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Topological states in quasicrystals

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.

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Acknowledgements

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

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Correspondence to Huaqing Huang.

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This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-021-1100-y.

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Fan, J., Huang, H. Topological states in quasicrystals. Front. Phys. 17, 13203 (2022). https://doi.org/10.1007/s11467-021-1100-y

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Keywords

  • topological states
  • quasicrystals
  • quantum Hall effect
  • topological insulator
  • topological superconductor