论文标题
旋转双层石墨烯中Hofstadter蝴蝶的副本高阶拓扑
Replica Higher-Order Topology of Hofstadter Butterflies in Twisted Bilayer Graphene
论文作者
论文摘要
发现扭曲的双层石墨烯的Hofstadter能量光谱具有递归的高阶拓扑特性。我们证明，以局部角状态为特征的高阶拓扑绝缘体（HOTI）阶段是原始HOTIS的复制品，以实现Hofstadter Spectrum的自相似性。我们显示了扭曲的双层石墨烯的确切通量翻译对称性的存在。基于此结果，我们仔细地确定零通量处的原始HOTI相是在半流量的周期性下重新输入的，其中保留了有效的双重旋转。此外，在不保护对称性的情况下发现了用于通量的原始hotis的许多复制品。与原始的hotis相似，复制品hotis具有局部角状态和边缘占地的真实空间拓扑标记。复制品Hotis来自不同的相互作用量表，即扭曲的双层石墨烯中的层次内和层间耦合。霍夫史塔特蝴蝶的拓扑方面在我们的结果中揭示了量子分形中受对称保护的拓扑结构。
The Hofstadter energy spectrum of twisted bilayer graphene is found to have recursive higher-order topological properties. We demonstrate that higher-order topological insulator (HOTI) phases, characterized by localized corner states, occur as replicas of the original HOTIs to fulfill the self-similarity of the Hofstadter spectrum. We show the existence of the exact flux translational symmetry of twisted bilayer graphene at all commensurate angles. Based on this result, we carefully identify that the original HOTI phase at zero flux is re-entrant at a half-flux periodicity, where the effective twofold rotation is preserved. In addition, numerous replicas of the original HOTIs are found for fluxes without protecting symmetries. Similar to the original HOTIs, replica HOTIs feature both localized corner states and edge-localized real-space topological markers. The replica HOTIs originate from the different interaction scales, namely, intralayer and interlayer couplings, in twisted bilayer graphene. The topological aspect of Hofstadter butterflies revealed in our results highlights symmetry-protected topology in quantum fractals.
