Topological states in quasicrystals

doi:10.1007/s11467-021-1100-y

Frontiers of Physics

2022, Vol. 17

Issue (1): 13203 https://doi.org/10.1007/s11467-021-1100-y

本期目录

Topological states in quasicrystals

Jiahao Fan^1,^2,³, Huaqing Huang^1,^2,³(

)

¹. School of Physics, Peking University, Beijing 100871, China
². Center for High Energy Physics, Peking University, Beijing 100871, China
³. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

全文: PDF(5621 KB)

Abstract：

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.

Key words： topological states quasicrystals quantum Hall effect topological insulator topological superconductor

收稿日期: 2021-04-01 出版日期: 2021-08-24

Corresponding Author(s): Huaqing Huang

引用本文:

. [J]. Frontiers of Physics, 2022, 17(1): 13203.
Jiahao Fan, Huaqing Huang. Topological states in quasicrystals. Front. Phys. , 2022, 17(1): 13203.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-021-1100-y
https://academic.hep.com.cn/fop/CN/Y2022/V17/I1/13203

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