期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 115, 期 20, 页码 5135-5139出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1804572115
关键词
graphene; superlattice; Hofstadter butterfly
资金
- Engineering and Physical Sciences Research Council (EPSRC)
- European Graphene Flagship
- Royal Society
- Lloyd's Register Foundation
- European Research Council (ERC)
- Netherlands Organisation for Scientific Research
- EPSRC [EP/N007131/1, EP/N509565/1, EP/M507969/1, EP/N010345]
- High Field Magnet Laboratory-Radboud University of the European Magnetic Field Laboratory
- Royal Society [UF120297]
- ERC Synergy Grant Hetero 2D [ERC-2012-SyG]
- European Graphene Flagship (H2020-SGA-FET-GRAPHENE)
- Graphene NOWNANO Doctoral Training Centre
- Royal Society [UF120297] Funding Source: Royal Society
- EPSRC [EP/N01085X/1, EP/N007131/1, EP/K005014/1] Funding Source: UKRI
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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