Quantum Hall Effect in Biased Bilayer Graphene

Abstract

We numerically study the quantum Hall effect in biased bilayer graphene based on a tight-binding model in the presence of disorder. Integer quantum Hall plateaus with quantized conductivity $σ_{xy}=νe^2/h$ (where $ν$ is any integer) are observed around the band center due to the split of the valley degeneracy by an opposite voltage bias added to the two layers. The central ($n=0$) Dirac Landau level is also split, which leads to a pronounced $ν=0$ plateau. This is consistent with the opening of a sizable gap between the valence and conduction bands. The exact spectrum in an open system further reveals that there are no conducting edge states near zero energy, indicating an insulator state with zero conductance. Consequently, the resistivity should diverge at Dirac point. Interestingly, the $ν=0$ insulating state can be destroyed by disorder scattering with intermediate strength, where a metallic region is observed near zero energy. In the strong disorder regime, the Hall plateaus with nonzero $ν$ are destroyed due to the float-up of extended levels toward the band center and higher plateaus disappear first.