@article { , title = {High-order fractal states in graphene superlattices}, abstract = {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.}, doi = {10.1073/pnas.1804572115}, eissn = {1091-6490}, issn = {0027-8424}, issue = {20}, journal = {Proceedings of the National Academy of Sciences}, publicationstatus = {Published}, publisher = {National Academy of Sciences}, url = {https://nottingham-repository.worktribe.com/output/932755}, volume = {115}, keyword = {Graphene, Superlattice, Hofstadter butterfly}, year = {2018}, author = {Krishna Kumar, R. and Mishchenko, A. and Chen, X. and Pezzini, S. and Auton, G.H. and Ponomarenko, L.A. and Zeitler, U. and Eaves, Laurence and Fal’ko, V.I. and Geim, A.K.} }