Impurity effects in the magnetic oscillations on doped graphene with Zeeman splitting

The aim of this work is to describe the electronic and magnetic properties of graphene in a constant magnetic field, in the long wavelength approximation with random disorder. Taking into account the Zeeman effect, the electronic density of states for each spin is found and the de Haas van Alphen oscillations (dHvA) are found. The magnetic field is found to modulate the de Haas-van Alphen magnetization through the ratio of the Zeeman coupling and pseudospin-Landau coupling. In turn, the Pauli magnetization is studied showing that the Zeeman splitting and disorder introduces a dHvA oscillation period that depends on the magnetic field strength and generalizes the Onsager relation. In turn, a beat frequency appears that does not depend on B but increase linearly with the chemical potential. These results, which are different from those obtained in the standard nonrelativistic 2D electron gas, are attributed to its anomalous Landau level spectrum in graphene.