Analysis of the Zeeman effect on the energy spectrum in graphenes

An analysis of the Zeeman effect with a strong external magnetic field on the energy spectrum in graphene is presented. In general, the Hamiltonian of graphene in applied electric and magnetic fields is not of SO(1, 2) invariance even in the nearest-neighbor approximation because of the Zeeman coupling. But an approximate SO(1, 2) invariance can be obtained when the applied magnetic field is very strong. This approximate invariance can be used to relate the energy structure of graphene in the presence of both electric and magnetic fields to that when there is only magnetic field. Therefore, it can help explain the recently found quantum Hall conductance (4q2/h)L for L = 0.1.