Orbital magnetization in axially symmetric two-dimensional carbon allotrope: influence of electric field and geometry

In this paper, we use supersymmetry formalism to study (2 + 1) dimensional Dirac-Weyl equation describing the motion of electrons in different axially symmetric carbon allotrope surfaces under the influence of crossed electromagnetic fields. In particular, we consider three carbon allotrope with different geometrical shapes and properties: open, half-open and closed geometries. The effect of the electric field and geometry on Landau levels and orbital magnetization has been examined. It has been shown that at a critical electric field the orbital magnetization exhibits a discontinuity which is associated with the collapse of Landau levels.