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Classification of time-reversal-invariant crystals with gauge structures

Author

Listed:
  • Z. Y. Chen

    (Nanjing University)

  • Zheng Zhang

    (Nanjing University)

  • Shengyuan A. Yang

    (Singapore University of Technology and Design)

  • Y. X. Zhao

    (Nanjing University
    Nanjing University)

Abstract

A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain largely unexplored. Despite recent advances in artificial crystals, whose intrinsic gauge structures necessarily require a projective description, a unified theory is yet to be established. Here, we establish such a unified theory by exhaustively classifying and representing all 458 projective symmetry algebras of time-reversal-invariant crystals from 17 wallpaper groups in two dimensions-189 of which are algebraically non-equivalent. We discover three physical signatures resulting from projective symmetry algebras, including the shift of high-symmetry momenta, an enforced nontrivial Zak phase, and a spinless eight-fold nodal point. Our work offers a theoretical foundation for the field of artificial crystals and opens the door to a wealth of topological states and phenomena beyond the existing paradigms.

Suggested Citation

  • Z. Y. Chen & Zheng Zhang & Shengyuan A. Yang & Y. X. Zhao, 2023. "Classification of time-reversal-invariant crystals with gauge structures," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-36447-7
    DOI: 10.1038/s41467-023-36447-7
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    References listed on IDEAS

    as
    1. Ji-Qian Wang & Zi-Dong Zhang & Si-Yuan Yu & Hao Ge & Kang-Fu Liu & Tao Wu & Xiao-Chen Sun & Le Liu & Hua-Yang Chen & Cheng He & Ming-Hui Lu & Yan-Feng Chen, 2022. "Extended topological valley-locked surface acoustic waves," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    2. Haoran Xue & Yong Ge & Hong-Xiang Sun & Qiang Wang & Ding Jia & Yi-Jun Guan & Shou-Qi Yuan & Yidong Chong & Baile Zhang, 2020. "Observation of an acoustic octupole topological insulator," Nature Communications, Nature, vol. 11(1), pages 1-6, December.
    3. Z. Y. Chen & Shengyuan A. Yang & Y. X. Zhao, 2022. "Brillouin Klein bottle from artificial gauge fields," Nature Communications, Nature, vol. 13(1), pages 1-5, December.
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