Quantum Hall effect in ABA- and ABC-stacked trilayer graphene

We numerically study the quantum Hall effect (QHE) in trilayer graphene with different stacking orders in the presence of interlayer bias under a strong magnetic field and disorder. In the biased ABA-stacked case, the Hall conductivity around the band center (Dirac point) is quantized as σxy = νe2/h, where the filling factor ν is a nonzero integer. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and higher plateaus disappear first. The central two plateaus around the band center are most robust against disorder scattering. With the increasing of the disorder strength, Hall plateaus are destroyed faster for the system with weaker magnetic field. In the biased ABC-stacked case, the Hall conductivity is quantized as σxy = νe2/h (where ν is any integer) due to the split of the valley degeneracy by an opposite voltage bias added to the two layers. The central (n = 0) Landau level is also split, which leads to a pronounced ν = 0 plateau. Interestingly, the ν = 0 insulating state can be destroyed by a relatively strong disorder strength, where a metallic region is observed near zero energy. In the strong-disorder regime, all QHE states are destroyed by disorder, and the system transits into an insulating phase.