Landau levels in a simple hexagonal bilayer graphene

A new approach, which makes the Hamiltonian of the Peierls tight-binding model change into a band matrix, is used to investigate the Landau levels in a AA-stacked bilayer graphene. The interlayer atomic hoppings could induce an energy gap, the asymmetry of the Landau levels about the chemical potential, the random variation in the level spacing, more fourfold degenerate Landau levels at low energy, and the oscillatory Landau levels and the complicated state degeneracies at moderate energy. For the low-energy Landau levels, their dependence on the quantum number and the field strength cannot be well characterized by a simple power law. They exhibit a anomalous oscillation during the variation of the magnetic field. The main features of the magnetoelectronic states are directly reflected in density of states.