Dynamical noncommutative graphene

Abstract

We study graphene in a two-dimensional dynamical noncommutative (NC) 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 NC (DNC) parameter [Formula: see text]. Using the accuracy of energy measurement, we put an upper bound on the noncommutativity parameter [Formula: see text]. 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 nondynamical and DNC spaces.