Excitonic Phase Transition in the Extended Three-Dimensional Falicov–Kimball Model

Abstract

We study the excitonic phase transition in a system of the conduction band electrons and valence band holes described by the three-dimensional (3D) extended Falicov-Kimball (EFKM) model with the tunable Coulomb interaction U between both species. By lowering the temperature, the electronhole system may become unstable with respect to the formation of the excitons, i.e, electron-hole pairs at temperature T = T∆, exhibiting a gap ∆ in the particle excitation spectrum. To this end we implement the functional integral formulation of the EFKM, where the Coulomb interaction term is expressed in terms of U(1) phase variables conjugate to the local particle number, providing a useful representation of strongly correlated system. The effective action formalism allows us to formulate a problem in the phase-only action in the form of the quantum rotor model and to obtain analytical formula for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.

Phase coherence and spectral functions in the two-dimensional excitonic systems

“…The e h − mass difference in the BCS-BEC transition scenario leads to a large suppression of the BEC transition temperature, which is proved to not be the same as the excitonic pair formation temperature [20,22,23]. This is in contrast with the previous treatments [5][6][7][8][9][10][11][12][13], where the EI state is associated with the BEC state of excitons, as to be identical.…”

“…(2) using the Hubbard-Stratonovich (HS) transformation [28]. We do not present here the calculation details [22,23] fter the HS linearisation, we got the total action of the system that is linear in terms of fermion density operators n rτ ( ) and n rτ( ).…”

“…However, a series of recent theoretical works suggest the importance of the phase correlations on the phase transition scenario in the excitonic systems [18][19][20][21][22][23]. Particularly, in Refs.…”

“…The importance of the phase coherence in the excitonic pair plasma is discussed there, with a classification of two distinct phase transitions in the excitonic plasma and the discussion about the exciton BEC is provided. It is shown [18][19][20]22,23] that in the low density limit of the excitonic pairs, the critical temperature of excitonic BEC should be much smaller than the temperature of the pair formation.…”

Density of states in the bilayer graphene with the excitonic pairing interaction

“…This situation is also typical for the double layer electronic structures at the half filling [21] when considering the electron-hole pair formation and condensation. In addition, it has been demonstrated that the excitonic insulator state and the excitonic condensation are two distinct phase transitions in the solid state [22,23], and the condensate states are due to the electronic phase stiffness [20,24], mechanism. Meanwhile, in the electronic bilayer systems, those mentioned phase transitions are indistinguishable as it was shown in references [12,21].…”