Dynamical Noncommutative Graphene

We study graphene in a two-dimensional dynamical noncommutative space in the presence of a constant magnetic field. The model is solved using perturbation theory and to the second order of perturbation. The energy levels of the system are calculated and the corresponding eigenstates are obtained. For all cases, the energy shift depends on the dynamical noncommutative parameter {\tau}. Using the accuracy of energy measurement we put an upper bound on the noncommutativity parameter {\tau}. In addition, we investigate some of the thermodynamic quantities of the system at zero temperature limit and extreme relativistic case, which reveals interesting differences between commutative and dynamical noncommutative spaces.