Existence of excitonic insulator phase in the extended Falicov-Kimball model: SO(2)-invariant slave-boson approach

Abstract

We re-examine the three-dimensional spinless Falicov-Kimball model with dispersive f electrons at half-filling, addressing the dispute about the formation of an excitonic condensate, which is closely related to the problem of electronic ferroelectricity. To this end, we work out a slave-boson functional integral representation of the suchlike extended Falicov-Kimball model that preserves the SO(2) ⊗ U (1) ⊗2 invariance of the action. We find a spontaneous pairing of c electrons with f holes, building an excitonic insulator state at low temperatures, also for the case of initially nondegenerate orbitals. This is in contrast to recent predictions of scalar slave-boson mean-field theory but corroborates previous Hartree-Fock and RPA results. Our more precise treatment of correlation effects, however, leads to a substantial reduction of the critical temperature. The different behavior of the partial densities of states in the weak and strong inter-orbital Coulomb interaction regimes supports a BCS-BEC transition scenario.

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

“…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.…”

Competing chiral and multipolar electric phases in the extended Falicov-Kimball model

“…[19][20][21] The FKM with two dispersive bands, the so-called extended Falicov-Kimball model (EFKM), was studied previously for describing different properties of the EI phase. [22][23][24][25][26] However, as it was shown for the case of opposite-parity orbitals, 15,16 the inclusion of a finite interband hybridization can be very relevant because it removes the U(1) symmetry associated with the conservation of the difference between the total number of particles in each band: N c − N f . In particular, this hybridization term is certainly relevant when the ground-state of the EFKM corresponds to an excitonic condensate.…”

Two-Band Model for Coherent Excitonic Condensates

“…1 the numerical results for the local excitonic order parameter ∆ are presented. The region, where ∆ = 0 defines the EI phase in the system [11][12][13][14]. …”

“…The low density system of excitons behaves like the usual Bose gas, while the high density system of bound e-h pairs behaves like the system of weakly coupled Cooper pairs. Thus the resulting BCS-BEC crossover [9][10][11][12][13][14] represents an interesting theoretical problem typical for the excitonic systems.…”

“…The particle coherence in the usual sense of hybridization between the conduction band electron and valence * corresponding author; e-mail: kopec@int.pan.wroc.pl band holes is discussed in many works [10][11][12][13][14] within the three-dimensional (3D) extended Falicov-Kimball model (EFKM) with a dispersive f -band electrons at half-filling. It is shown recently [17] that the EI state is unstable when the case of pure Falicov-Kimball model (FKM) [18] (with fully localized bands) is approached.…”