Topological states in quasicrystals

• 作者: Jiahao Fan Huaqing Huang
• 来源期刊: 物理学前沿
• 年，卷（期）: 2022,（1）
• 所属期刊栏目: Condensed Matter & Materials Physics
• 页码范围: 115-134
• 页数: 20页
• 语种: 英文

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 topo-logical 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 topo-logical 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 crys-talline counterpart.