Journal of Electronic Materials

, Volume 48, Issue 5, pp 2677–2684 | Cite as

Thermal Fluctuations in the Phase Structure of the Excitonic Insulator Charge Density Wave State in the Extended Falicov–Kimball Model

  • Thi-Hong-Hai Do
  • Huu-Nha Nguyen
  • Van-Nham PhanEmail author


Excitonic insulator (EI) instability accompanied by a charge density wave (CDW) state in the two-dimensional extended Falicov–Kimball model including electron–phonon interaction is investigated by applying the unrestricted Hartree–Fock approximation. Treating both the Coulomb attraction and the electron–phonon coupling on an equal footing, we have derived a set of self-consistent equations, which allows us to determine both the excitonic insulator order parameter and the lattice displacement. The phase structures show us that both the Coulomb interaction and the electron–phonon coupling act together in establishing the EI-CDW state, which typifies either a phononic-CDW or an excitonic-CDW state depending on the competition of the interactions. At a given low temperature, the EI-CDW state is found between two critical values of the Coulomb interaction. The window of the condensation state grows when increasing the electron–phonon coupling. Depending on the temperature and the Coulomb interaction the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS–BEC) crossover of the EI-CDW state in the systems has been established. Under the effects of phonons, the BCS–BEC crossover deviates to a larger Coulomb interaction while the semimetal–semiconductor transition in the normal state remains.


Excitonic condensation charge density wave unrestricted Hartree–Fock approximation semimetal–semiconductor transition 


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This work was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 103.01-2017.68.


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Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  • Thi-Hong-Hai Do
    • 1
    • 2
    • 3
  • Huu-Nha Nguyen
    • 4
  • Van-Nham Phan
    • 5
    Email author
  1. 1.Faculty of PhysicsGraduate University of Science and Technology, Vietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.Department of PhysicsHanoi University of Mining and GeologyHanoiVietnam
  3. 3.Institute of PhysicsVietnam Academy of Science and TechnologyHanoiVietnam
  4. 4.Department of PhysicsHCMC University of ScienceHo Chi Minh CityVietnam
  5. 5.Institute of Research and DevelopmentDuy Tan UniversityDanangVietnam

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