. The topology of the charge configuration of the clusters depends on the electron density and the number of ions. The clustered phases are a realization of the coexistence of the charge checkerboard ordering and segregation.