# A complete catalogue of high-quality topological materials

## Abstract

Using a recently developed formalism called topological quantum chemistry, we perform a high-throughput search of ‘high-quality’ materials (for which the atomic positions and structure have been measured very accurately) in the Inorganic Crystal Structure Database in order to identify new topological phases. We develop codes to compute all characters of all symmetries of 26,938 stoichiometric materials, and find 3,307 topological insulators, 4,078 topological semimetals and no fragile phases. For these 7,385 materials we provide the electronic band structure, including some electronic properties (bandgap and number of electrons), symmetry indicators, and other topological information. Our results show that more than 27 per cent of all materials in nature are topological. We provide an open-source code that checks the topology of any material and allows other researchers to reproduce our results.

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## Data availability

All data is available in the Supplementary Information.

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## Acknowledgements

We thank B. Bradlyn, J. Cano and M. Aroyo for countless discussions and collaborations, and for their help with the development of the BANDREP section of the BCS, without which none of the present work would have been possible. We thank H. Gross, S. Parkin, U. Schmidt, M. Rampp and the computational resources of the Max Planck Institute at Halle and Garching, as well as the staff at the Atlas supercomputer of the Donostia International Physics Center. We are grateful to H. Lederer and I. Weidl for allowing us access to the Cobra Supercomputer at the Max Planck Gesellschaft (MPG) computing centre. We also thank H. Borrmann of the Max Planck Institute in Dresden for help with the ICSD database. L.E. was supported by the Government of the Basque Country (project IT779-13), the Spanish Ministry of Economy and Competitiveness (MINECO), and the European Fund for Economic and Regional Development (FEDER; project MAT2015-66441-P). M.G.V. was supported by national project IS2016-75862-P of the Spanish MINECO. B.A.B. and Z.W. acknowledge support for the analytical work from the Department of Energy (de-sc0016239), a Simons Investigator Award, the Packard Foundation, and the Schmidt Fund for Innovative Research. Z.W. was also supported by the CAS Pioneer Hundred Talents Program. The computational part of the Princeton work was performed under National Science Foundation (NSF) Early-concept Grants for Exploratory Research (EAGER): DMR 1643312 NOA-AWD1004957, ONR-N00014-14-1-0330, ARO MURI W911NF-12-1-0461, NSF-MRSECDMR-1420541.

### Reviewer information

Nature thanks Joseph Checkelsky, Marcel Franz and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

All authors contributed to performing the calculations and analysing the results.

Correspondence to B. Andrei Bernevig or Zhijun Wang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

This file contains Supplementary Text A–U; which includes Supplementary Tables and Figures.

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Vergniory, M.G., Elcoro, L., Felser, C. et al. A complete catalogue of high-quality topological materials. Nature 566, 480–485 (2019). https://doi.org/10.1038/s41586-019-0954-4

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