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Topological materials discovery from crystal symmetry

Nature Reviews Materials volume 7, pages 196–216 (2022)Cite this article

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Abstract

Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline insulators (TCIs) and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures — including the theory of topological quantum chemistry (TQC) — researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent application of TQC and related methods to high-throughput materials discovery has revealed that over half of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85 per cent of the known stoichiometric materials host energetically isolated topological bands, and just under two-thirds of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. In this Review, we survey topological electronic materials discovery in nonmagnetic crystalline solids from the prediction of the first 2D and 3D TIs to the recently introduced methods that have facilitated large-scale searches for topological materials. We also discuss future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices.

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Fig. 1: Wannier centres and Wilson loops.
Fig. 2: Experimentally verified topological response effects in topological materials.
Fig. 3: The twofold Dirac-cone surface states of 3D topological insulators.
Fig. 4: 3D topological crystalline insulators.
Fig. 5: Chiral topological semimetal phases in structurally chiral crystals.
Fig. 6: Higher-order topological crystalline insulators.
Fig. 7: Representative materials with novel topological properties identified in the Topological Materials Database.

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Acknowledgements

This Review is dedicated to A. A. Soluyanov, who passed away during its preparation. B.J.W., N.R. and B.A.B. were supported by the Department of Energy (grant no. DE-SC0016239), the NSF EAGER (grant no. DMR 1643312), the NSF-MRSEC (grant no. DMR-142051), a Simons Investigator grant (grant no. 404513), the ONR (grant no. N00014-20-1-2303), the Packard Foundation, the Schmidt Fund for Innovative Research, the BSF Israel US Foundation (grant no. 2018226), the Gordon and Betty Moore Foundation (through grant no. GBMF8685 towards the Princeton theory programme), and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. B.B. acknowledges the support of the Alfred P. Sloan Foundation and the National Science Foundation (grant no. DMR-1945058). J.C. acknowledges support from the National Science Foundation (grant no. DMR 1942447) and the Flatiron Institute, a division of the Simons Foundation. Z.W. was supported by the National Natural Science Foundation of China (grant no. 11974395), the Strategic Priority Research Program of the Chinese Academy of Sciences (CAS) (grant no. XDB33000000), and the Center for Materials Genome. M.G.V. acknowledges support from the DFG (grant no. INCIEN2019-000356), from Gipuzkoako Foru Aldundia and the Spanish Ministerio de Ciencia e Innovacion (grant no. PID2019-109905GB-C21). L.E. was supported by the Government of the Basque Country (project IT1301-19) and the Spanish Ministry of Science and Innovation (grant no. PID2019-106644GB-I00). C.F. was supported by the ERC (advanced grant nos. 291472 ‘Idea Heusler’ and 742068 ‘TOPMAT’). T.N. acknowledges support from the European Union’s Horizon 2020 Research and Innovation Program (grant no. ERC-StG-Neupert-757867-PARATOP). A.A.S. and T.N. additionally acknowledge support from the Swiss National Science Foundation (grant no. PP00P2_176877). L.E., N.R. and B.A.B. acknowledge additional support through the ERC Advanced Grant Superflat, and B.A.B. received additional support from the European Union’s Horizon 2020 Research and Innovation Program (grant no. 101020833) and the Max Planck Society.

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Author notes

  1. Deceased: A. A. Soluyanov.

Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Benjamin J. Wieder

  2. Department of Physics, Northeastern University, Boston, MA, USA

    Benjamin J. Wieder

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

    Benjamin J. Wieder, Nicolas Regnault & B. Andrei Bernevig

  4. Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Barry Bradlyn

  5. Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA

    Jennifer Cano

  6. Center for Computational Quantum Physics, The Flatiron Institute, New York, NY, USA

    Jennifer Cano

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

    Zhijun Wang

  8. University of Chinese Academy of Sciences, Beijing, China

    Zhijun Wang

  9. Donostia International Physics Center, Donostia/San Sebastian, Spain

    Maia G. Vergniory & B. Andrei Bernevig

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

    Maia G. Vergniory & B. Andrei Bernevig

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

    Maia G. Vergniory & Claudia Felser

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

    Luis Elcoro

  13. Department of Physics, University of Zurich, Zurich, Switzerland

    Alexey A. Soluyanov & Titus Neupert

  14. Department of Physics, St Petersburg State University, St Petersburg, Russia

    Alexey A. Soluyanov

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

    Nicolas Regnault

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  1. Benjamin J. Wieder
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Contributions

This Review was written and edited by B.J.W. All authors contributed to researching data for this article and to the preparation of the manuscript.

Corresponding authors

Correspondence to Benjamin J. Wieder or B. Andrei Bernevig.

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ICSD 14349: https://www.topologicalquantumchemistry.com/#/detail/14349

ICSD 15569: https://www.topologicalquantumchemistry.com/#/detail/15569

ICSD 15571: https://www.topologicalquantumchemistry.com/#/detail/15571

ICSD 16585: https://www.topologicalquantumchemistry.com/#/detail/16585

ICSD 23062: https://www.topologicalquantumchemistry.com/#/detail/23062

ICSD 24145: https://www.topologicalquantumchemistry.com/#/detail/24145

ICSD 26881: https://www.topologicalquantumchemistry.com/#/detail/26881

ICSD 35190: https://www.topologicalquantumchemistry.com/#/detail/35190

ICSD 39597: https://www.topologicalquantumchemistry.com/#/detail/39597

ICSD 42545: https://www.topologicalquantumchemistry.com/#/detail/42545

ICSD 52115: https://www.topologicalquantumchemistry.com/#/detail/52115

ICSD 54609: https://www.topologicalquantumchemistry.com/#/detail/54609

ICSD 56201: https://www.topologicalquantumchemistry.com/#/detail/56201

ICSD 56390: https://www.topologicalquantumchemistry.com/#/detail/56390

ICSD 58396: https://www.topologicalquantumchemistry.com/#/detail/58396

ICSD 58786: https://www.topologicalquantumchemistry.com/#/detail/58786

ICSD 61352: https://www.topologicalquantumchemistry.com/#/detail/61352

ICSD 62305: https://www.topologicalquantumchemistry.com/#/detail/62305

ICSD 64703: https://www.topologicalquantumchemistry.com/#/detail/64703

ICSD 74704: https://www.topologicalquantumchemistry.com/#/detail/74704

ICSD 76455: https://www.topologicalquantumchemistry.com/#/detail/76455

ICSD 76139: https://www.topologicalquantumchemistry.com/#/detail/76139

ICSD 77109: https://www.topologicalquantumchemistry.com/#/detail/77109

ICSD 79233: https://www.topologicalquantumchemistry.com/#/detail/79233

ICSD 81218: https://www.topologicalquantumchemistry.com/#/detail/81218

ICSD 81493: https://www.topologicalquantumchemistry.com/#/detail/81493

ICSD 82092: https://www.topologicalquantumchemistry.com/#/detail/82092

ICSD 85507: https://www.topologicalquantumchemistry.com/#/detail/85507

ICSD 105699: https://www.topologicalquantumchemistry.com/#/detail/105699

ICSD 150530: https://www.topologicalquantumchemistry.com/#/detail/150530

ICSD 151748: https://www.topologicalquantumchemistry.com/#/detail/151748

ICSD 166865: https://www.topologicalquantumchemistry.com/#/detail/166865

ICSD 167811: https://www.topologicalquantumchemistry.com/#/detail/167811

ICSD 185808: https://www.topologicalquantumchemistry.com/#/detail/185808

ICSD 187534: https://www.topologicalquantumchemistry.com/#/detail/187534

ICSD 193346: https://www.topologicalquantumchemistry.com/#/detail/193346

ICSD 260148: https://www.topologicalquantumchemistry.com/#/detail/260148

ICSD 260982: https://www.topologicalquantumchemistry.com/#/detail/260982

ICSD 261111: https://www.topologicalquantumchemistry.com/#/detail/261111

ICSD 425966: https://www.topologicalquantumchemistry.com/#/detail/425966

ICSD 426972: https://www.topologicalquantumchemistry.com/#/detail/426972

ICSD 601065: https://www.topologicalquantumchemistry.com/#/detail/601065

ICSD 601659: https://www.topologicalquantumchemistry.com/#/detail/601659

ICSD 602710: https://www.topologicalquantumchemistry.com/#/detail/602710

ICSD 609930: https://www.topologicalquantumchemistry.com/#/detail/609930

ICSD 611451: https://www.topologicalquantumchemistry.com/#/detail/611451

ICSD 615755: https://www.topologicalquantumchemistry.com/#/detail/615755

ICSD 616956: https://www.topologicalquantumchemistry.com/#/detail/616956

ICSD 617192: https://www.topologicalquantumchemistry.com/#/detail/617192

ICSD 626175: https://www.topologicalquantumchemistry.com/#/detail/626175

ICSD 635132: https://www.topologicalquantumchemistry.com/#/detail/635132

ICSD 644091: https://www.topologicalquantumchemistry.com/#/detail/644091

ICSD 649753: https://www.topologicalquantumchemistry.com/#/detail/649753

ICSD 648185: https://www.topologicalquantumchemistry.com/#/detail/648185

ICSD 648570: https://www.topologicalquantumchemistry.com/#/detail/648570

ICSD 648585: https://www.topologicalquantumchemistry.com/#/detail/648585

ICSD 648588: https://www.topologicalquantumchemistry.com/#/detail/648588

ICSD 650381: https://www.topologicalquantumchemistry.com/#/detail/650381

ICSD 672362: https://www.topologicalquantumchemistry.com/#/detail/672362

ICSD 672345: https://www.topologicalquantumchemistry.com/#/detail/672345

ICSD 672522: https://www.topologicalquantumchemistry.com/#/detail/672522

Inorganic Crystal Structure Database (ICSD): https://icsd.products.fiz-karlsruhe.de/

Materials Project: https://materialsproject.org/

REPRESENTATIONS DSG: http://www.cryst.ehu.es/cgi-bin/cryst/programs/representations.pl?tipogrupo=dbg

Topological Materials Arsenal: https://ccmp.nju.edu.cn/

Topological Materials Database: https://www.topologicalquantumchemistry.com/

VASP2Trace: https://github.com/zjwang11/irvsp

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Wieder, B.J., Bradlyn, B., Cano, J. et al. Topological materials discovery from crystal symmetry. Nat Rev Mater 7, 196–216 (2022). https://doi.org/10.1038/s41578-021-00380-2

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