Collective Excitations, Stability of the Excitonic Phase, and Electronic Ferroelectricity in the Extended Falicov--Kimball Model
Title: "Collective Excitations, Stability of the Excitonic Phase, and Electronic Ferroelectricity in the Extended Falicov--Kimball Model"
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 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).
Our results on stability and degeneracies of the excitonic insulator phase imply that the presence of both hybridisation and narrow-band hopping is required for electronic ferroelectricity. When only one of these is present, the dielectric constant diverges, yet the electrostatic dipole interactions preclude the formation of spontaneous polarisation.
References: Phys Rev B vol 86, 155134 (2012)
Phys. Status Solidi B vol. 250, p. 557 (2013)