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arXiv:1204.6499 · Physical Review B

Collective excitations and stability of the excitonic phase in the extended Falicov-Kimball model

Denis I. Golosov

Published Oct 18, 2012• 11 citations
arXivHTMLPDF

Abstract

We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov-Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridization. This allows to probe the mean-field stability of the excitonic insulator. The latter is found to be unstable when the case of the pure FKM (no hybridization with a fully localized band) is approached. The instability is due to the presence of another, lower-lying ground state and not to the degeneracy of the excitonic phase in the pure FKM. The excitonic phase, however, may be stabilized further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains important information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).

DOI
10.1103/physrevb.86.155134

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We obtain exact ground states for the spinless Falicov-Kimball model with hybridization in one dimension $(d=1).$ Ground-state energies and their corresponding wave functions are given for a restricted region of the parameter space in the limit of strong interactions for the half-filling condition. We find that the ground states possess a diagonal long range order and constitute a condensation of excitons in a zero momentum state. On the other hand, the correlation function $A=〈{d}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{f}_{i}〉$ is purely imaginary, indicating that the ground state does not exhibit spontaneous ferroelectricity.

Physical Review B•Feb 20, 2004•15 citations
We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov-Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridization. This allows to probe the mean-field stability of the excitonic insulator. The latter is found to be unstable when the case of the pure FKM (no hybridization with a fully localized band) is approached. The instability is due to the presence of another, lower-lying ground state and not to the degeneracy of the excitonic phase in the pure FKM. The excitonic phase, however, may be stabilized further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains important information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).
We consider an extended spinless Falicov-Kimball model at an arbitrary doping level, focusing on the range of parameter values where a uniform excitonic insulator is stabilized at half-filling. In the two-dimensional case, we compare the properties of possible uniform phases and construct the Hartree--Fock phase diagrams, which include sizable phase separation regions. It is seen that the excitonic insulator can appear as a component phase in a mixed-phase state in a broad interval of doping levels. In addition, in a certain range of parameter values the excitonic metal (doped excitonic insulator) is identified as the lowest-energy uniform phase. We suggest that this phase, which is unstable with respect to phase separation, may be stabilized when the phase separation is suppressed by the long-range Coulomb interaction. Overall, we find that excitonic correlations can affect the behavior of the system relatively far away from half-filling.
The density matrix renormalization group (DMRG) method is used to examine the effects of the interband Coulomb interaction U between f and d electrons as well as the f -electron hopping on the stability of the excitonic phase in the one-dimensional Falicov-Kimball model (FKM) with local hybridization V . It is found that the interband Coulomb interaction significantly enhances the excitonic average and that this effect is especially strong in the limit of small hybridization, where the interacting excitonic value is enhanced several hundred times in comparison to its non-interacting value. The further increase in P df is observed due to the non-zero f -electron hopping, but these changes are considerable only if the d and f bands have opposite parity. In addition, the examination of the interplay between the excitonic effects and the charge density wave (CDW) instability showed that the CDW and excitonic phase coexist up to relatively large values of local hybridization . The ground-state phase diagram of the model in the plane is discussed.
Using exact numerical techniques, we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram of the model exhibits, besides band-insulator and staggered orbital ordered phases, an excitonic insulator (EI) with power-law correlations. The criticality of the EI state shows up in the von Neumann entropy. The anomalous spectral function and condensation amplitude provide the binding energy and coherence length of the electron-hole pairs which, on their part, point towards a Coulomb interaction driven crossover from BCS-like electron-hole pairing fluctuations to tightly bound excitons. We show that while a mass imbalance between electrons and holes does not affect the location of the BCS-BEC crossover regime, it favors staggered orbital ordering to the disadvantage of the EI. Within the Bose-Einstein condensation (BEC) regime, the quasiparticle dispersion develops a flat valence-band top, in accord with the experimental finding for Ta2NiSe5.
The extended Falicov-Kimball model, with both an on-site hybridization potential and dispersive narrow band, is examined within the saddle-point approximation to the Kotliar-Ruckenstein [Phys. Rev. Lett. 57, 1362 (1986)] slave-boson theory. We first set the hybridization potential to zero and find that the phase diagram depends strongly on the orbital structure: for degenerate orbitals, a correlated-insulating state is found at sufficiently strong interaction strengths, whereas a finite orbital energy difference can lead to discontinuous valence transitions. The obtained phase diagram is very sensitive to the presence of a finite hybridization potential. As in Hartree-Fock theory, we find an enhancement of the hybridization by the interorbital Coulomb repulsion. The more precise treatment of correlation effects, however, leads to large deviations from the Hartree-Fock results. In the limit of vanishing hybridization, an excitonic insulator state is only found when the orbitals are degenerate, which restricts this phase to a much smaller parameter space than in other available mean-field theories.
Two-dimensional spinless Falicov-Kimball model (FKM) with correlated hopping is studied perturbatively in the limit of large on-site Coulomb interaction U. In the half filled case (i.e., ${\ensuremath{\rho}}_{i}+{\ensuremath{\rho}}_{e}=1,$ where ${\ensuremath{\rho}}_{i},{\ensuremath{\rho}}_{e}$ are densities of ions and electrons, respectively) the effective Hamiltonian in spin variables is derived up to terms proportional to ${U}^{\ensuremath{-}3}.$ Unlike the simplest FKM case, it contains odd parity terms (resulting from the correlated hopping) in addition to even parity ones. The ground-state phase diagram of the effective Hamiltonian is examined in the (a/t,h)(a/t,h)(a/t,h) plane, where a/ta/ta/t is a parameter characterizing strength of the correlated hopping and h is a difference of chemical potentials of two sorts of particles present in the system. It appears to be asymmetric with respect to the change $\stackrel{\ensuremath{\rightarrow}}{h}\ensuremath{-}h$ and an additional ordered phase is found for a certain interval of a/t.a/t.a/t.
We obtain exact ground states for the spinless Falicov-Kimball model with hybridization in one dimension (d=1).(d=1).(d=1). Ground-state energies and their corresponding wave functions are given for a restricted region of the parameter space in the limit of strong interactions for the half-filling condition. We find that the ground states possess a diagonal long range order and constitute a condensation of excitons in a zero momentum state. On the other hand, the correlation function $A=〈{d}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{f}_{i}〉$ is purely imaginary, indicating that the ground state does not exhibit spontaneous ferroelectricity.