High-order fractal states in graphene superlattices - Krishna Kumar, R.; Mishchenko, A.; Chen, X.; Pezzini, S.; Auton, G.H.; Ponomarenko, L.A.; Zeitler, U.; Eaves, Laurence; Fal’ko, V.I.; Geim, A.K. (National Academy of Sciences, 2018)
Graphene superlattices were shown to exhibit high-temperature quantum oscillations due to periodic emergence of delocalized Bloch states in high magnetic fields such that unit fractions of the flux quantum pierce a superlattice unit cell. Under these conditions, semiclassical electron trajectories become straight again, similar to the case of zero magnetic field. Here, we report magnetotransport measurements that reveal second-, third-, and fourth-order magnetic Bloch states at high electron densities and temperatures above 100 K. The recurrence of these states creates a fractal pattern intimately related to the origin of Hofstadter butterflies. The hierarchy of the fractal states is determined by the width of magnetic minibands, in qualitative agreement with our band-structure calculations.