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.

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.

Citation

Krishna Kumar, R., Mishchenko, A., Chen, X., Pezzini, S., Auton, G., Ponomarenko, L., …Geim, A. (2018). High-order fractal states in graphene superlattices. Proceedings of the National Academy of Sciences, 115(20), https://doi.org/10.1073/pnas.1804572115

• Journal Article Type: Article
• Acceptance Date: Apr 11, 2018
• Publication Date: May 15, 2018
• Deposit Date: May 18, 2018
• Publicly Available Date: May 18, 2018
• Journal: Proceedings of the National Academy of Sciences
• Print ISSN: 0027-8424
• Electronic ISSN: 1091-6490
• Publisher: National Academy of Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 115
• Issue: 20
• DOI: https://doi.org/10.1073/pnas.1804572115
• Keywords: Graphene; Superlattice; Hofstadter butterfly
• Public URL: https://nottingham-repository.worktribe.com/output/932755
• Publisher URL: http://www.pnas.org/content/115/20/5135