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

TL;DR

This paper develops a theory linking real-space and momentum-space nonsymmorphic symmetries through gauge flux, revealing how flux can induce structural correspondence between these symmetries in crystals.

Contribution

It introduces a flux-mediated bi-nonsymmorphicity relation that connects real-space and momentum-space nonsymmorphic symmetries via projective representations and gauge flux.

Findings

Real-space nonsymmorphicity can enforce momentum-space nonsymmorphicity under symmetric gauge flux.

A fundamental flux-mediated relation links real- and momentum-space nonsymmorphic symmetries.

Guides for designing artificial crystals with combined real- and momentum-space nonsymmorphic symmetries.

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.