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Due to Landau quantization, the conductance of two-dimensional electronsexposed to a perpendicular magnetic field exhibits oscillations that generate afan of linear trajectories when plotted in the parameter space spanned bydensity and magnetic field. This fan looks identical irrespective of theelectron dispersion details that determines the field dependence of the Landaulevel energy. This is no surprise, since the position of conductance minimasolely depends on the level degeneracy which is linear in flux. The fractalenergy spectrum that emerges within each Landau band when electrons are alsoexposed to a two-dimensional superlattice potential produces numerousadditional oscillations, but they too create just linear fans for the samereason. Here, we report on conductance oscillations of graphene electronsexposed to a moir\'e potential that defy this general rule of flux linearityand attribute the anomalous behavior to the simultaneous occupation of multipleminibands and magnetic breakdown.

Non-linear Landau fan diagram for graphene electrons exposed to a moir\'e potential