Slave-boson field fluctuation approach to the extended Falicov-Kimball model: Charge, orbital, and excitonic susceptibilities

Based on the SO(2)-invariant slave-boson scheme, the static charge, orbital, and excitonic susceptibilities in the extended Falicov--Kimball model are calculated. Analyzing the phase without long-range order, we find instabilities toward charge order, orbital order, and the excitonic insulator (EI) phase. The instability toward the EI is in agreement with the saddle-point phase diagram. We also evaluate the dynamic excitonic susceptibility, which allows the investigation of uncondensed excitons. We find qualitatively different features of the exciton dispersion at the semimetal-EI and at the semiconductor-EI transition supporting a crossover scenario between a BCS-type electron-hole condensation and a Bose--Einstein condensation of preformed bound electron-hole pairs.