Mass imbalance and electron-phonon correlation impact on the excitonic insulator state in semimetal/semiconducting materials

Signatures of the excitonic insulator in the mass-imbalance extended Falicov-Kimball model with the electron-phonon correlation are investigated. Based on the unrestricted Hartree-Fock approximation, we derive a set of self-consistent equations specifying the excitonic insulator order parameter and then construct the complex phase diagram of the excitonic insulator states. For a given intermediate Coulomb interaction, the excitonic insulator states at nearly zero temperature are found if the electronic hybridization-phonon coupling is sufficiently large. The window of the excitonic insulator states expands as suppression of the mass anisotropy. The influence of the mass imbalance and electron-phonon correlations on the nature of the BCS-BEC crossover of the condensation states is also addressed in the signatures of the optical conductivity. The preformed excitonic bound states in the normal semiconducting side are inspected in the features of the imaginary part of the dynamical excitonic susceptibility function. By increasing the electronic hybridization-phonon coupling or suppressing the mass imbalance, we find the dominance of the excitonic coherent bound states. The compact influence of the mass imbalance and electron-phonon correlations on the whole picture of the excitonic insulator state thus has been discussed.