Supplementary Data for "Non-Abelian band topology in noninteracting metals"
Creators
- 1. Institute of Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland and National Centre for Computational Design and Discovery of Novel Materials MARVEL, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- 2. Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland and Department of Physics, St. Petersburg State University, St. Petersburg, 199034 Russia
- 3. Department of Physics, McCullough Building, Stanford University, Stanford, CA 94305, USA and Stanford Center for Topological Quantum Physics, Stanford University, Stanford, CA 94305, USA
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Description
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 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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References
Preprint (Paper where the data is discussed.) QuanSheng Wu, Alexey A. Soluyanov, Tomáš Bzdušek, arxiv: 1808.07469 (2018)
Journal reference (Paper in which the data is described) QuanSheng Wu, Alexey A. Soluyanov, Tomáš Bzdušek, Non-Abelian band topology in noninteracting metals. Science 365, 1273–1277 (2019), doi: 10.1126/science.aau8740
Journal reference (Paper in which the data is described) QuanSheng Wu, Alexey A. Soluyanov, Tomáš Bzdušek, Non-Abelian band topology in noninteracting metals. Science 365, 1273–1277 (2019)