论文标题
石墨烯中的Hofstadter Butterfly
Hofstadter Butterfly in Graphene
论文作者
论文摘要
这是对石墨烯中Hofstadter Butterfly最近进展的简短评论，该进展是在下面组织的。我们首先简要介绍了Hofstadter蝴蝶，包括磁场中Bloch电子的理论玩具模型，由此产生的Harper方程及其解决方案以及在非透明烯系统中的实现。然后，我们讨论实现石墨烯中分形的霍夫史塔光谱的方法，并引入三种类型的石墨烯超晶格结构，包括石墨烯-HBN，扭曲的石墨烯层，纳米破坏性石墨烯超级晶格。特别是，将在石墨烯HBN超晶格和扭曲的双层石墨烯中集中并讨论有关石墨烯中分形Hofstadter光谱的详细信息。
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.
