Low-energy Landau level spectrum in ABC-stacked trilayer graphene.

The low-lying Landau level (LL) properties of ABC-stacked trilayer graphene are investigated by the tight-binding (TB) model. The LL spectra exhibit an asymmetric structure around the Fermi level and three finely split LLs close to the Fermi level. The LL wave functions are described by six magnetic TB Bloch functions associated with six sublattices. These Bloch functions possess oscillation modes and localization features. An effective quantum number, which is used to define a LL, is defined by the oscillation mode of the Bloch function with the largest amplitude. The LL energies in the low-field and high-field regions exhibit different features since the trigonal warping effect strongly dominates the LL properties in the low-field region. Furthermore, the LLs do not present a simple relation between the magnetic field strength (effective quantum number) and the LL energy. A detailed comparison of the calculation with all atomic interactions taken into account and that ignoring some interlayer interactions is offered. The dissimilarities between these two calculations demonstrate that interlayer interactions strongly affect the main features of LLs and should not be ignored. The dissimilarities could be further examined by experimental measurements.