Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A complete catalogue of high-quality topological materials

Nature volume 566, pages 480–485 (2019)Cite this article

Subjects

An Author Correction to this article was published on 28 May 2020

This article has been updated

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Workflow diagram.
Fig. 2: Band structures of some newly identified topological compounds.

Data availability

All data is available in the Supplementary Information.

Change history

  • 28 May 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

References

  1. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    Article  ADS  CAS  Google Scholar 

  2. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    Article  ADS  CAS  Google Scholar 

  3. Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).

    Article  ADS  Google Scholar 

  4. Wang, Z., Alexandradinata, A., Cava, R. J. & Bernevig, B. A. Hourglass fermions. Nature 532, 189–194 (2016).

    Article  ADS  CAS  Google Scholar 

  5. Wieder, B. J. et al. Wallpaper fermions and the nonsymmorphic Dirac insulator. Science 361, 246–251 (2018).

    Article  ADS  CAS  Google Scholar 

  6. Wang, Z., Weng, H., Wu, Q., Dai, X. & Fang, Z. Three-dimensional Dirac semimetal and quantum transport in Cd3As2. Phys. Rev. B 88, 125427 (2013).

    Article  ADS  Google Scholar 

  7. Wang, Z. et al. Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb). Phys. Rev. B 85, 195320 (2012).

    Article  ADS  Google Scholar 

  8. Weng, H., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl semimetal phase in non- centrosymmetric transition-metal monophosphides. Phys. Rev. X 5, 011029 (2015).

    Google Scholar 

  9. Huang, S.-M. et al. An inversion breaking Weyl semimetal state in the TaAs material class. Nat. Commun. 6, 7373 (2015).

    Article  ADS  CAS  Google Scholar 

  10. Lv, B. Q. et al. Experimental discovery of weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).

    Google Scholar 

  11. Xu, S.-Y. et al. Discovery of a weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).

    Article  ADS  CAS  Google Scholar 

  12. Bzdušek, T., Wu, Q., Rüegg, A., Sigrist, M. & Soluyanov, A. Nodal-chain metals. Nature 538, 75–78 (2016).

    Article  ADS  Google Scholar 

  13. Bradlyn, B. et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).

    Article  MathSciNet  Google Scholar 

  14. Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).

    Article  ADS  CAS  Google Scholar 

  15. Cano, J. et al. Topology of disconnected elementary band representations. Phys. Rev. Lett. 120, 266401 (2018).

    Article  ADS  CAS  Google Scholar 

  16. Elcoro, L. et al. Double crystallographic groups and their representations on the Bilbao Crystallographic Server. J. Appl. Crystallogr. 50, 457–1477 (2017).

    Article  Google Scholar 

  17. Vergniory, M. G. et al. Graph theory data for topological quantum chemistry. Phys. Rev. E 96, 023310 (2017).

    Article  ADS  CAS  Google Scholar 

  18. Bradlyn, B. et al. Band connectivity for topological quantum chemistry: band structures as a graph theory problem. Phys. Rev. B 97, 035138 (2018).

    Article  ADS  CAS  Google Scholar 

  19. Band representations of the double space group (BANDREP). Bilbao Crystallographic Server www.cryst.ehu.es/cryst/bandrep.

  20. Compatibility relations between representations of the double space groups (DCOMPREL). Bilbao Crystallographic Server www.cryst.ehu.es/cryst/dcomprel.

  21. Kruthoff, J., de Boer, J., van Wezel, J., Kane, C. L. & Slager, R.-J. Topological classification of crystalline insulators through band structure combinatorics. Phys. Rev. X 7, 041069 (2017).

    Google Scholar 

  22. Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Quantized electric multipole insulators. Science 357, 61–66 (2017).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  23. Schindler, F. et al. Higher-order topological insulators. Sci. Adv. 4, eaat0346 (2018).

    Article  ADS  Google Scholar 

  24. Song, Z., Fang, Z. & Fang, C. (d−2)-dimensional edge states of rotation symmetry protected topological states. Phys. Rev. Lett. 119, 246402 (2017).

    Article  ADS  Google Scholar 

  25. Langbehn, J., Peng, Y., Trifunovic, L., von Oppen, F. & Brouwer, P. W. Reflection-symmetric second-order topological insulators and superconductors. Phys. Rev. Lett. 119, 246401 (2017).

    Article  ADS  Google Scholar 

  26. Schindler, F. et al. Higher-order topology in bismuth. Nat. Phys. 14, 918–924 (2018); correction 14, 1067 (2018).

    Article  CAS  Google Scholar 

  27. Po, H. C., Watanabe, H. & Vishwanath, A. Fragile topology and wannier obstructions. Phys. Rev. Lett. 121, 126402 (2017).

    Article  ADS  Google Scholar 

  28. Bouhon, A., Black-Schaffer, A. M. & Slager, R.-J. Wilson loop approach to topological crystalline insulators with time reversal symmetry. Preprint at https://arxiv.org/abs/1804.09719 (2018).

  29. Song, Z. et al. All “magic angles” are “stable” topological. Preprint at https://arxiv.org/abs/1807.10676 (2018).

  30. Bradlyn, B., Wang, Z., Cano, J. & Bernevig, B. A. Disconnected elementary band representations, fragile topology, and Wilson loops as topological indices. Phys. Rev. B 99, 045140 (2019).

    Article  ADS  CAS  Google Scholar 

  31. Song, Z., Zhang, T., Fang, Z. & Fang, C. Quantitative mappings between symmetry and topology in solids. Nat. Commun. 8, 3530 (2018).

    Article  ADS  Google Scholar 

  32. Song, Z., Zhang, T. & Fang, C. Diagnosis for nonmagnetic topological semimetals in the absence of spin-orbital coupling. Phys. Rev. X 8, 031069 (2018).

    CAS  Google Scholar 

  33. Po, H. C., Vishwanath, A. & Watanabe, H. Symmetry-based indicators of band topology in the 230 space groups. Nat. Commun. 8, 50 (2017).

    Article  ADS  Google Scholar 

  34. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

    Article  ADS  CAS  Google Scholar 

  35. Check Topological Mat. Bilbao Crystallographic Server www.cryst.ehu.es/cryst/checktopologicalmat.

  36. Xu, Q., Yu, R., Fang, Z., Dai, X. & Weng, H. Topological nodal line semimetals in the CaP3 family of materials. Phys. Rev. B 95, 045136 (2017).

  37. Fang, C. & Fu, L. Rotation anomaly and topological crystalline insulators. Preprint at https://arxiv.org/abs/1709.01929 (2017).

  38. Zhou, X. et al. Topological crystalline insulator states in the Ca2As family. Phys. Rev. B 98, 241104(R) (2018).

    Article  ADS  Google Scholar 

  39. Tang, F., Po, H. C., Vishwanath, A. & Wan, X. Efficient topological materials discovery using symmetry indicators. Preprint at https://arxiv.org/abs/1805.07314 (2018).

  40. Tang, F., Po, H. C., Vishwanath, A. & Wan, X. Topological materials discovery by large-order symmetry indicators. Preprint at https://arxiv.org/abs/1806.04128 (2018).

Download references

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 and ab initio calculations from the Department of Energy (de-sc0016239). B.A.B. and Z.W. acknowledge additional support from 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

Author notes

  1. These authors contributed equally: M. G. Vergniory, L. Elcoro

Authors and Affiliations

  1. Donostia International Physics Center, San Sebastian, Spain

    M. G. Vergniory

  2. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    M. G. Vergniory

  3. Applied Physics Department II, University of the Basque Country UPV/EHU, Bilbao, Spain

    M. G. Vergniory

  4. Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Bilbao, Spain

    L. Elcoro

  5. Max Planck Institute for Chemical Physics of Solids, Dresden, Germany

    Claudia Felser

  6. Laboratoire de Physique de l’École Normale Supérieure, PSL University, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France

    Nicolas Regnault

  7. Department of Physics, Princeton University, Princeton, NJ, USA

    B. Andrei Bernevig & Zhijun Wang

  8. Physics Department, Freie Universität Berlin, Berlin, Germany

    B. Andrei Bernevig

  9. Max Planck Institute of Microstructure Physics, Halle, Germany

    B. Andrei Bernevig

  10. Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing, China

    Zhijun Wang

Authors
  1. M. G. Vergniory
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Elcoro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Claudia Felser
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nicolas Regnault
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. Andrei Bernevig
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhijun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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

Corresponding authors

Correspondence to B. Andrei Bernevig or Zhijun Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-019-0954-4

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing