中国物理B ›› 2026, Vol. 35 ›› Issue (5): 57305-057305.doi: 10.1088/1674-1056/ae6906

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Topological property of graphene with triangular array of nanoholes

Yong-Cheng Jiang(江咏城)1,2, Xing-Xiang Wang(王星翔)1, and Xiao Hu(胡晓)1,2,†   

  1. 1 Institute for Quantum Science and Technology, Shanghai University, Shanghai 200444, China;
    2 Department of Physics, College of Sciences, Shanghai University, Shanghai 200444, China
  • 收稿日期:2026-04-30 出版日期:2026-05-06 发布日期:2026-05-06
  • 通讯作者: Xiao Hu E-mail:hu_xiao@shu.edu.cn
  • 基金资助:
    The authors are grateful to T. Kariyado for valuable discussions. Project supported by Shanghai Science and Technology Innovation Action Plan (Grant No. 24LZ1400800).

Topological property of graphene with triangular array of nanoholes

Yong-Cheng Jiang(江咏城)1,2, Xing-Xiang Wang(王星翔)1, and Xiao Hu(胡晓)1,2,†   

  1. 1 Institute for Quantum Science and Technology, Shanghai University, Shanghai 200444, China;
    2 Department of Physics, College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2026-04-30 Online:2026-05-06 Published:2026-05-06
  • Contact: Xiao Hu E-mail:hu_xiao@shu.edu.cn
  • Supported by:
    The authors are grateful to T. Kariyado for valuable discussions. Project supported by Shanghai Science and Technology Innovation Action Plan (Grant No. 24LZ1400800).

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摘要： The nontrivial band topology for graphene with regular arrays of nanoholes with $C_{6v}$ symmetry is investigated theoretically. For the case of the $3\sqrt{3}\times 3\sqrt{3}$ triangular array of nanoholes, we find an energy gap at the $\varGamma$ point around the Fermi level associated with a band inversion which induces a change in parity indices, whereas deep below the Fermi level there is a bunch of valence bands (VBs) characterized as an obstructed atomic limit (OAL) which also accommodates an imbalance in parity indices. This band structure renders the gap at the Fermi level topologically trivial and carrying no edge states, while the nontrivial band topology of the OAL manifests in two flat bands in the ribbon structure associated with localized electronic states at the ribbon edges. The present results exhibit rich topological behaviors in graphene derivatives waiting for exploration.

关键词: topological crystalline insulator, graphene derivative, Wannier center, parity index

Abstract: The nontrivial band topology for graphene with regular arrays of nanoholes with $C_{6v}$ symmetry is investigated theoretically. For the case of the $3\sqrt{3}\times 3\sqrt{3}$ triangular array of nanoholes, we find an energy gap at the $\varGamma$ point around the Fermi level associated with a band inversion which induces a change in parity indices, whereas deep below the Fermi level there is a bunch of valence bands (VBs) characterized as an obstructed atomic limit (OAL) which also accommodates an imbalance in parity indices. This band structure renders the gap at the Fermi level topologically trivial and carrying no edge states, while the nontrivial band topology of the OAL manifests in two flat bands in the ribbon structure associated with localized electronic states at the ribbon edges. The present results exhibit rich topological behaviors in graphene derivatives waiting for exploration.

Key words: topological crystalline insulator, graphene derivative, Wannier center, parity index

中图分类号:  (Electronic structure of graphene)

  • 73.22.Pr
02.40.-k (Geometry, differential geometry, and topology)