Low-energy Landau levels of Bernal zigzag graphene ribbons

Low-energy Landau levels of Bernal zigzag graphene ribbons in the presence of a uniform perpendicular magnetic field (B) are investigated by the Peierls coupling tight-binding model. State energies and associated wave functions are dominated by the B-field strength and the k(z)-dependent inter-ribbon interactions. The occupied valence bands are asymmetric to the unoccupied conduction bands about the Fermi level. Many doubly degenerate Landau levels and singlet curving magnetobands exist along the k(x) and k(z) directions, respectively. The k(z)-dependent inter-ribbon interactions dramatically modify the magnetobands, such as the lift of double degeneracy, the change in state energies, and the production of two groups of curving magnetobands. They also change the characteristics of the wave functions and cause the redistribution of the charge-carrier density. The k(z)-dependent wave functions are further used to predict the selection rule of the optical transition.