Abstract
AbstractA 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.
Funder
Ministry of Education - Singapore
National Natural Science Foundation of China
Basic Research Program of Jiangsu Province
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Biochemistry, Genetics and Molecular Biology,General Chemistry,Multidisciplinary
Cited by
8 articles.
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