ABSTRACT
The quantum Hall effects in sliding bilayer graphene and a AAB-stacked trilayer system are investigated using the Kubo formula and a generalized tight-binding model. The various stacking configurations can greatly diversify the magnetic quantization and thus create rich and unique transport properties. Since the first discovery of few-layer graphene systems in 2004 by the mechanical exfoliation, its unconventional quantum Hall effects have stirred many theoretical and experimental researches. The geometric symmetries, band structures, Landau-level energy spectra and wave functions, and quantum Hall conductivities are thoroughly studied for the sliding bilayer graphenes through the generalized tight-binding model and the static Kubo formula. On the experimental side, the high-resolution transport measurements are available in verifying the theoretical predictions on the quantum Hall conductivities of the sliding bilayer graphene systems. In short, the experimental verifications are very useful in directly proving the close relations among the stacking symmetries, the complex hopping integrals, the magneto-electronic properties, and the quantum Hall effects.
