We consider the effect of the external magnetic field on the in-plane conductivity in the AA-stacked bilayer graphene system in the strong excitonic condensate regime. We include the effects of the applied inter-layer electric field and the Coulomb interactions. The on-site and inter-layer Coulomb interactions were treated via the bilayer Hubbard model. Using the solutions for the physical parameters in the system, we calculate the in-plane conductivity of the bilayer graphene. By employing the Green-Kubo formalism for the polarization function in the system, we show that the conductivity in the AA bilayer system is fully controlled by the applied magnetic field. For the partial filling in the layers, the electrical conductivity is different for different spin orientations, and, at the high values of the magnetic field, only one component remains with the given spin orientation. Meanwhile, for the half-filling limit, there is no spin-splitting observed in the conductivity function. The theory evaluated here shows the new possibility for spin-controlled electronic transport in the excitonic bilayer graphene system.

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.