Electron-phonon correlations inducing excitonic excitations in semimetal and semiconducting materials

Abstract

The influence of phonons on the low-energy excitonic excitations at zero temperature in the extended Falicov-Kimball model has been investigated. In the framework of the unrestricted Hartree-Fock approximation, a set of self-consistent equations for the excitonic condensate order parameter and a lattice distortion is derived when both electron-phonon coupling and electron-hole Coulomb interaction are treated on an equal footing. The low-energy excitation properties of the excitonic condensate are addressed in signatures of the optical conductivity and the dynamical excitonic susceptibility function. The real part of the optical conductivity is evaluated by the Kubo linear response theory and the imaginary part of the dynamical excitonic susceptibility is found by adapting the random phase approximation. In the semimetal state, one always finds a sharp peak in the optical conductivity spectrum indicating the stability of the excitonic condensation in the BCS type if the correlation between electrons and phonons becomes significant. In contrast, the peak is smeared out on the semiconducting side indicating the stability of the BEC-type excitonic condensate. In this semiconducting side, the sharp peak signature appears and the system turns to the BCS-type excitonic condensation state by increasing the electron-phonon correlations. In either the semimetal or the semiconducting normal state, increasing the electron-phonon correlations always reinforces a low-energy sharp peak in the dynamical excitonic susceptibility spectrum, indicating the existence of the tightly bound excitonic excitations before the condensation state. Specifically, on the semiconducting side, the ``halo'' phase with the preformed excitons exiting outside of the BEC-excitonic condensation state has been specified. The halo phase becomes more recognizable by raising the electron-phonon correlations.