Flux-Mediated Correspondence Between Real- and Momentum-Space Nonsymmorphicity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911632641228800 |
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| author | Chen, Z. Y. Zhao, Y. X. |
| author_facet | Chen, Z. Y. Zhao, Y. X. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26575 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flux-Mediated Correspondence Between Real- and Momentum-Space Nonsymmorphicity Chen, Z. Y. Zhao, Y. X. Mesoscale and Nanoscale Physics 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. |
| title | Flux-Mediated Correspondence Between Real- and Momentum-Space Nonsymmorphicity |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2604.26575 |