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.

Jiahao Fan;Huaqing Huang

School of Physics,Peking University,Beijing 100871,China;Center for High Energy Physics,Peking University,Beijing 100871,China;Collaborative Innovation Center of Quantum Matter,Beijing 100871,China

物理学前沿

[1]Jiahao Fan;Huaqing Huang-.Topological states in quasicrystals)[J].物理学前沿,2022(01):115-134

quasicrystals,quasicrystalline

Topological,states,With,rapid,development,topological,study,been,extended,recent,years,In,this,review,we,summarize,progress,particularly,focusing,one,dimensional,1D,2D,systems,We,first,give,brief,introduction,structures,Then,discuss,phases,where,nature,attributed,synthetic,dimensions,associated,quasiperiodic,order,further,present,generalization,various,types,real,space,expressions,corresponding,invariants,are,introduced,due,lack,translational,symmetry,Finally,since,possess,forbidden,symmetries,such,five,fold,eight,rotation,provide,overview,unique,protected,without,counterpart

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