Collective Excitations and Stability of the Excitonic Phase in the Extended Falicov--Kimball Model

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 hybridisation. 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 hybridisation with a fully localised 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 stabilised further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains new information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).

8 pages, LaTeX-Revtex, 3 PostScript figures, minor corrections. Phys. Rev. B, in press

References in corpus (8)

• Electron-hole pair condensation at the semimetal-semiconductor transition: a BCS-BEC crossover scenario
• A BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach
• Bound state formation and nature of the excitonic insulator phase in the extended Falicov-Kimball model
• Hybridization wave as the 'Hidden Order' in URu${}_2$Si${}_2$
• Weak-coupling Treatment of Electronic (Anti-)Ferroelectricity in the Extended Falicov-Kimball Model
• Hartree-Fock study of electronic ferroelectricity in the Falicov-Kimball model with $f$-$f$ hopping
• Excitonic resonances in the 2D extended Falicov-Kimball model
• Competing chiral and multipolar electric phases in the extended Falicov-Kimball model

Cited by in corpus (9)

• Exciton condensation due to electron-phonon interaction
• Excitonic phase transition in the extended three-dimensional Falicov-Kimball model
• An On-Site Density Matrix Description of the Extended Falicov--Kimball Model at Finite Temperatures
• Mott transition in two-band fermion model with on-site Coulomb repulsion
• Instability of the chiral phase and electronic ferroelectricity in the extended Falicov--Kimball model
• A Description of Phases with Induced Hybridisation at Finite Temperatures
• Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model
• Excitonic Insulator and the Extended Falicov--Kimball Model Away from Half-Filling
• Two band model for coherent excitonic condensates