Phonon effects in the excitonic condensation induced in the extended Falicov-Kimball model

¹ Graduate University of Science and Technology, Vietnam Academy of Science and Technology 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
² Institute of Physics, Vietnam Academy of Science and Technology - 10 Dao Tan, Cau Giay, Hanoi, Vietnam
³ Department of Physics, Hanoi University of Mining and Geology - Duc Thang, Bac Tu Liem, Hanoi, Vietnam
⁴ Physics Department, Hue University's college of Education - 34 Le Loi, Hue, Vietnam
⁵ Institute of Research and Development, Duy Tan University - 3 Quang Trung, Danang, Vietnam

Received: 26 May 2017
Accepted: 13 September 2017

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 self-consistent 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.