The Interaction of Bilayer Graphene with an External Magnetic Field

Abstract

In this phenomenological approach to the study of magnetism in bilayer graphene, the chiral model of graphene was employ to describe the interaction of the bilayer graphene with an external magnetic field. The simplest scalar chiral model of graphene suggested earlier and based on the SU (2) order parameter is generalized by including 8-spinor field as an additional order parameter for the description of spin (magnetic) excitations in the bilayer graphene. As an illustration we study the interaction of the bilayer graphene with the external magnetic field orthogonal to the plane. The Lagrangian density of the model was constructed; The Lagrangian density of the model includes the three interacting terms, the spinor field, chiral field, and the electromagnetic field. The domain wall solution describing the bilayer graphene configuration is introduced for studying the magnetic field behavior in the central domain of the material; the solution to the inhomogeneous equations were found using the Green's function method, at small radial field, the paramagnetic behavior of the material was revealed and the strengthening of the magnetic intensity inside the material in the central domain of the material was also revealed.