Magnetotransport in bilayer graphene in the presence of a weak and periodic potential is investigated in the presence of a perpendicular magnetic field $B$. The modulation broadens the Landau levels into bands and for weak magnetic fields leads to the well-known Weiss oscillations in their bandwidth and their transport coefficients at very low $B$ and to the Shubnikov–de Haas oscillations at larger $B$. The amplitude of the Weiss oscillations is severely reduced if the periodic potentials applied to the two layers oscillate out of phase. We also contrast some results with those corresponding to single-layer graphene. Relative to them the flat-band condition and the oscillation amplitude differ substantially, due to the interlayer coupling, and agree only when this coupling is extremely weak. We further show that the Hall conductivity exhibits the well-known steps at half-integer and integer multiples of $4e^2/h$ in single-layer and bilayer graphene, respectively, even for very weak magnetic fields. The results are pertinent to weak and periodic corrugations when the potential modulation dominates the strain-induced magnetic modulation.

• Received 12 March 2012

DOI:https://doi.org/10.1103/PhysRevB.85.245426