Abstract
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.
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Data availability
All the data used to arrive at the conclusions presented in this work are publicly available in the following data repository: https://doi.org/10.5281/zenodo.18954513.
Code availability
All the Python code used to generate and analyze the data and to arrive at the conclusions presented in this work is publicly available in the form of annotated notebooks in the following data repository: https://doi.org/10.5281/zenodo.18954513.
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Acknowledgements
We would like to thank A. Iliasov, M. Marciani, T. Neupert, and A. Tiwari for valuable discussions. Z.G., L.K.U., and T.B. were supported by the Starting Grant No. 211310 by the Swiss National Science Foundation. R.-J.S. acknowledges funding from an EPSRC ERC underwrite grant EP/X025829/1, and a Royal Society exchange grant IES/R1/221060.
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L.K.U. and T.B. conceived the project. Z.G. and T.B. analyzed the presented tight-binding models. R.-J.S. advised on the gauge theory aspects. L.K.U. and T.B. devised the electric-circuit blueprint. All authors contributed to developing the theoretical framework, discussed together, and wrote the manuscript.
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Guba, Z., Slager, RJ., Upreti, L.K. et al. Topological non-Abelian gauge structures in Cayley-Schreier lattices. Nat Commun (2026). https://doi.org/10.1038/s41467-026-71401-3
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DOI: https://doi.org/10.1038/s41467-026-71401-3
