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

QuanSheng Wu1*, Alexey A. Soluyanov2, Tomáš Bzdušek3*

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

* Corresponding authors emails: ,
DOI10.24435/materialscloud:2019.0040/v1 [version v1]

Publication date: Aug 09, 2019

How to cite this record

QuanSheng Wu, Alexey A. Soluyanov, Tomáš Bzdušek, Supplementary Data for “Non-Abelian band topology in noninteracting metals”, Materials Cloud Archive 2019.0040/v1 (2019), doi: 10.24435/materialscloud:2019.0040/v1.


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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File name Size Description
48.1 MiB This file contains necessary scripts and data to generate the figures both in the main text and the supplementary materials for paper "Non-Abelian band topology in noninteracting metals, QuanSheng Wu, Alexey A. Soluyanov, Tomáš Bzdušek" The data includes 1. The input files for VASP which is a software to do first-principle calculations. 2. The input files for Wannier90 which is an open-source software to generate the Wannier tight-binding model. 3. The input files for WannierTools which is an open-source software to analyze the topological properties of Sc. 4. Some necessary model data to generate the relevant figures.


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.

External references

Preprint (Paper where the data is discussed.)


MARVEL Topological materials VASP WannierTools Non-Abelian Band topology Wannier90 Model hamiltonian PT symmetric crystalline metals Weak spin-orbit coupling

Version history:

2019.0040/v1 (version v1) [This version] Aug 09, 2019 DOI10.24435/materialscloud:2019.0040/v1