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Catalogue of flat-band stoichiometric materials

An Author Correction to this article was published on 08 July 2022

This article has been updated


Topological electronic flattened bands near or at the Fermi level are a promising route towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to engineered materials, such as moiré systems1,2,3. Here we present a catalogue of the naturally occuring three-dimensional stoichiometric materials with flat bands around the Fermi level. We consider 55,206 materials from the Inorganic Crystal Structure Database catalogued using the Topological Quantum Chemistry website4,5, which provides their structural parameters, space group, band structure, density of states and topological characterization. We combine several direct signatures and properties of band flatness with a high-throughput analysis of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices—in either two or three dimensions—that probably lead to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theoretical and experimental studies. We use the database to extract a curated list of 2,379 high-quality flat-band materials, from which we identify 345 promising candidates that potentially host flat bands with charge centres that are not strongly localized on the atomic sites. We showcase five representative materials and provide a theoretical explanation for the origin of their flat bands close to the Fermi energy using the S-matrix method introduced in a parallel work6.

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Fig. 1: An illustration of the three possible types of flat band.
Fig. 2: Crystal and band structures of the representative flat-band materials.

Data availability

All data are available in the Supplementary Information and through our public website, the Materials Flatband Database (

Change history


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We thank X. Dai, D. Calugaru, A. Chew, M. Vergniory and C. Chiu for discussions. We acknowledge the computational resources Cobra/Draco in the Max Planck Computing and Data Facility (MPCDF) and Atlas in the Donostia International Physics Center (DIPC). This research also used the resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility operated under contract number DE-AC02-05CH11231. This work is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 101020833). B.A.B. and N.R. were also supported by the US Department of Energy (grant number DE-SC0016239), and were partially supported by the National Science Foundation (EAGER grant number DMR 1643312), a Simons Investigator grant (number 404513), the Office of Naval Research (ONR grant number N00014-20-1-2303), the Packard Foundation, the Schmidt Fund for Innovative Research, the BSF Israel US foundation (grant number 2018226), the Gordon and Betty Moore Foundation through grant number GBMF8685 towards the Princeton theory programme, and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. A.Y., N.P.O., R.J.C., L.M.S., B.A.B. and N.R. were supported by the NSF-MRSEC (grant number DMR-2011750). A.Y. was supported by NSF-DMR-1904442. B.A.B., L.M.S. and N.R. acknowledge financial support from the Schmidt DataX Fund at Princeton University made possible through a major gift from the Schmidt Futures Foundation. L.M.S. acknowledges financial support from the Packard and Sloan Foundation. L.E. was supported by the Government of the Basque Country (Project IT1301-19) and the Spanish Ministry of Science and Innovation (PID2019-106644GB-I00). C.F. was supported by the European Research Council (ERC) advanced grant number 742068 ‘TOP-MAT’, Deutsche Forschungsgemeinschaft (DFG) through SFB 1143, and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter-ct.qmat (EXC 2147, project number 390858490). S.S.P.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number 314790414.

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Authors and Affiliations



B.A.B. and N.R. conceived this work; N.R. and M.-R.L. performed the high-throughput calculations with the help from L.E. and Y.X.; Y.X., D.-S.M., Z.-D.S., M.-R.L., L.E. and N.R. worked out the theoretical explanations for the flat-band materials detailed in Supplementary Section F; the material lists in Supplementary Section H were manually selected by Y.X., M.-R.L., Z.-D.S., M.J. and N.R.; N.R. built the flat-band material database; D.-S.M. performed the ab initio ferromagnetic calculations advised by Y.X.; M.J., L.S. and C.F. helped curate the list of materials to find the most experimentally relevant. All authors discussed the results and wrote the main text and Methods; Y.X., Z.-D.S., M-.R.L., D.-S.M., M.J., L.E. and N.R. wrote the Supplementary Information.

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Correspondence to Nicolas Regnault, Yuanfeng Xu or B. Andrei Bernevig.

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Regnault, N., Xu, Y., Li, MR. et al. Catalogue of flat-band stoichiometric materials. Nature 603, 824–828 (2022).

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