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arXiv:cond-mat/9912178 · Physical review. B, Condensed matter

Segregation and charge-density-wave order in the spinless Falicov-Kimball model

James K. Freericks, R. Lemański

Published May 15, 2000• 26 citations
arXivHTMLPDF

Abstract

The spinless Falicov-Kimball model is solved exactly in the limit of infinite dimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large $U,$ and charge-density-wave order, which is prevalent at moderate $U,$ is examined in detail. We find a rich phase diagram that displays both of these phases. The model also shows nonanalytic behavior in the charge-density-wave transition temperature when $U$ is large enough to generate a correlation-induced gap in the single-particle density of states.

DOI
10.1103/physrevb.61.13438

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The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions contain both second-order phase transitions and first-order phase transitions (that involve phase separation or segregation) which are likely to illustrate the precursor physics behind the static charge-stripe ordering in cuprate systems. In addition, we find that the spinodal-decomposition temperature satisfies an approximate scaling law.
The phase diagram for the spinless Falicov-Kimball model on a hypercubic lattice is reexamined in the limits of large and small dimensions (for the half-filled ion case). This model is identical to the thermodynamical problem of an annealed binary alloy with diagonal disorder. The phase diagram for the infinite-dimensional case is remarkably similar to the conjectured phase diagram for the one-dimensional case. The system orders in short-period phases, orders in long-period (possibly incommensurate) phases, or segregates, depending on the interaction strength and the electron concentration. The analysis for this simple model provides hope that recently proposed solutions for other interacting fermion models in infinite dimensions will accurately represent the solutions in two and three dimensions.
We study the spectral properties of the charge-density-wave (CDW) phase of the half-filled spinless Falicov-Kimball model within the framework of the dynamical mean field theory. We present detailed results for the spectral function in the CDW phase as a function of temperature and UUU. We show how the proximity of the non-Fermi liquid phase affects the CDW phase, and show that there is a region in the phase diagram where we get a CDW phase without a gap in the spectral function. This is a radical deviation from the mean-field prediction where the gap is proportional to the order parameter.
The ground-state density of states of the half-filled Falicov-Kimball model contains a charge-density-wave gap. At finite temperature, this gap is not immediately closed, but is rather filled in by subgap states. For a specific combination of parameters, this leads to a stable phase where the system is in an ordered charge-density-wave phase, but there is high density of states at the Fermi level. We show that this property can be, in finite dimensions, traced to a crossing of sharp states resulting from the single particle excitations of the localized subsystem. The analysis of the inverse participation ratio points to a strong localization in the discussed regime. However, the pronounced subgap density of states can still lead to a notable increase of charge transport through a finite size system. We show this by focusing on the transmission in heterostructures where a Falicov-Kimball system is sandwiched between two metallic leads.
The spin-12\frac{1}{2}21​ Falicov-Kimball model is solved exactly on an infinite-coordination-number Bethe lattice in the thermodynamic limit. This model is a paradigm for a charge-transfer metal-insulator transition, where the occupancy of localized and delocalized electronic orbitals rapidly changes at the metal-insulator transition (rather than the character of the electronic states changing from insulating to metallic as in a Mott-Hubbard transition). The exact solution displays both continuous and discontinuous (first-order) transitions.