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.
Highlights
Since the very discovery of this novel material it has attracted deep interest of researchers due to its extraordinary properties [1]
The simplest scalar chiral model is based on the so-called sp-hybridization effect of the carbon atom valence electrons
The new variable for our spinor field is introduced: L A and &M signifies the differentiation with respect to 4 and 3
Summary
Since the very discovery of this novel material it has attracted deep interest of researchers (theoretical and experimental) due to its extraordinary properties [1]. The electrons in graphene are conferred to move on a plane, the electromagnetic field through which they interact extends throughout the 3D space [11] Another important observation is that the electron mobility in graphene is about ten times higher than the mobility of commercial silicon wafers and electrons can travel huge distances (300nm or more) without being scattered [12]. In this phenomenological approach to the description of magnetism in bilayer graphene, the action of the external magnetic field orthogonal to the bilayer graphene planes was investigate, considering the fact that magnetism in graphene and other carbon structures prove to be extremely anisotropic [13]
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