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
Open Access articles citing this article.
Scientific Reports Open Access 28 January 2023
npj Computational Materials Open Access 29 September 2022
Communications Physics Open Access 16 September 2022
Subscribe to Nature+
Get immediate online access to Nature and 55 other Nature journal
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Fu, L. Topological crystalline insulators. Phys. Rev. Lett. 106, 106802 (2011).
Slager, R.-J., Mesaros, A., Juricic, V. & Zaanen, J. The space group classification of topological band-insulators. Nat. Phys. 9, 98–102 (2013).
Ando, Y. & Fu, L. Topological crystalline insulators and topological superconductors: from concepts to materials. Annu. Rev. Condens. Matter Phys. 6, 361–381 (2015).
Hsieh, T. H. et al. Topological crystalline insulators in the SnTe material class. Nat. Commun. 3, 982 (2012).
Wang, Z., Alexandradinata, A., Cava, R. J. & Bernevig, B. A. Hourglass fermions. Nature 532, 189–194 (2016).
Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Quantized electric multipole insulators. Science 357, 61–66 (2017).
Schindler, F. et al. Higher-order topological insulators. Sci. Adv. 4, eaat0346 (2018).
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).
Song, Z., Fang, Z. & Fang, C. (d−2)-dimensional edge states of rotation symmetry protected topological states. Phys. Rev. Lett. 119, 246402 (2017).
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).
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).
Wieder, B. J. et al. Wallpaper fermions and the nonsymmorphic Dirac insulator. Science 361, 246–251 (2018).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).
Wang, Z. et al. Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb). Phys. Rev. B 85, 195320 (2012).
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).
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).
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).
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).
Burkov, A. A., Hook, M. D. & Balents, L. Topological nodal semimetals. Phys. Rev. B 84, 235126 (2011).
Bzdušek, T., Wu, Q., Rüegg, A., Sigrist, M. & Soluyanov, A. A. Nodal-chain metals. Nature 538, 75–78 (2016).
Bradlyn, B. et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).
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).
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).
Scanlon, D. O. et al. Controlling bulk conductivity in topological insulators: key role of anti-site defects. Adv. Mater. 24, 2154–2158 (2012).
Kushwaha, S. K. et al. Sn-doped Bi1.1Sb0.9Te2S bulk crystal topological insulator with excellent properties. Nat. Commun. 7, 11456 (2016).
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).
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).
Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).
Watanabe, H., Po, H. C. & Vishwanath, A. Structure and topology of band structures in the 1651 magnetic space groups. Sci. Adv. 4, eaat8685 (2018).
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).
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).
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).
Hellenbrandt, M. The inorganic crystal structure database (ICSD)—present and future. Crystallogr. Rev. 10, 17–22 (2004).
Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951 (2006).
Mravlje, J., Aichhorn, M. & Georges, A. Origin of the high Néel temperature in SrTcO3. Phys. Rev. Lett. 108, 197202 (2012).
Baumberger, F. et al. Fermi surface and quasiparticle excitations of Sr2RhO4. Phys. Rev. Lett. 96, 246402 (2006).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Tran, F. & Blaha, P. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. Phys. Rev. Lett. 102, 226401 (2009).
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).
Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).
Fang, C., Gilbert, M. J. & Bernevig, B. A. Bulk topological invariants in noninteracting point group symmetric insulators. Phys. Rev. B 86, 115112 (2012).
Song, Z., Zhang, T., Fang, Z. & Fang, C. Quantitative mappings between symmetry and topology in solids. Nat. Commun. 9, 3530 (2018).
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).
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).
Koller, D., Tran, F. & Blaha, P. Merits and limits of the modified Becke-Johnson exchange potential. Phys. Rev. B 83, 195134 (2011).
Singh, D. J. Structure and optical properties of high light output halide scintillators. Phys. Rev. B 82, 155145 (2010).
Oinuma, H. et al. Three-dimensional band structure of LaSb and CeSb: absence of band inversion. Phys. Rev. B 96, 041120(R) (2017).
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.
Nature thanks Joseph Checkelsky and Marcel Franz for their contribution to the peer review of this work.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
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
This article is cited by
Scientific Reports (2023)
Science China Physics, Mechanics & Astronomy (2023)
Structure inversion asymmetry enhanced electronic structure and electrical transport in 2D A3SnO (A = Ca, Sr, and Ba) anti-perovskite monolayers
Nano Research (2023)
npj Computational Materials (2022)
Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
npj Quantum Materials (2022)