Topological states in quasicrystals

作     者：Jiahao Fan Huaqing Huang Jiahao Fan;Huaqing Huang

作者机构：School of PhysicsPeking UniversityBeijing100871China Center for High Energy PhysicsPeking UniversityBeijing100871China Collaborative Innovation Center of Quantum MatterBeijing100871China 

出 版 物：《Frontiers of physics》 (物理学前沿（英文版）)

年 卷 期：2022年第17卷第1期

页      面：123-142页

核心收录：

学科分类：07[理学] 070205[理学-凝聚态物理] 0702[理学-物理学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.12074006) the Start-up Funds from Peking University 

主　　题：topological states quasicrystals quantum Hall effect topological insulator topological superconductor 

摘      要：With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.