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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| Veröffentlicht in: | Proceedings of the National Academy of Sciences - PNAS 2018-05, Vol.115 (20), p.5135-5139 |
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| container_title | Proceedings of the National Academy of Sciences - PNAS |
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| creator | Kumar, R. Krishna Mishchenko, A. Chen, X. Pezzini, S. Auton, G. H. Ponomarenko, L. A. Zeitler, U. Eaves, L. Fal’ko, V. I. Geim, A. K. |
| 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. |
| doi_str_mv | 10.1073/pnas.1804572115 |
| format | Article |
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Krishna ; Mishchenko, A. ; Chen, X. ; Pezzini, S. ; Auton, G. H. ; Ponomarenko, L. A. ; Zeitler, U. ; Eaves, L. ; Fal’ko, V. I. ; Geim, A. K.</creator><creatorcontrib>Kumar, R. Krishna ; Mishchenko, A. ; Chen, X. ; Pezzini, S. ; Auton, G. H. ; Ponomarenko, L. A. ; Zeitler, U. ; Eaves, L. ; Fal’ko, V. I. ; Geim, A. K.</creatorcontrib><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. 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| subjects | Carbon Crystal lattices Electron trajectories Fractals Graphene High temperature Magnetic fields Magnetism Oscillations Physical Sciences Qualitative analysis Superlattices Unit cell |
| title | High-order fractal states in graphene superlattices |
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