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Catalogue of topological electronic materials

Abstract

Topological electronic materials such as bismuth selenide, tantalum arsenide and sodium bismuthide show unconventional linear response in the bulk, as well as anomalous gapless states at their boundaries. They are of both fundamental and applied interest, with the potential for use in high-performance electronics and quantum computing. But their detection has so far been hindered by the difficulty of calculating topological invariant properties (or topological nodes), which requires both experience with materials and expertise with advanced theoretical tools. Here we introduce an effective, efficient and fully automated algorithm that diagnoses the nontrivial band topology in a large fraction of nonmagnetic materials. Our algorithm is based on recently developed exhaustive mappings between the symmetry representations of occupied bands and topological invariants. We sweep through a total of 39,519 materials available in a crystal database, and find that as many as 8,056 of them are topologically nontrivial. All results are available and searchable in a database with an interactive user interface.

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Fig. 1: Flow chart for our automatic diagnostic algorithm.
Fig. 2: Definition of valence bands and conduction bands.
Fig. 3: The five candidates for the five classes of topological material.

Data availability

All results are available and searchable with an interactive user interface at http://materiae.iphy.ac.cn. Codes for obtaining the irreducible representations are available from the corresponding author upon reasonable request.

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Acknowledgements

We are grateful for suggestions and comments from M. Liu, B. Bradlyn, H. Watanabe and B. Wieder. We acknowledge support from the Ministry of Science and Technology of China under grant numbers 2016YFA0302400, 2016YFA0300600 and 2018YFA0305700; the National Science Foundation of China under grant numbers 11674370, 11421092 and 11674369; and the Chinese Academy of Sciences under grant numbers XXH13506-202, XDB07020100 and XDB28000000. We also acknowledge support from the Science Challenge Project (number TZ2016004), the K. C. Wong Education Foundation (GJTD-2018-01), the Beijing Municipal Science and Technology Commission (Z181100004218001) and the Beijing Natural Science Foundation (Z180008).

Reviewer information

Nature thanks J. Checkelsky, M. Franz and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Affiliations

Authors

Contributions

C.F. conceived the work; H.W. and Z.F. were in charge of the numerical methods and checked for consistency with previous works; T.Z. did the major part of the calculations and analyses of materials; Y.J., Z.S., H.H. and Y.H. wrote the code for analysing irreducible representations and symmetry-based indicators; H.H. and Y.H. built the website. C.F., H.W. and Z.F. wrote the main text; and T.Z., Y.J. and Z.S wrote the Methods section and the Supplementary Information.

Corresponding authors

Correspondence to Hongming Weng or Chen Fang.

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Extended data figures and tables

Extended Data Fig. 1 Nodal-ring configuration in BaC20 (nsoc setting).

This material is in space group \({\rm{Pm}}\bar{{\rm{3n}}}\). a, The three equivalent nodal rings in the \({{\boldsymbol{k}}}_{i}=0\left(i=x,y,z\right)\) planes, protected by the mirror symmetries on these planes. b, The six equivalent nodal rings in the \({{\boldsymbol{k}}}_{i}\pm {{\boldsymbol{k}}}_{j}=0\left(i,j=x,y,z,\hspace{2.77626pt}i\ne j\right)\) planes, protected by the glide symmetries on these planes.

Extended Data Fig. 2 Topological invariants and surface states of Zr(TiH2)2.

a, Brillouin zone for Zr(TiH2)2, in which the yellow plane is \({m}_{1\bar{1}0}\). b, Wilson loop for Zr(TiH2)2 in the \({m}_{1\bar{1}0}\) plane. c, One-dimensional helical modes in a cubic Zr(TiH2)2 sample. d, Two-dimensional surface states on each surface of a cubic Zr(TiH2)2 sample.

Extended Data Table 1 Possible invariants for space group 227

Supplementary information

Supplementary Tables

This file contains five tables. These are the lists of all topological materials theoretically discovered in this work. The materials are sorted into the five classes of “high-symmetry-point semimetals”, “high-symmetry-line semimetals”, “generic-momenta semimetals”, “topological insulators” and “topological crystalline insulators” in Tables I, II, III, IV and V, respectively.

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Zhang, T., Jiang, Y., Song, Z. et al. Catalogue of topological electronic materials. Nature 566, 475–479 (2019). https://doi.org/10.1038/s41586-019-0944-6

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