BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

Seki, Koh‐ichi; Eder, R.; Ohta, Y.

doi:10.1103/physrevb.84.245106

Cited by 97 publications

(145 citation statements)

References 43 publications

(50 reference statements)

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“…From the theoretical side, the extended FalicovKimball model was considered as a paradigmatic model to describe the EI formation and the closely related phenomenon of electronic ferroelectricity [30][31][32][33][34][35][36][37][38][39][40][41] . Here the spin degrees of freedom were not taken into account, however.…”

Section: Introductionmentioning

confidence: 99%

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

et al. 2015

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We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an "excitonic" CDW if predominantly triggered by the effective interorbital electron-hole attraction or a "phononic" CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.

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Section: Introductionmentioning

confidence: 99%

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

et al. 2015

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“…[33][34][35][36][37][38][39][40][41] Assuming a two-dimensional square lattice, we define the Hamiltonian of the EFKM as…”

Section: Extended Falicov-kimball Modelmentioning

confidence: 99%

“…With increasing U from the noninteracting semimetallic state, the EI state shows a smooth crossover from the weak-coupling BCS state to the strong-coupling BEC state. [36][37][38][39] Thus, the EFKM is used to discuss the BCS-BEC crossover of the excitonic condensation.…”

Section: Extended Falicov-kimball Modelmentioning

confidence: 99%

“…For example, the number of electrons in the valence and conduction bands changes discontinuously as a function of energy-level splitting between the valence and conduction orbitals. This is because the number of electrons in the cluster is fixed, or the electron-number fluctuation in the cluster is prohibited, so that the finite-size effects appear even in the VCA, 38,44) where the system of connecting the clusters is treated variationally in the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

“…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][34][35][36][37][38][39][40][41] The multiband Hubbard model, taking into account the spin de- * ohta@faculty.chiba-u.jp grees of freedom, has also been used to discuss, for example, the relative stability of the spin-singlet and spintriplet excitonic phases. [42][43][44][45][46][47][48][49] We have so far studied the excitonic phases of the EFKM and multiband Hubbard models using the variational cluster approximation (VCA) based on the exact diagonalization of small clusters.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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-

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Excitonic Phase Transition in the Extended Three-Dimensional Falicov–Kimball Model

Apinyan

Kopeć

2014

J Low Temp Phys

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We study the excitonic phase transition in a system of the conduction band electrons and valence band holes described by the three-dimensional (3D) extended Falicov-Kimball (EFKM) model with the tunable Coulomb interaction U between both species. By lowering the temperature, the electronhole system may become unstable with respect to the formation of the excitons, i.e, electron-hole pairs at temperature T = T∆, exhibiting a gap ∆ in the particle excitation spectrum. To this end we implement the functional integral formulation of the EFKM, where the Coulomb interaction term is expressed in terms of U(1) phase variables conjugate to the local particle number, providing a useful representation of strongly correlated system. The effective action formalism allows us to formulate a problem in the phase-only action in the form of the quantum rotor model and to obtain analytical formula for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.

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BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

Cited by 97 publications

References 43 publications

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

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

Excitonic Phase Transition in the Extended Three-Dimensional Falicov–Kimball Model

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