Excitonic Effects and Antiferromagnetism in the Doped-Biased AB-Stacked Bilayer Graphene

We consider the direct orbital effect of an external magnetic field on the motion of electrons in reciprocal space in AB-stacked bilayer graphene subjected to a perpendicular magnetic field and an external electric field. For this purpose, the Peierls substitution is implemented using the symmetric gauge for the vector potential, and the electronic dispersion is reconstructed. The Lorentz potential arising from the Lorentz force acting on the electrons is included in the calculations. The effective chemical potential method is employed to incorporate the effects of Hubbard on-site repulsion, the external electric field, and Landau quantization of the allowed electronic states in reciprocal space. Local canted antiferromagnetic states are discussed, and their coexistence with excitonic states is found.