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Efficient topological materials discovery using symmetry indicators

Nature Physics volume 15, pages 470–476 (2019)Cite this article

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Abstract

Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty in ascertaining band topology in realistic calculations. Here, we integrate the recently established theory of symmetry indicators of band topology into first-principles band-structure calculations, and test it on a database of previously synthesized crystals. On applying our algorithm to just 8 out of the 230 space groups, we are able to efficiently unearth topological materials and predict a diversity of topological phenomena, including: a screw-protected three-dimensional TC insulator, β-MoTe2, with gapped surfaces except for one-dimensional helical hinge states; a rotation-protected TC insulator, BiBr, with coexisting surface Dirac cones and hinge states; non-centrosymmetric \({\Bbb Z}_2\) topological insulators undetectable using the well-established parity criterion, AgXO (X = Na, K, Rb); a Dirac semimetal MgBi2O6; a Dirac nodal-line semimetal AgF2; and a metal with three-fold degenerate band crossing near the Fermi energy, AuLiMgSn. Our work showcases how recent theoretical insights into the fundamentals of band structures can aid in the practical goal of discovering new topological materials.

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Fig. 1: Topological materials discovery algorithm.
Fig. 2: Relations of TI/TCI to \({\Bbb Z}_4\) SI group and numerical results of MoTe2.
Fig. 3: Numerical results of BiBr.
Fig. 4: Electronic structure of the non-centrosymmetric strong TI AgNaO.
Fig. 5: Electronic structure of Dirac semimetal MgBi2O6.
Fig. 6: Statistics of topological materials.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

H.C.P. and A.V. thank E. Khalaf and H. Watanabe for earlier collaborations on related topics. F.T. and X.W. were supported by National Key R&D Program of China (Nos. 2018YFA0305704 and 2017YFA0303203), the NSFC (Nos. 11525417, 11834006, 51721001 and 11790311) and the excellent programme in Nanjing University. F.T. was also supported by the program B for Outstanding PhD candidate of Nanjing University. X.W. was partially supported by a QuantEmX award funded by the Gordon and Betty Moore Foundation’s EPIQS Initiative through ICAM-I2CAM, Grant GBMF5305 and by the Institute of Complex Adaptive Matter (ICAM). A.V. is supported by NSF DMR-1411343, a Simons Investigator Grant, and by the ARO MURI on topological insulators, grant W911NF- 12-1-0961. H.C.P. is supported by a Pappalardo Fellowship at MIT.

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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

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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. Efficient topological materials discovery using symmetry indicators. Nat. Phys. 15, 470–476 (2019). https://doi.org/10.1038/s41567-019-0418-7

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