On the existence of the excitonic insulator phase in the extended Falicov-Kimball model: an SO(2)-invariant slave-boson approach

TL;DR

This paper demonstrates the existence of an excitonic insulator phase in the three-dimensional extended Falicov-Kimball model using an SO(2)-invariant slave-boson approach, clarifying previous disputes and highlighting a BCS-BEC transition.

Contribution

It introduces a new SO(2)-invariant slave-boson functional integral method that confirms excitonic condensation in the model, contrasting with earlier scalar slave-boson predictions.

Findings

Spontaneous pairing of c electrons with f holes at low temperatures.

Reduction of critical temperature compared to previous theories.

Evidence of a BCS-BEC transition scenario based on density of states.

Abstract

We re-examine the three-dimensional spinless Falicov-Kimball model with dispersive $f$ electrons at half-filling, addressing the dispute about the formation of an excitonic condensate, which is closely related to the problem of electronic ferroelectricity. To this end, we work out a slave-boson functional integral representation of the suchlike extended Falicov-Kimball model that preserves the $SO(2)\otimes U(1)^{\otimes 2}$ invariance of the action. We find a spontaneous pairing of $c$ electrons with $f$ holes, building an excitonic insulator state at low temperatures, also for the case of initially non-degenerate orbitals. This is in contrast to recent predictions of scalar slave-boson mean-field theory but corroborates previous Hartree-Fock and RPA results. Our more precise treatment of correlation effects, however, leads to a substantial reduction of the critical temperature. The different behavior of the partial densities of states in the weak and strong inter-orbital Coulomb interaction regimes supports a BCS-BEC transition scenario.