Probing Phase Coherence Via Density of States for Strongly Correlated Excitons

Abstract

We present the calculation of the coherent spectral functions and density of states (DOS) for excitonic systems in the frame of the three-dimensional extended Falicov-Kimball model. Using gage-invariant U(1) transformation to the usual fermions, we represent the electron operator as a fermion attached to the U(1) phase-flux tube. The emergent bosonic gage field, related to the phase variables, is crucial for the Bose-Einstein condensation (BEC) of excitons. Employing the path-integral formalism, we manipulate the bosonic and fermionic degrees of freedom to obtain the effective actions related to fermionic and bosonic sectors. Considering the normal and anomalous excitonic Green functions, we calculate the spectral functions, which have the forms of convolutions in the reciprocal space between bosonic and fermionic counterparts. For the fermionic incoherent part of the DOS, we have found the strong evidence of the hybridization gap in DOS spectra. Furthermore, considering Bogoliubov coherence mechanism, we calculate the coherent DOS spectra. For the coherent normal fermionic DOS, there is no hybridization gap found in the system due to strong coherence effects and phase stiffness. The similar behavior is observed also for the condensate part of the anomalous excitonic DOS spectra. We show that for small values of the Coulomb interaction the fermionic DOS exhibits a Bardeen-Cooper-Schrieffer (BCS)-like double-peak structure. In the BEC region of the BCS-BEC crossover, the double-peak structure disappears totally for both: coherent and incoherent DOS spectra. We discuss also the temperature dependence of DOS functions.

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

“…This scenario of the excitonic condensation at the zero interlayer coupling is converging well with the general discussion about coherent excitonic density of states in the semiconducting systems (see in Ref. [20]), where it has been shown that a large amount of states in the DOS (without the hybridization gap) is the sign of the coherent excitonic condensates in these systems.…”

“…More recently, it has been shown [19,20] that the single-particle coherent density of states (DOS) in the usual two-dimensional (2D) [19] and three-dimensional (3D) [20] semiconducting systems at the zero temperature limit is always finite, reflecting with the excitonic condensate regime in these systems. For the 3D semiconducting systems, the coherent DOS spectra survive also for the higher temperatures [20]. 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.…”

“…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].…”

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

“…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.…”