Instability of the chiral phase and electronic ferroelectricity in the extended Falicov--Kimball model

TL;DR

This paper investigates the stability of the chiral phase in the extended Falicov--Kimball model, finding it unstable, and discusses conditions necessary for electronic ferroelectricity involving hybridisation and narrow-band hopping.

Contribution

It demonstrates the instability of the chiral phase in the model and clarifies the conditions needed for electronic ferroelectricity to occur.

Findings

Chiral phase is unstable within the Hartree--Fock approximation.

Both hybridisation and narrow-band hopping are necessary for electronic ferroelectricity.

Review of stability and degeneracies of the excitonic insulator phase.

Abstract

We consider a spinless extended Falicov--Kimball model at half-filling, for the case of opposite-parity bands. Within the Hartree--Fock approach, we calculate the excitation energies in the chiral phase, which is a possible mean-field solution in the presence of a hybridisation. It is shown that the chiral phase is unstable. We then briefly review the accumulated results on stability and degeneracies of the excitonic insulator phase. Based on these, we conclude that the presence of both hybridisation and narrow-band hopping is required for electronic ferroelectricity.