Research Article

Non-Abelian band topology in noninteracting metals

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Science  20 Sep 2019:
Vol. 365, Issue 6459, pp. 1273-1277
DOI: 10.1126/science.aau8740

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The topology of line nodes

Band structure degeneracies in topological materials can take the form of lines or even chains of interconnected loops. Wu et al. study theoretically these nodal lines and how they evolve as the system parameters are varied. They focus on a class of materials that have weak spin-orbit coupling and that respect a combination of inversion- and time-reversal symmetry. Noncommutative topological charges are associated with nodal lines in such materials that place constraints on the configurations of these lines. Calculations indicate that elemental scandium under strain may provide a test system for this unconventional topology.

Science, this issue p. 1273


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 crystalline metals with space-time inversion (𝒫𝒯) symmetry and 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 one-dimensional topological phases not present in existing classifications.

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