Excitonic Insulator State of the Extended Falicov–Kimball Model in the Cluster Dynamical Impurity Approximation

Abstract

We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity approximation (CDIA). In the latter, the particle-bath sites are included in the reference cluster to take into account the particle-number fluctuations in the correlation sites. We thus calculate the particle-number distribution, order parameter, ground-state phase diagram, anomalous Green's function, and pair coherence length, thereby demonstrating the usefulness of the CDIA in the discussion of the excitonic condensation in the EFKM. IntroductionThe excitonic phases, often referred to as excitonic insulators (EIs), are the states where the valence and conduction bands are hybridized spontaneously by the interband Coulomb interaction, and have been predicted to occur near the semimetal-semiconductor phase boundary as the quantum condensation of electron-hole pairs (excitons). [1][2][3][4][5][6] In the semimetallic region, where the Coulomb interaction is largely screened by free carriers, the excitonic phase is described in analogy to the BCS theory of superconductivity, whereas in the semiconducting region, it is described as the Bose-Einstein condensation (BEC) of preformed excitons (or strongly bound electron-hole pairs). Thus, the BCS-BEC crossover is expected to occur by controlling the band gap from a negative value to a positive one. [7][8][9] In recent years, the possible realization of spinsinglet excitonic condensation has been suggested for transition-metal chalcogenides such as 1T -TiSe 2 and Ta 2 NiSe 5 . 10-23) The spin-triplet excitonic condensation has also been suggested to occur in the high-spin/lowspin crossover region of some cobalt oxide materials with the cubic perovskite structure. 24-29) Because these materials are among transition-metal chalcogenides and oxides, where the effects of electron correlations are strong, one must reconsider the excitonic phases from the standpoint of strongly correlated electron systems. 30-32) Thus, the lattice models such as Hubbard models, rather than the gas models, are appropriate for use. The spinless extended Falicov-Kimball model (EFKM) is the simplest lattice model for describing the excitonic phases, and has been used to discuss, for example, the BCS-BEC crossover of the excitonic condensation. 33-41) The multiband Hubbard model, taking into account the spin de-

Excitonic Phase Diagram of the Three-Chain Hubbard Model for Semiconducting and Semimetallic Ta2NiSe5

“…12,13) Several theoretical studies [14][15][16][17][18] have revealed that the transition is well accounted for by the excitonic condensation from a normal semiconductor (orthorhombic) to the EI (monoclinic) from a mean-field analysis for the 1-D threechain Hubbard model with electron-lattice coupling 14,16) and from a variational cluster approximation for the extended Falicov-Kimball model. 15,19) Recent optical measurements are also consistent with the EI phase below T c . 20,21) When the pressure is applied for Ta 2 NiSe 5 , 22,23) the structural phase transition temperature T c is suppressed and the system changes from semiconducting to semimetallic both above and below T c , and then, T c finally becomes zero at a critical pressure P c ∼ 8GPa, around which the superconductivity is observed.…”

Extended Falicov-Kimball model: Exact solution for the ground state

“…Some studies on the subject have also been performed for the extended version of the FKM (EFKM); e.g., Refs. [51][52][53].…”

Extended Falicov-Kimball model: Exact solution for finite temperatures

“…The effects of Coulomb's interactions between electrons located on neighboring lattice sites have already been intensively investigated for the extended Hubbard model, e.g., Refs. [35][36][37][38][39][40][41][42][43][44] and references therein, while for the EFKM only very few results have been reported so far [34,[45][46][47][48][49]. As far as we know, exact results for the EFKM were only reported in Refs.…”