Supplementary Data for “Non-Abelian band topology in noninteracting metals”

QuanSheng Wu, Alexey A. Soluyanov & Tomáš Bzdušek
Electron energy bands, which are studied to explain electronic and optical properties of crystalline solids, often exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of -symmetric crystalline metals with weak spin-orbit coupling. We show that these are quaternion charges, similar to those describing disclinations in biaxial nematics. Starting from two-band considerations, we develop the complete many-band description of nodes in the presence of and...
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