Thermal fluctuations and mass imbalance in low-energy excitonic condensate excitations

Low-energy excitations of the excitonic states in the semimetal and semiconducting materials described by the extended Falicov-Kimball model with phonon correlation are investigated. In the framework of the unrestricted Hartree-Fock approximation, we derive a set of self-consistent equations to find the quasiparticle energies and excitonic condensate order parameters. The real part of the optical conductivity and then the dynamical excitonic susceptibility function are analytically evaluated by means of the linear response theory. Numerical results reveal the significant expansion of the excitonic condensation window in the temperature--Coulomb interaction plane by lowering the mass imbalance. Under the influence of the mass imbalance and thermal fluctuations, the BCS-BEC crossover of the excitonic condensation states has been also addressed in the collective mode signatures of the optical conductivity. Out of the condensation state, the collective excitation of the excitonic bound state is examined by analyzing the imaginary part of the dynamical excitonic susceptibility function. At large mass imbalance and low thermal fluctuations, we find an extremely sharp peak with high intensity at low frequency in the imaginary part of the dynamical excitonic susceptibility spectrum, specifying the long-lifetime exciton existence before it becomes condensed.