PACS 71.35.Lk -Collective effects (Bose effects, phase space filling, and excitonic phase transitions) PACS 71.10.Li -Excited states and pairing interactions in model systems PACS 67.85.Hj -Bose-Einstein condensates in optical potentials Abstract -A ground state of the excitonic condensate in the 2D extended Falicov-Kimball model involving the coupling of electrons and vibrational degrees of freedom has been investigated. Adapting the unrestricted Hartree-Fock approximation, we have derived a set of explicitly selfconsistent equations determining both an excitonic order parameter and a lattice distortion when both the electron-phonon coupling and the electron-electron interaction are treated on an equal footing. A ground-state phase diagram of the excitonic condensate depending on the model parameters is constructed. The phase diagram shows us that a window of the excitonic condensate with lattice distortion increases when increasing the electron-phonon coupling or moving up the f -electron level, whereas, it is confined in between two critical values of the Coulomb interaction. The Coulomb interaction and the electron-phonon coupling have been affirmed to act together in establishing the excitonic condensate phase with lattice distortion in dichalcogenide systems. The BCS-BEC crossover of the excitonic condensation in the systems is also addressed.

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The exciton‐polariton condensation scenario in a microcavity matter–light system at finite temperature is investigated in the framework of the unrestricted Hartree–Fock approximation applying the two‐dimensional exciton‐polariton model. Treating electron–hole Coulomb interaction and matter–light coupling effects on an equal footing, we analyze the temperature influence on the excitonic and photonic order parameters. In the thermal equilibrium limit, the Kosterlitz–Thouless type phase transition of the exciton‐polariton condensation has been found. Depending on detuning and excitation density one finds that the system either favors the photonic or excitonic condensate. The effect of temperature on a crossover from a BCS‐excitonic to a BEC‐polaritonic condensed state then is discussed.

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