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

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

2009-12-15

arxiv.org/abs/0912.2854v2

Phys. Rev. B 81, 115122 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

slightly revised version, 10 pages, 6 figures

Scientific paper

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.

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