Anwendungen und Erweiterungen des Falicov-Kimball-Modells : CDW-Phasen und exzitonische Isolatorphasen im erweiterten FKM

Abstract

The Falicov-Kimball Model (FKM) is one of the simplest two-band models for correlated electrons in solid state theory. It describes itinerant c-electrons which interact with localized f-electrons by short-range Coulomb repulsion :i:U:/i:. Since its introduction in 1969 it has been used to study metal-insulator transitions, mixed-valence phenomena, crystallization etc. During the past few years the possibility of electronic ferroelectricity (EFE) has been suggested and controversely discussed.:p:This work extends the FKM by an f-f hopping :i:t:/i::sub:f:/sub:, giving the f-band a realistic finite bandwidth. Our aim is to study phase transitions and to create a ground state phase diagram in the weak-coupling limit. Using self-consistent Hartree-Fock calculations, we examine charge density waves (CDW) and electronic ferroelectricity (EFE) simultaneously.:p:As a result, we find a rich phase diagram for :i:t:/i::sub:f:/sub: and the f-level energy :i:E:/i::sub:f:/sub:. Near the symmetric case (:i:E:/i::sub:f:/sub:=0) the system builds a stable CDW phase with an insulating intraband gap in both c- and f-densities of states. For higher values of :i:E:/i::sub:f:/sub: it undergoes a first order phase transitionleading to an (anti-)ferroelectric phase depending on the sign of :i:t:/i::sub:f:/sub:. The intraband gap persists as an effective hybridization gap, giving rise to an interpretation as excitonic insulator phase. If one raises the f-level energy further the ferroelectronic phase vanishes and is replaced by a band insulator (for high values of :i:U:/i:) or, alternatively, by a semi-metal phase (for low values of :i:U:/i:). The (anti-)ferroelectric phase transition is of second order. No coexistence of CDW and excitonic insulator phases is found in the numerical Hartree-Fock treatment.