Stacking-enriched magneto-transport properties of few-layer graphenes

The quantum Hall effects in the sliding bilayer graphene and AAB-stacked trilayer system are investigated by the Kubo formula and the generalized tight-binding model. The various stacking configurations can greatly diversify the magnetic quantization and thus create the rich and unique transport properties. The quantum conductivities are very sensitive to the Fermi energy and magnetic-field strength. The diverse features cover the specific non-integer conductivities, the integer conductivities with the distinct steps, the splitting-created reduction and complexity of quantum conductivity, a vanishing or non-zero conductivity at the neutral point, and the well-like, staircase, composite, and abnormal plateau structures in the field-dependencies. Such stacking-dependent characteristics mainly originate from the crossing, anticrossing and splitting Landau-level energy spectra and three kinds of quantized modes.