Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
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.

  • Article
  • Published:

Comprehensive search for topological materials using symmetry indicators

Nature volume 566, pages 486–489 (2019)Cite this article

Subjects

Abstract

Over the past decade, topological materials—in which the topology of electron bands in the bulk material leads to robust, unconventional surface states and electromagnetism—have attracted much attention. Although several theoretically proposed topological materials have been experimentally confirmed, extensive experimental exploration of topological properties, as well as applications in realistic devices, has been restricted by the lack of topological materials in which interference from trivial Fermi surface states is minimized. Here we apply our method of symmetry indicators to all suitable nonmagnetic compounds in all 230 possible space groups. A database search reveals thousands of candidate topological materials, of which we highlight 241 topological insulators and 142 topological crystalline insulators that have either noticeable full bandgaps or a considerable direct gap together with small trivial Fermi pockets. Furthermore, we list 692 topological semimetals that have band crossing points located near the Fermi level. These candidate materials open up the possibility of using topological materials in next-generation electronic devices.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Band structures for strong topological insulators.
Fig. 2: Band structures for topological crystalline insulators.
Fig. 3: Band structure for a topological semimetal.

Similar content being viewed by others

Data availability

All data that support the conclusions of this work can be required from the corresponding author upon reasonable request. All the structures of the topological materials and their electronic energy band plots can be found at ccmp.nju.edu.cn.

References

  1. Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  CAS  Google Scholar 

  2. Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    Article  ADS  CAS  Google Scholar 

  3. Fu, L. Topological crystalline insulators. Phys. Rev. Lett. 106, 106802 (2011).

    Article  ADS  Google Scholar 

  4. Slager, R.-J., Mesaros, A., Juricic, V. & Zaanen, J. The space group classification of topological band-insulators. Nat. Phys. 9, 98–102 (2013).

    Article  CAS  Google Scholar 

  5. Ando, Y. & Fu, L. Topological crystalline insulators and topological superconductors: from concepts to materials. Annu. Rev. Condens. Matter Phys. 6, 361–381 (2015).

    Article  ADS  CAS  Google Scholar 

  6. Hsieh, T. H. et al. Topological crystalline insulators in the SnTe material class. Nat. Commun. 3, 982 (2012).

    Article  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators. Phys. Rev. B 96, 245115 (2017).

    Article  ADS  Google Scholar 

  11. 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 

  12. 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 

  13. Khalaf, E., Po, H. C., Vishwanath, A. & Watanabe, H. Symmetry indicators and anomalous surface states of topological crystalline insulators. Phys. Rev. X 8, 031070 (2018).

    Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  15. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  16. Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).

    Article  ADS  CAS  Google Scholar 

  17. 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 

  18. Wang, Z., Weng, H. M., 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 

  19. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  21. Huang, S.-M. et al. A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015).

    Article  CAS  Google Scholar 

  22. Burkov, A. A., Hook, M. D. & Balents, L. Topological nodal semimetals. Phys. Rev. B 84, 235126 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  25. Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438–442 (2009).

    Article  CAS  Google Scholar 

  26. Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398–402 (2009).

    Article  CAS  Google Scholar 

  27. Scanlon, D. O. et al. Controlling bulk conductivity in topological insulators: key role of anti-site defects. Adv. Mater. 24, 2154–2158 (2012).

    Article  CAS  Google Scholar 

  28. Kushwaha, S. K. et al. Sn-doped Bi1.1Sb0.9Te2S bulk crystal topological insulator with excellent properties. Nat. Commun. 7, 11456 (2016).

    Article  ADS  CAS  Google Scholar 

  29. Wang, N. et al. Microscopic origin of the p-type conductivity of the topological crystalline insulator SnTe and the effect of Pb alloying. Phys. Rev. B 89, 045142 (2014).

    Article  ADS  Google Scholar 

  30. Po, H. C., Vishwanath, A. & Watanabe, H. Symmetry-based indicators of band topology in the 230 space groups. Nat. Commun. 8, 50 (2017); erratum 8, 931 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  32. Watanabe, H., Po, H. C. & Vishwanath, A. Structure and topology of band structures in the 1651 magnetic space groups. Sci. Adv. 4, eaat8685 (2018).

    Article  ADS  Google Scholar 

  33. 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).

  34. 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).

  35. Wang, Z., Wieder, B. J., Li, J., Yan, B. & Bernevig, B. A. Higher-order topology, monopole nodal lines, and the origin of large Fermi arcs in transition metal dichalcogenides XTe2 (X=Mo,W). Preprint at https://arxiv.org/abs/1806.11116 (2018).

  36. Hellenbrandt, M. The inorganic crystal structure database (ICSD)—present and future. Crystallogr. Rev. 10, 17–22 (2004).

    Article  CAS  Google Scholar 

  37. Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951 (2006).

    Article  ADS  CAS  Google Scholar 

  38. Mravlje, J., Aichhorn, M. & Georges, A. Origin of the high Néel temperature in SrTcO3. Phys. Rev. Lett. 108, 197202 (2012).

    Article  ADS  Google Scholar 

  39. Baumberger, F. et al. Fermi surface and quasiparticle excitations of Sr2RhO4. Phys. Rev. Lett. 96, 246402 (2006).

    Article  ADS  CAS  Google Scholar 

  40. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  CAS  Google Scholar 

  41. Tran, F. & Blaha, P. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. Phys. Rev. Lett. 102, 226401 (2009).

    Article  ADS  Google Scholar 

  42. Feng, W., Xiao, D., Zhang, Y. & Yao, Y. Half-Heusler topological insulators: a first-principles study with the Tran-Blaha modified Becke-Johnson density functional. Phys. Rev. B 82, 235121 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. Fang, C., Gilbert, M. J. & Bernevig, B. A. Bulk topological invariants in noninteracting point group symmetric insulators. Phys. Rev. B 86, 115112 (2012).

    Article  ADS  Google Scholar 

  45. Song, Z., Zhang, T., Fang, Z. & Fang, C. Quantitative mappings between symmetry and topology in solids. Nat. Commun. 9, 3530 (2018).

    Article  ADS  Google Scholar 

  46. 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 

  47. Blaha, P., Schwarz, K., Madsen, G. K. H., Kvasnicka, D. & Luitz, J. WIEN2K, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Technische Univ. Wien, Austria, 2001).

    Google Scholar 

  48. Koller, D., Tran, F. & Blaha, P. Merits and limits of the modified Becke-Johnson exchange potential. Phys. Rev. B 83, 195134 (2011).

    Article  ADS  Google Scholar 

  49. Singh, D. J. Structure and optical properties of high light output halide scintillators. Phys. Rev. B 82, 155145 (2010).

    Article  ADS  Google Scholar 

  50. Oinuma, H. et al. Three-dimensional band structure of LaSb and CeSb: absence of band inversion. Phys. Rev. B 96, 041120(R) (2017).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

F.T. and X.W. were supported by the National Key R&D Program of China (grants 2017YFA0303203 and 2018YFA0305704), the National Natural Science Foundation of China (NSFC; grants 11525417, 11834006, 51721001 and 11790311) and the Excellent Programme at Nanjing University. F.T. was also supported by Program B for outstanding PhD candidates of Nanjing University. X.W. was partially supported by a QuantEmX award funded by the Gordon and Betty Moore Foundation’s Emergent Phenomena in Quantum Systems (EPIQS) Initiative through the Institute for Complex Adaptive Matter (ICAM-I2CAM; grant GBMF5305) and by ICAM. A.V. is supported by National Science Foundation (NSF) grant DMR-1411343, and by a Simons Investigator Grant. H.C.P. is supported by a Pappalardo Fellowship at MIT. We also thank G. Yao for technical support with computers and in setting up the website.

Reviewer information

Nature thanks Joseph Checkelsky and Marcel Franz for their contribution to the peer review of this work.

Author information

Authors and Affiliations

  1. National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing, China

    Feng Tang & Xiangang Wan

  2. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China

    Feng Tang & Xiangang Wan

  3. Department of Physics, Harvard University, Cambridge, MA, USA

    Hoi Chun Po & Ashvin Vishwanath

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

    Hoi Chun Po

Authors
  1. Feng Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hoi Chun Po
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ashvin Vishwanath
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiangang Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X.W., A.V. and H.C.P. conceived and designed the project. F.T. performed ab initio calculations. All authors contributed to the writing and editing of the manuscript.

Corresponding author

Correspondence to Xiangang Wan.

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 Information I-VI and References; including Tables I-VIII.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, F., Po, H.C., Vishwanath, A. et al. Comprehensive search for topological materials using symmetry indicators. Nature 566, 486–489 (2019). https://doi.org/10.1038/s41586-019-0937-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-019-0937-5

This article is cited by

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