Spectral signatures of the BCS-BEC crossover in the excitonic insulator phase of the extended Falicov-Kimball model

TL;DR

This paper investigates the BCS-BEC crossover in the excitonic insulator phase of the extended Falicov-Kimball model, revealing how spectral features change with Coulomb interaction strength.

Contribution

It provides analytical and numerical insights into the spectral signatures of the BCS-BEC transition within the excitonic insulator phase of the model.

Findings

Valence transition linked to excitonic insulator formation

Spectral differences between weak and strong Coulomb regimes

Evidence of BCS-BEC crossover in spectral functions

Abstract

We explore the spontaneous formation of an excitonic insulator state at the semimetal-semiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct $f$-$f$ electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized $c$- and $f$-electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral functions. Our numerical results proved the valence transition picture, related to the appearance of the excitonic insulator phase, in the case of overlapping $c$ and $f$ bands. Thereby the photoemission spectra show significant differences between the weak-to-intermediate and intermediate-to-strong Coulomb attraction regimes, indicating a BCS-BEC transition of the excitonic condensate.