Abstract
Nodal semimetals are classes of topological materials that have nodal-point or nodal-line Fermi surfaces, which give them novel transport and topological properties. Despite being highly sought after, there are currently very few experimental realizations, and identifying new materials candidates has mainly relied on exhaustive database searches. Here we show how recent studies on the interplay between electron filling and nonsymmorphic space-group symmetries can guide the search for filling-enforced nodal semimetals. We recast the previously derived constraints on the allowed band-insulator fillings in any space group into a new form, which enables effective screening of materials candidates based solely on their space group, electron count in the formula unit, and multiplicity of the formula unit. This criterion greatly reduces the computation load for discovering topological materials in a database of previously synthesized compounds. As a demonstration, we focus on a few selected nonsymmorphic space groups which are predicted to host filling-enforced Dirac semimetals. Of the more than 30,000 entires listed, our filling criterion alone eliminates 96% of the entries before they are passed on for further analysis. We discover a handful of candidates from this guided search; among them, the monoclinic crystal Ca2Pt2Ga is particularly promising.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
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).
Burkov, A. A., Hook, M. D. & Balents, L. Topological nodal semimetals. Phys. Rev. B 84, 235126 (2011).
Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).
Steinberg, J. A. et al. Bulk Dirac points in distorted spinels. Phys. Rev. Lett. 112, 036403 (2014).
Chen, Y., Lu, Y.-M. & Kee, H.-Y. Topological crystalline metal in orthorhombic perovskite iridates. Nat. Commun. 6, 6593 (2015).
Fang, C., Chen, Y., Kee, H.-Y. & Fu, L. Topological nodal line semimetals with and without spin-orbital coupling. Phys. Rev. B 92, 081201 (2015).
Wieder, B. J., Kim, Y., Rappe, A. M. & Kane, C. L. Double Dirac semimetals in three dimensions. Phys. Rev. Lett. 116, 186402 (2016).
Fang, C., Lu, L., Liu, J. & Fu, L. Topological semimetals with helicoid surface states. Nat. Phys. 12, 936–941 (2016).
Bzdušek, T., Wu, Q., Rüegg, A., Sigrist, M. & Soluyanov, A. A. Nodal-chain metals. Nature 538, 75–78 (2016).
Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).
Bradlyn, B. et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).
Lim, L.-K. & Moessner, R. Pseudospin vortex ring with a nodal line in three dimensions. Phys. Rev. Lett. 118, 016401 (2017).
Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2 . Nat. Mater. 14, 280–284 (2015).
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).
Huang, X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015).
Moll, P. J. W. et al. Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2 . Nature 535, 266–270 (2016).
Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2017).
Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014).
Neupane, M. et al. Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2 . Nat. Commun. 5, 3786 (2014).
Jeon, S. et al. Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2 . Nat. Mater. 13, 851–856 (2014).
Liu, Z. K. et al. A stable three-dimensional topological Dirac semimetal Cd3As2 . Nat. Mater. 13, 677–681 (2014).
Yang, B.-J. & Nagaosa, N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 5, 4898 (2014).
König, A. & Mermin, N. D. Electronic level degeneracy in nonsymmorphic periodic or aperiodic crystals. Phys. Rev. B 56, 13607–13610 (1997).
Parameswaran, S. A., Turner, A. M., Arovas, D. P. & Vishwanath, A. Topological order and absence of band insulators at integer filling in non-symmorphic crystals. Nat. Phys. 9, 299–303 (2013).
Chen, Y., Kim, H.-S. & Kee, H.-Y. Topological crystalline semimetals in nonsymmorphic lattices. Phys. Rev. B 93, 155140 (2016).
Liang, Q-F., Zhou, J., Yu, R., Wang, Z. & Weng, H. Node-surface and node-line fermions from nonsymmorphic lattice symmetries. Phys. Rev. B 93, 085427 (2016).
Parameswaran, S. A. Topological ‘Luttinger’ invariants protected by non-symmorphic symmetry in semimetals. Preprint at http://arXiv.org/abs/1508.01546 (2015).
Gibson, Q. D. et al. Three-dimensional Dirac semimetals: design principles and predictions of new materials. Phys. Rev. B 91, 205128 (2015).
Watanabe, H., Po, H. C., Vishwanath, A. & Zaletel, M. P. Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals. Proc. Natl Acad. Sci. USA 112, 14551–14556 (2015).
Watanabe, H., Po, H. C., Zaletel, M. P. & Vishwanath, A. Filling-enforced gaplessness in band structures of the 230 space groups. Phys. Rev. Lett. 117, 096404 (2016).
Hellenbrandt, M. The inorganic crystal structure database (ICSD)—present and future. Crystallogr. Rev. 10, 17–22 (2004).
Zaheer, S. Three Dimension Dirac Semimetals PhD dissertation, Univ. Pennsylvania (2014); http://repository.upenn.edu/edissertations/1514
Ponou, S. & Miller, G. J. Synergistic geometrical and electronic features in the intermetallic phases Ca2AgM2, Ca2MgM2, and Ca2GaM2 (M = Pd, Pt). Z. Anorg. Allg. Chem. 641, 1069–1079 (2015).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three dimensional solids. Preprint at http://arXiv.org/abs/1705.01111 (2017).
Kargarian, M., Randeria, M. & Lu, Y.-M. Are the surface Fermi arcs in Dirac semimetals topologically protected? Proc. Natl Acad. Sci. USA 113, 8648–8652 (2016).
Wang, Z., Weng, H., Wu, Q., Dai, X. & Fang, Z. Three-dimensional Dirac semimetal and quantum transport in Cd3As2 . Phys. Rev. B 88, 125427 (2013).
Hahn, T. (ed.) International Tables for Crystallography Vol. A: Space-group Symmetry 5th edn (Springer, 2006).
Po, H. C., Watanabe, H., Zaletel, M. & Vishwanath, A. Filling-enforced quantum band insulators in spin-orbit coupled crystals. Sci. Adv. 2, e1501782 (2016).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).
Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).
Feng, H. L., Sathish, C. I., Li, J., Wang, X. & Yamaura, K. Synthesis, structure, and magnetic properties of a new double perovskite Ca2InOsO6 . Phys. Procedia 45, 117–120 (2013).
Watanabe, H., Po, H. C. & Vishwanath, A. Structure and topology of band structures in the 1651 magnetic space groups. Preprint at http://arXiv.org/abs/1707.01903 (2017).
Bradley, C. J. & Cracknell, A. P. The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Oxford Univ. Press, 1972).
Dascoulidou-Gritner, K. & Schuster, H.-U. Darstellung und Kristallstrukturen der Verbindungen CaPtGa, CaPtIn und CaPd0,4Ga1,6 . Z. Anorg. Allg. Chem. 620, 1151–1156 (1994).
Topological insulators. in Contemporary Concepts of Condensed Matter Science Vol. 6 (eds Franz, M. & Molenkamp, L.) (Elsevier, 2013).
Kushwaha, S. K. et al. Sn-doped Bi1.1Sb0.9Te2S bulk crystal topological insulator with excellent properties. Nat. Commun. 7, 11456 (2016).
Momma, K. & Izumi, F. VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).
Acknowledgements
We thank H. Watanabe and M. P. Zaletel for collaboration on earlier works and helpful comments on the manuscript. We also thank T. Smidt for helpful discussions. R.C. and J.B.N. were supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under DOE Contract no. DE-AC02-05CH11231. Portions of the high-throughput workflow development were additionally supported by the Materials Project (Grant no. EDCBEE) through the US Department of Energy (DOE), Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-05CH11231. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy, and Laboratory Directed Research and Development Program at the Lawrence Berkeley National Laboratory, under Contract no. DE-AC02-05CH11231. A.V. and H.C.P. were supported by NSF DMR-141134 and ARO MURI Program W911NF-12-1-0461. We also thank NERSC for computational resources. A.V. and R.C. were also partly funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract no. DE-AC02-05-CH11231 (Quantum Materials program KC2202).
Author information
Authors and Affiliations
Contributions
R.C. and H.C.P. performed the calculations and analysis, and contributed equally to this work. J.B.N. and A.V. supervised the project.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 434 kb)
Rights and permissions
About this article
Cite this article
Chen, R., Po, H., Neaton, J. et al. Topological materials discovery using electron filling constraints. Nature Phys 14, 55–61 (2018). https://doi.org/10.1038/nphys4277
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphys4277
This article is cited by
-
An automatically curated first-principles database of ferroelectrics
Scientific Data (2020)
-
Symmetry-protected metallic and topological phases in penta-materials
Scientific Reports (2019)
-
Effective models for nearly ideal Dirac semimetals
Frontiers of Physics (2019)
-
Topological quantum properties of chiral crystals
Nature Materials (2018)