In this paper, we describe the antiferromagnetic and excitonic correlations in the AA-stacked bilayer graphene. We consider the applied external electric field potential to the structure which leads to the electronic charge imbalance between the layers in the system. By using the generalized two-layer Hubbard Hamiltonian, we consider different particle-filling regimes in the layers. We calculate the important energy scales in the system and we establish the conditions for the appearance of the antiferromagnetic order in the system. We consider both large and small Coulomb interaction limits in the layers and the effect of the electric field potential on the calculated order parameters. We discuss the coexistence of antiferromagnetism and excitonic phases and we show that they can coexist only in the regime away from half-filling. In the case away from the half-filling, we show the existence of a critical value $U_{\mathrm{C}}$ of the Coulomb interaction potential at which we establish the transition from the single-valued to the triple-valued excitonic states, governed by the strong electronic reconfiguration, in the system. The zero-temperature limit is considered in the problem.

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 furthermost 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 electron–hole system may become unstable with respect to the formation of the excitons, i.e, electron–hole pairs at temperature \(T=T_{\Delta }\) , exhibiting a gap \(\Delta \) 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 formulas for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.

In this paper, the effects of the external transverse magnetic field $B$ (perpendicular to the surface of the layers) on electronic and excitonic properties are studied in AA-stacked bilayer graphene (BLG). The effects of the Coulomb interactions and excitonic pairing have been taken into account and analyzed in detail within the bilayer Hubbard model. Both half-filling and partial-filling regimes have been taken into account and the magnetic field dependence of a series of physical parameters was found. It is shown that the difference between the average electron concentrations in the layers vanishes at some critical value of magnetic field $B_c$ and the chemical potential is calculated numerically above and below that value. The role of the Coulomb interactions on the average carrier concentrations in the layers has been analyzed and the excitonic order parameters have been calculated for different spin orientations. We found a possibility for the particle population inversion between the layers when varying the external magnetic field. The calculated electronic band structure in AA-BLG shows the presence of a metal-semiconductor transition, governed by the strength of the applied magnetic field or the interlayer interaction potential. We show that for high magnetic fields, the band gap is approaches the typical values of the gaps in the usual semiconductors. It is demonstrated that, at some parameter regimes, AA-BLG behaves like a spin-valve device by permitting the electron transport with only one spin direction. All calculations have been performed at the zero-temperature limit.

We have considered the AB-stacked bilayer graphene tunnel junction construction. The bilayers are supposed to be in the charge equilibrium states and at the half-filling in each of the electronic layers of the construction and at each value of the external gate potential. By considering the interacting bilayers in both sides of the junction and by taking into account both intralayer and interlayer Coulomb interaction effects, we have calculated the normal and excitonic tunnel currents through the junction. The electronic band renormalizations have been taken into account, due to the excitonic pairing effects and condensation in the BLGs. The exact four-band energy dispersions, including the excitonic renormalizations, have been used for the bilayers without any low-energy approximation. The normal and excitonic tunneling currents have been calculated for different values of the gate potential and for different values of the interlayer interaction parameters in both sides of the tunnel junction. We demonstrate the existence of the excitonic Josephson current through the junction which persist even for the non-interacting bilayer graphene junction. For the non-interacting case, the mechanism of the excitonic condensates formation and tunneling between the condensates is attributed to the interlayer hopping between the layers. The role of the charge neutrality point has been discussed in details.