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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.

Authors

R. Krishna Kumar

A. Mishchenko

X. Chen

S. Pezzini

G.H. Auton

L.A. Ponomarenko

U. Zeitler

Laurence Eaves

V.I. Fal’ko

A.K. Geim



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.

Journal Article Type Article
Publication Date May 15, 2018
Journal Proceedings of the National Academy of Sciences
Electronic ISSN 1091-6490
Publisher National Academy of Sciences
Peer Reviewed Peer Reviewed
Volume 115
Issue 20
APA6 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), doi:10.1073/pnas.1804572115
DOI https://doi.org/10.1073/pnas.1804572115
Keywords Graphene; Superlattice; Hofstadter butterfly
Publisher URL http://www.pnas.org/content/115/20/5135
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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