Classification of time-reversal-invariant crystals with gauge structures

Z. Y. Chen, Zheng Zhang, Shengyuan A. Yang and Y. X. Zhao ()
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Z. Y. Chen: Nanjing University
Zheng Zhang: Nanjing University
Shengyuan A. Yang: Singapore University of Technology and Design
Y. X. Zhao: Nanjing University

Nature Communications, 2023, vol. 14, issue 1, 1-9

Abstract: 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.

Date: 2023
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DOI: 10.1038/s41467-023-36447-7

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