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

TL;DR

This paper investigates the formation of excitonic bound states and the nature of the excitonic insulator phase in an extended Falicov-Kimball model, revealing a transition between BCS-like and BEC-like condensate regimes.

Contribution

It introduces an extension of the Falicov-Kimball model with a finite f-hole bandwidth and analyzes the excitonic insulator phase, highlighting a BCS-BEC transition scenario.

Findings

Excitonic bound states form above a critical Coulomb attraction.

Coherence between c- and f-states leads to an excitonic insulator phase.

The insulator exhibits a BCS-BEC crossover as Coulomb interactions increase.

Abstract

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 towards a BCS-BEC transition scenario as Coulomb correlations increase.