Effect of torus-shape curved space on energy spectrum and magnetization of Dirac fermions in graphene

In this paper, the dynamical properties of charge carriers in the two-dimensional atomic layer of graphene lattice with torus-shape geometry is studied in the presence of a gauge field. The curved space considerations involves Dirac equation along with a magnetic field for relativistic quasiparticles in graphene. By using the Heun's differential equation, we are able to analytically find discrete Landau levels of graphene in torus-like curved space. The magnetization of energy states is investigated. (paper)