Applied electric and magnetic field effects on the bandgap formation and antiferromagnetic ordering in AA-stacked Bilayer Graphene

In this study, we consider a two-layer graphene structure stacked in the AA form and exposed to the influence of two different electric fields applied to different layers. The graphene layers are also subjected to an external magnetic field perpendicular to the planes of the layers. We investigate the possible effects of the applied in-plane fields and the magnetic field on excitonic pairing, antiferromagnetic order, and the chemical potential. Simultaneously, we analyze the effects of the interlayer Coulomb interaction potential on the physical properties of the considered system. We demonstrate that the application of planar electric fields leads to the formation of an unusually large bandgap in the electronic band structure, which is not typical for AA-stacked bilayer graphene. We discuss various values of the applied electric field potentials and show their influence on the electronic band structure of the system. Additionally, we identify the existence of a critical value of the magnetic field above which Wigner crystallization-like effect is present for the electrons, also affecting the excitonic gap in one spin channel. The results obtained in this study could be important for applications of AA-stacked bilayer graphene as a large band-gap material.