We have studied the excitonic gap formation in the Bernal Stacked, bilayer graphene (BLG) structures at half-filling. Considering the local Coulomb interaction between the layers, we calculate the excitonic gap parameter and we discuss the role of the interlayer and intralayer Coulomb interactions and the interlayer hopping on the excitonic pair formation in the BLG. Particularly, we predict the origin of excitonic gap formation and condensation, in relation to the farthermost interband optical transition spectrum. The general diagram of excitonic phase transition is given, explaining different interlayer correlation regimes. The temperature dependence of the excitonic gap parameter is shown and the role of the chemical potential, in the BLG, is discussed in details.

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.

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.

In this paper, we consider the spectral properties of the bilayer graphene with the local excitonic pairing interaction between the electrons and holes. We consider the generalized Hubbard model, which includes both intralayer and interlayer Coulomb interaction parameters. The solution of the excitonic gap parameter is used to calculate the electronic band structure, single-particle spectral functions, the hybridization gap, and the excitonic coherence length in the bilayer graphene. We show that the local interlayer Coulomb interaction is responsible for the semimetal-semiconductor transition in the double layer system, and we calculate the hybridization gap in the band structure above the critical interaction value. The formation of the excitonic band gap is reported as the threshold process and the momentum distribution functions have been calculated numerically. We show that in the weak coupling limit the system is governed by the Bardeen-Cooper-Schrieffer (BCS)-like pairing state. Contrary, in the strong coupling limit the excitonic condensate states appear in the semiconducting phase, by forming the Dirac's pockets in the reciprocal space.PACS numbers: 68.65. Pq, 73.22.Pr, 73.22.Gk, 71.35.Lk, 71.10.Li, 78.67.Wj, 73.30.+y INTRODUCTIONThe electronic band gap of semiconductors and insulators largely determines their optical, transport properties and governs the operation of semiconductor based devices such as p-n junctions, transistors, photodiodes and lasers [1]. Opening up a band gap in the bilayer graphene (BLG), by applying the external electric field and finding a suitable substrate are two challenges for constituting the modern nano-electronic equipment [2,3]. The imposition of external electrical field can tune the bilayer graphene from the semimetal to the semiconducting state [2]. On the other hand, the possibility of formation of the excitonic insulator state and the excitonic condensation in the bilayer graphene structures remains controversial in the modern solid state physics [4][5][6][7][8][9][10][11][12][13][14]. In difference with the quasi two-dimensional (2D) semiconducting systems, where those two states have been observed experimentally and well discussed theoretically [15][16][17][18][19][20][21][22][23][24][25][26][27], the formation of the excitonic condensate states in the BLG system, from the original electron-hole pairing states, is much more obscure because of the complicated nature of the single-particle correlations in these systems [6,8,10,13,14]. The weak correlation diagrammatic mechanism, discussed in the Refs.13, 14, is restricted only to the closed loop expansion in the diagrammatic series, and in this case, only the density fluctuation effects could affect the formation of the excitonic condensate states. Meanwhile, it has been shown [28][29][30] that even the undoped graphene can provide a variety of electron-hole type pairing chiral symmetry breaking * Corresponding author. Tel.: +48 71 3954 284; E-mail address: v.apinyan@int.pan.wroc.pl.orders especially for the strong C...

We consider the pairing between conduction band electrons, and the valence band holes in the neutral bilayer-type structures. By employing the bilayer Hubbard model, we show the possibility of the inter-plane exciton formation in the system without applied external field. The in-plane and inter-plane Coulomb interaction effects on the pairing mechanism are considered, and the role of the in-plane particle hopping asymmetry on the gap behavior is analyzed in the paper. We show that both Frenkel-type pairing channel and Wannier-Mott-type excitonic pairings are present in the considered system. We analyze also the structure of the chemical potential in the bilayer system. The temperature effects, and the tunable inter-plane electron hopping effects are discussed. For the Frenkel channel, we have shown a particular behavior of the chemical potential at the very low temperatures, which is related to the degenerated Frenkel-gap.I.