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

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 $\text{SO}(2)\ensuremath{\bigotimes}\text{U}{(1)}^{\ensuremath{\bigotimes}2}$ 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 nondegenerate orbitals. This is in contrast to recent predictions of scalar slave-boson mean-field theory but corroborates previous Hartree-Fock and random-phase approximation results. Our more precise treatment of correlation effects, however, leads to a substantial reduction in the critical temperature. The different behavior of the partial densities of states in the weak and strong interorbital Coulomb interaction regimes supports a BCS-Bose-Einstein condensate transition scenario.