High-order fractal states in graphene superlattices

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 b...

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Main Authors: 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.
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Published: National Academy of Sciences 2018
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Online Access:https://eprints.nottingham.ac.uk/51866/
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author 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.
author_facet 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.
author_sort Krishna Kumar, R.
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-518662020-05-04T19:36:40Z https://eprints.nottingham.ac.uk/51866/ 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. 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. National Academy of Sciences 2018-05-15 Article PeerReviewed Krishna Kumar, R., Mishchenko, A., Chen, X., Pezzini, S., Auton, G.H., Ponomarenko, L.A., Zeitler, U., Eaves, Laurence, Fal’ko, V.I. and Geim, A.K. (2018) High-order fractal states in graphene superlattices. Proceedings of the National Academy of Sciences, 115 (20). pp. 5135-5139. ISSN 1091-6490 Graphene; Superlattice; Hofstadter butterfly http://www.pnas.org/content/115/20/5135 doi:10.1073/pnas.1804572115 doi:10.1073/pnas.1804572115
spellingShingle Graphene; Superlattice; Hofstadter butterfly
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.
High-order fractal states in graphene superlattices
title High-order fractal states in graphene superlattices
title_full High-order fractal states in graphene superlattices
title_fullStr High-order fractal states in graphene superlattices
title_full_unstemmed High-order fractal states in graphene superlattices
title_short High-order fractal states in graphene superlattices
title_sort high-order fractal states in graphene superlattices
topic Graphene; Superlattice; Hofstadter butterfly
url https://eprints.nottingham.ac.uk/51866/
https://eprints.nottingham.ac.uk/51866/
https://eprints.nottingham.ac.uk/51866/