Landau-level dispersion and the quantum Hall plateaus in bilayer graphene

We study the quantum Hall effect (QHE) in bilayer graphene using the Kubo-Greenwood formula. At zero temperature the Hall conductivity σyx is given by σyx = 4(N+1)e2/h with N the index of the highest occupied Landau level (LL). Including the dispersion of the LLs and their width, due to e.g. scattering by impurities, produces the plateau of the n = 0 LL in agreement with experimental results on doped samples and similar theoretical results on single-layer graphene plateaus widen with impurity concentration. Further, the evaluated resistivity ρxx exhibits a strong, oscillatory dependence on the electron concentration. Explicit results are obtained for δ-function impurities