Landau-level characterization of AB-stacked graphite

Magneto-electronic structures of AB-stacked bulk graphite are investigated by the Peierls tight-binding model, which takes account of all interlayer interactions and field-induced Peierls phases simultaneously. This model is feasible for all $\pi$ electronic states and capable of drawing the analytic solution for state wave functions. The external magnetic field $B_0\hat{z}$ condenses the planar motion of electrons into Landau levels, and the coupling between layers causes these levels to oscillate along $k_z$. The band edge states are mainly located at the Brillouin zone boundaries, where their frequencies as a function of field are closely related to the atomic hopping integrals. Landau levels are divided into two groups based on the wave function distribution. Besides, wave functions undergo a particular transition between atomic sites in response to $k_z$. From the behavior of energies and wave functions, we can infer the monolayer-like plus bilayer-like features in bulk graphite. The explicit characterization of Landau levels in this work could be applied to clarify and elucidate the experimental measurements on graphene layers.