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Hofstadter Butterfly in Graphene

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arxiv 2203.05821 v2 pith:OUPEXPE2 submitted 2022-03-11 cond-mat.mes-hall cond-mat.mtrl-sci

Wei Yang , Guangyu Zhang This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords graphenehofstadterbutterflysuperlatticefractalgraphene-hbnincludingintroduce
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This is a short review of the recent progresses on Hofstadter butterfly in graphene, organized in the following. We first briefly introduce the Hofstadter butterfly, including the theoretic toy model of Bloch electrons in the magnetic field, the resulting Harper's equation and its solution, and realizations in non-graphene systems. Then, we discuss the ways to realize the fractal Hofstadter spectra in graphene, and introduce three types of graphene superlattice structure, including graphene-hBN, twisted graphene layers, nanofabricated graphene superlattice. In particular, details about the fractal Hofstadter spectrum in graphene will be focused and discussed in the graphene-hBN superlattice and the twisted bilayer graphene.

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