Comprehensive search for topological materials using symmetry indicators


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.

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

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


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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.

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

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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.

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Correspondence to Xiangang Wan.

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Tang, F., Po, H.C., Vishwanath, A. et al. Comprehensive search for topological materials using symmetry indicators. Nature 566, 486–489 (2019).

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