Magnetic Susceptibility, Specific Heat, and Entropy of Graphene Using Non-Abelian Quantization

A simple nonrelativistic model is proposed using a non-Abelian magnetic quantization approach. In this model, a deformed of the Heisenberg algebra is used. In the model, the commutator of momenta is considered proportional to the pseudo-spin. Due to the use of non-commutative algebra, a linear term in the momentum is appeared. By this model, the low-energy excitations of graphene are determined. The Landau problem is solved under a uniform magnetic field perpendicular to the plane. Then, the partition function is calculated for two branches: positive and negative. Finally, the thermal and magnetic properties of graphene are calculated. The results show that the magnetic susceptibility has a transition from paramagnetic to diamagnetic in each branch. The transition point depends on the temperature and magnetic field.