Bound state formation and the nature of the excitonic insulator phase in the extended Falicov-Kimball model

Motivated by the possibility of pressure-induced exciton condensation in intermediate-valence Tm[Se,Te] compounds, we study the Falicov-Kimball model extended by a finite $f$-hole valence bandwidth. Calculating the Frenkel-type exciton propagator we obtain excitonic bound states above a characteristic value of the local interband Coulomb attraction. Depending on the system parameters coherence between $c$ and $f$ states may be established at low temperatures, leading to an excitonic insulator phase. We find strong evidence that the excitonic insulator typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate (BEC) of preformed excitons (strong-coupling regime), which points toward a BCS-BEC transition scenario as Coulomb correlations increase.