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arXiv · 2604.26575

Flux-Mediated Correspondence Between Real- and Momentum-Space Nonsymmorphicity

Z. Y. Chen·Y. X. Zhao
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Abstract

Momentum-space nonsymmorphic symmetries have recently attracted significant interest in both artificial and condensed-matter crystals, whereas real-space nonsymmorphic symmetries have long played an important role in the study of crystalline topological phases. Here, we establish a general theory of momentum-space crystallographic groups that emerge from projective representations of real-space crystallographic groups in the presence of gauge flux, applicable in particular to real-space nonsymmorphic groups. A central result is a flux-mediated ``bi-nonsymmorphicity'' relation that reveals a structural correspondence between real-space and momentum-space nonsymmorphicity mediated by gauge flux. This relation implies that, under a symmetric gauge flux, real-space nonsymmorphicity can enforce momentum-space nonsymmorphicity, and that in some cases a symmetric gauge flux requires nonsymmorphicity in both real and momentum space. Our work not only identifies a fundamental structure in projective crystal symmetries, but also provides guiding principles for designing artificial crystals and condensed-matter platforms that exhibit both real-space and momentum-space nonsymmorphic symmetries.

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Z. Y. Chen, Y. X. Zhao. 2026-04-29. Flux-Mediated Correspondence Between Real- and Momentum-Space Nonsymmorphicity. https://arxiv.org/abs/2604.26575

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