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Non-Abelian band topology in noninteracting metals


Wu, QuanSheng; Soluyanov, Alexey A; Bzdušek, Tomáš (2019). Non-Abelian band topology in noninteracting metals. Science, 365(6459):1273-1277.

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 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.

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 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Health Sciences > Multidisciplinary
Uncontrolled Keywords:Multidisciplinary
Language:English
Date:20 September 2019
Deposited On:13 Feb 2020 09:20
Last Modified:29 Jul 2020 13:17
Publisher:American Association for the Advancement of Science
ISSN:0036-8075
Additional Information:This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science {365, 20 Sept 2019, 10.1126/science.aau8740}.
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1126/science.aau8740
Related URLs:https://www.zora.uzh.ch/id/eprint/187931/
Other Identification Number:1808.07469v3

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