2025/09/29 by Zoltán Guba, Robert-Jan Slager, Guba, Zoltán +5 · 1 voice
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum many-body systems #Topological Materials and Phenomena
paper · pdf · doi:10.1038/s41467-026-71401-3
openalex publication_date 2026/04/01 · openalex created_date 2026/04/02 · openalex updated_date 2026/07/23
Crystalline constructions known as Cayley-Schreier lattices have been suggested as a platform for realizing arbitrary gauge fields in synthetic crystals with real hopping amplitudes. Here, we reveal that Cayley-Schreier lattices can naturally give rise to implementable lattice systems that incorporate non-Abelian gauge structures transforming into a space-group symmetry. We show that their symmetry sectors can be interpreted as blocks of pseudospin models–some of which correspond to true spinors–that can realize a wealth of different topological invariants in a single setup. We underpin these general results with concrete models and illustrate how they can be implemented in technologically available experimental platforms. Our work sets the stage for a systematic investigation of topological insulators and metals with non-Abelian gauge structures. Cayley-Schreier lattices have been shown to enable the inclusion of non-commutative translations into Abelian systems. Here, authors theoretically demonstrate that these crystalline systems can also bring to the emergence of non-Abelian gauge structures, providing a perspective on realistic experimental implementations.