Research Article

Non-Abelian band topology in noninteracting metals

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Science  20 Sep 2019:
eaau8740
DOI: 10.1126/science.aau8740

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Abstract

Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of

𝓟𝓣-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 𝓟𝓣 and mirror symmetries, which allows us to investigate the topological stability of nodal chains in metals. The non-Abelian charges put strict constraints on the possible nodal line configurations. Our analysis goes beyond the standard approach to band topology, and implies the existence of 1D topological phases not present in existing classifications.

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