Dirac donor states controlled by magnetic field in gapless and gapped graphene
In this paper, the exact solutions of Dirac electronic states of graphene in Coulomb and magnetic fields are acquired. The Coulomb field not only causes the splitting of Landau levels in gapless graphene but also leads to the variation of the energy level ordering in gapped graphene. The dependence of the binding energies on the gap and the magnetic field is discussed. Furthermore, the valley degree of freedom and the valley splitting spacing can be controlled by the Coulomb and magnetic fields in gapped graphene. The intervalley mixing of graphene is estimated and calculated in the direct sum spaces of the two valleys. The results obtained help us to understand the behaviors of the planar Dirac electron in electromagnetic fields and can be applied to the controlling of the electron's behaviors in graphene.