Antiferromagnetic ordering and excitonic pairing in the AA-stacked bilayer graphene

In the present 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 $U_{\rm C}$ 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.