A BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

TL;DR

This study investigates the excitonic insulator state in the extended Falicov-Kimball model, revealing a crossover from BCS-like behavior at weak coupling to BEC-like behavior at strong coupling, using variational cluster and Hartree-Fock methods.

Contribution

It demonstrates the BCS-BEC crossover in the model and compares the effectiveness of VCA and HFA across different coupling regimes.

Findings

Weak-to-intermediate coupling regime aligns with BCS theory.

Strong coupling results are consistent with BEC picture.

Hartree-Fock approximation is effective in both weak and strong regimes.

Abstract

We study the spontaneous symmetry breaking of the excitonic insulator state induced by the Coulomb interaction $U$ in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation (VCA) and Hartree-Fock approximation (HFA), we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, coherence length of excitons, and single-particle and anomalous excitation spectra, as a function of $U$ at zero temperature. We find that in the weak-to-intermediate coupling regime, the Fermi surface plays an essential role and calculated results can be understood in close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface plays no role and results are consistent with the picture of BEC. Moreover, we find that HFA works well both in the weak- and strong-coupling regime, and that the difference between the results of VCA and HFA mostly appears in the intermediate-coupling regime. The reason for this is discussed from a viewpoint of the self-energy. We thereby clarify the excitonic insulator state that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime).