The Excitonic Susceptibility Function in Semimetal/semiconductor Materials: Formation of the Excitonic Condensate State

The condensate state of excitons in semimetal/semiconductor materials has been considered by analyzing the excitonic susceptibility function in the 2D extended Falicov-Kimbol model including electron-phonon interaction. The excitonic susceptibility in the system has calculated by using the Hartree-Fock approximation. From numerical results, we have set up phase diagrams ofthe excitonic condensate state. Phase diagrams confirm that the electron-phonon coupling plays an important role as well as the Coulomb attraction does in establishing the excitonic condensed phase at low temperature. The condensate phase of excitons is found within a limited range of the Coulomb attraction as the electron-phonon coupling is large enough. Depending on theelectron-phonon coupling and the Coulomb attraction, the BCS-BEC crossover of the excitonic condensation phase has also been pointed out.