期刊名称:Proceedings of the National Academy of Sciences
印刷版ISSN:0027-8424
电子版ISSN:1091-6490
出版年度:2018
卷号:115
期号:20
页码:5135-5139
DOI:10.1073/pnas.1804572115
语种:English
出版社:The National Academy of Sciences of the United States of America
摘要: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.