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

TL;DR

This study investigates the collective excitations and stability of the excitonic insulator phase within an extended Falicov--Kimball model, revealing conditions under which this phase is stable or unstable based on collective mode analysis.

Contribution

It provides a detailed calculation of the low-energy excitation spectrum and stability conditions of the excitonic phase in an extended FKM using Hartree--Fock approximation.

Findings

The excitonic insulator is unstable in the pure FKM limit due to a lower-lying ground state.

Stability of the excitonic phase improves away from the pure FKM limit.

The excitation spectrum reveals properties of the condensate, including suppressed critical temperature.

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).