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In this paper, the effects of the external transverse magnetic field $B$(perpendicular to the surface of the layers) on the electronic and excitonicproperties are studied in the AA-stacked bilayer graphene (BLG). The effects ofthe Coulomb interactions and excitonic pairing have been taken into account andanalyzed in detail within the bilayer Hubbard model. Both half-filling andpartial filling regimes have been taken into account and the magnetic fielddependence of a series of physical parameters was found. It is shown that thedifference between the average electron concentrations in the layers vanishesat some critical value of magnetic field $B_{c}$ and the chemical potential iscalculated numerically above and below that value. The role of the Coulombinteractions on the average carrier concentrations in the layers has beenanalyzed, and the excitonic order parameters have been calculated for differentspin orientations. We found a possibility for the particle population inversionbetween the layers when varying the external magnetic field. The calculatedelectronic band structure in the AA-BLG shows the presence ofmetal-semiconductor transition, governed by the strength of the appliedmagnetic field or the interlayer interaction potential. We show that for highmagnetic fields the band-gap is approaching the typical values of the gaps inthe usual semiconductors. It is demonstrated that, at some parameter regimes,the AA-BLG behaves like a spin-valve device, by permitting the electrontransport with only one spin direction. All calculations have been performed atthe zero-temperature limit.

Excitonic condensation and metal-semiconductor transition in AA bilayer graphene in the external magnetic field