Excitonic condensation state in the assistance of the adiabatic and anti-adiabatic phonons.

The excitonic condensate in semimetal and semiconducting materials with the assistance of the phonons in both the adiabatic and anti-adiabatic regimes has been investigated. In the framework of the random phase approximation, we analyse the static excitonic susceptibility function once the electrons and holes are described in the extended Falicov-Kimball model involving the electron-phonon interaction. The excitonic condensate transition point is detected as a divergence of the susceptibility function.