Landau subband and Landau level properties of AA-stacked graphene superlattice.

Magneto-electronic properties of AA-stacked graphene superlattice (simple hexagonal graphite) are studied by the tight-binding model with an exact diagonalization method. The Landau subbands (LSs) with strong energy dispersions exist along k(z) and each subband possesses two band-edge states. Density of states reflects main features of the LSs, such as asymmetric prominent peak structures and the semimetallic behavior. Under the AA-stacked configuration, the LS wave functions are characterized by two sublattices, a and b. The quantum number (n(c,v)) of each LS, which corresponds to the number of zero points in the dominating carrier distributions, is determined by a certain sublattice and independent of k(z). For each LS, the difference between the number of zero point of the a and b sublattices is fixed and equals one. Furthermore, a reliable approximate solution of the low-lying LS energy is obtained. Through observing this solution, the dependence of the LS energy on the field strength and quantum number, k(z)-dependent energy spacing between two LSs, and the values of atomic hopping integrals are reasonably determined. A comparison of the AA-stacked graphene superlattice and monolayer graphene demonstrates that they possess some similar magneto-electronic properties.