  Low-energy Landau levels of AB-stacked zigzag graphene ribbons in the
presence of a uniform perpendicular magnetic field (\textbf{B}) are
investigated by the Peierls coupling tight-binding model. State energies and
associated wave functions are dominated by the \textbf{B}-field strength and
the $k_z$-dependent interribbon 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
$k_x$ and $k_z$ directions, respectively. Such features are directly reflected
in density of states, which exhibits a lot of asymmetric prominent peaks
because of 1D curving bands. The $k_z$-dependent interribbon interactions
dramatically modify the magnetobands, such as the lift of double degeneracy,
the change of 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.
