Excitonic Insulator and the Extended Falicov--Kimball Model Away from Half-Filling

TL;DR

This paper investigates the stability and properties of excitonic insulators in an extended Falicov--Kimball model away from half-filling, revealing potential phases and the influence of excitonic correlations at various doping levels.

Contribution

It provides a comprehensive phase diagram analysis of the extended Falicov--Kimball model, highlighting the emergence of excitonic insulators and metals beyond half-filling, including phase separation effects.

Findings

Excitonic insulators can exist as a component in mixed-phase states at various doping levels.

Doped excitonic insulators can form an excitonic metal phase as the lowest-energy uniform state.

Long-range Coulomb interactions may stabilize the excitonic metal by suppressing phase separation.

Abstract

We consider an extended spinless Falicov--Kimball model at an arbitrary doping level, focusing on the range of parameter values where a uniform excitonic insulator is stabilised at half-filling. We compare the properties of possible uniform phases and construct the Hartree--Fock phase diagrams, which include sizeable phase separation regions. It is seen that the excitonic insulator can appear as a component phase in a mixed-phase state in a broad interval of doping levels. In addition, in a certain range of parameter values the excitonic metal (doped excitonic insulator) is identified as the lowest-energy uniform phase. We suggest that this phase, which is unstable with respect to phase separation, may be stabilised when the phase separation is suppressed by the long-range Coulomb interaction. Overall, we find that excitonic correlations can affect the behaviour of the system relatively far away from half-filling.