Study of Magnetic and Thermal Properties of Graphene by Tsallis Formalism: Deformed of the Heisenberg Model

A simple nonrelativistic model is introduced based on the deformed of the Heisenberg algebra. In this model, the commutator of momenta is proposed proportional to the pseudospin. The low-energy excitations of graphene are derived by using this model. The Landau problem has been solved by taking into account a uniform magnetic field perpendicular to the plane. Then, the Tsallis non-additive formalism is employed to obtain the probability and the partition function for two branches, the positive and negative. Finally, the magnetic susceptibility and thermodynamic properties of graphene are determined. The findings reveal that the magnetic susceptibility has a positive value and shows a paramagnetic behavior in each branch. The susceptibility in the negative branch has a lower value in comparison to the positive branch for any values of non-extensive parameter. The specific heat displays a peak structure. For a given non-extensive parameter, the peak position of the specific heat occurs at a particular temperature in each branch. The results show that both parameters, temperature and non-extensive parameter, have important roles in magnetic susceptibility and thermal properties of the system.