@article{e47b80c315bb4dd3bf3850a936a18caf,
title = "General construction and topological classification of crystalline flat bands",
abstract = "Exotic phases of matter can emerge from the interplay between strong electron interactions and non-trivial topology. Materials that have non-dispersing bands in their electronic band structure, such as twisted bilayer graphene, are prime candidates for strongly interacting physics. However, existing theoretical models for obtaining these {\textquoteleft}flat bands{\textquoteright} in crystals are often too restrictive for experimental realizations. Here we present a generic theoretical technique for constructing perfectly flat bands from bipartite crystalline lattices. Our prescription encapsulates and generalizes the various flat-band models in the literature and is applicable to systems with any orbital content, with or without spin–orbit coupling. Using topological quantum chemistry, we build a complete topological classification in terms of symmetry eigenvalues of all the gapped and gapless flat bands. We also derive criteria for the existence of symmetry-protected band touching points between the flat and dispersive bands, and identify the gapped flat bands as prime candidates for fragile topological phases. Finally, we show that the set of all perfectly flat bands is finitely generated and construct the corresponding bases for all 1,651 Shubnikov space groups.",
author = "Dumitru C{\u a}lug{\u a}ru and Aaron Chew and Luis Elcoro and Yuanfeng Xu and Nicolas Regnault and Song, {Zhi Da} and Bernevig, {B. Andrei}",
note = "Funding Information: 20-1-2303), the Packard Foundation, the Schmidt Fund for Innovative Research, the BSF Israel US foundation (grant no. 2018226), the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the Princeton theory programme and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. B.A.B. and N.R. were supported by the NSF-MRSEC (grant bo. DMR-2011750). B.A.B. and N.R. gratefully acknowledge financial support from the Schmidt DataX Fund at Princeton University made possible through a major gift from the Schmidt Futures 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). Further support was provided by the NSF-MRSEC no. DMR-1420541, BSF Israel US Foundation no. 2018226 and the Princeton Global Network Funds. Funding Information: Elementary band representations. The symmetry properties of an electronic band are completely described by its decomposition into (co)irreps at high-symmetry momenta in the Brillouin zone35–39. For a given gapped band or set of bands, the (co)irreps at two different momentum points are not independent, but instead have to satisfy certain compatibility relations35–39,45,46. The (co)irreps at the maximal momenta determine the (co)irreps across the entire Brillouin zone35,36. For any set of bands, we define an augmented symmetry data vector B35,36, which contains the multiplicities of all its (co)irreps at maximal momenta in the Brillouin zone (Supplementary Section IIIA,B) We thank M.-R. Li and D.-S. Ma for fruitful discussions and collaboration on related projects. This work is part of a project that has received funding from the European Research Council under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement no. 101020833). B.A.B. and N.R. were also supported by the US Department of Energy (grant no. DE-SC0016239), and were partially supported (8) Investigator grant (no.404513),the Office of Naval Research (ONR grant no.N00014-by the National Science Foundation (EAGER grant no.DMR 1643312), a Simons Funding Information: We thank M.-R. Li and D.-S. Ma for fruitful discussions and collaboration on related projects. This work is part of a project that has received funding from the European Research Council under the European Union?s Horizon 2020 research and innovation programme (grant agreement no. 101020833). B.A.B. and N.R. were also supported by the US Department of Energy (grant no. DE-SC0016239), and were partially supported by the National Science Foundation (EAGER grant no. DMR 1643312), a Simons Investigator grant (no. 404513), the Office of Naval Research (ONR grant no. N00014-20-1-2303), the Packard Foundation, the Schmidt Fund for Innovative Research, the BSF Israel US foundation (grant no. 2018226), the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the Princeton theory programme and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. B.A.B. and N.R. were supported by the NSF-MRSEC (grant bo. DMR-2011750). B.A.B. and N.R. gratefully acknowledge financial support from the Schmidt DataX Fund at Princeton University made possible through a major gift from the Schmidt Futures 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). Further support was provided by the NSF-MRSEC no. DMR-1420541, BSF Israel US Foundation no. 2018226 and the Princeton Global Network Funds. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Limited.",
year = "2022",
month = feb,
doi = "10.1038/s41567-021-01445-3",
language = "English (US)",
volume = "18",
pages = "185--189",
journal = "Nature Physics",
issn = "1745-2473",
publisher = "Nature Publishing Group",
number = "2",
}