Maia G. Vergniory, Luis Elcoro, Benjamin J. Wieder, Titus Neupert, Alexey A. Soluyanov, Claudia Felser, Zhijun Wang, Nicolas Regnault, B. Andrei Bernevig, Barry Bradlyn, Jennifer Cano, Department of Physics [MIT Cambridge], Massachusetts Institute of Technology (MIT), Department of Physics, Northeastern University, Northeastern University [Boston], Department of Physics, Princeton University (DPPU), Princeton University, Department of Electrical and Computer Engineering [Urbana] (University of Illinois), University of Illinois at Urbana-Champaign [Urbana], University of Illinois System-University of Illinois System, Department of Physics and Astronomy [Stony Brook], Stony Brook University [SUNY] (SBU), State University of New York (SUNY)-State University of New York (SUNY), Flatiron Institute, Simons Foundation, Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, China, University of Chinese Academy of Sciences [Beijing] (UCAS), Donostia International Physics Center - DIPC (SPAIN), Donostia International Physics Center (DIPC), University of the Basque Country/Euskal Herriko Unibertsitatea (UPV/EHU)-University of the Basque Country/Euskal Herriko Unibertsitatea (UPV/EHU), Ikerbasque - Basque Foundation for Science, Max Planck Institute for Chemical Physics of Solids (CPfS), Max-Planck-Gesellschaft, University of the Basque Country/Euskal Herriko Unibertsitatea (UPV/EHU), Department of Physics, Saint-Petersburg State University, Saint-Petersburg State University, Universität Zürich [Zürich] = University of Zurich (UZH), Théorie de la Matière Condensée, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), University of Zurich, Wieder, Benjamin J, Bernevig, B Andrei, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline insulators (TCIs), and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures - including the theory of Topological Quantum Chemistry (TQC) - researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent application of TQC and related methods to high-throughput materials discovery has revealed that over half of all of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85% of the known stoichiometric materials host energetically isolated topological bands, and that just under $2/3$ of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. In this Review, we survey topological electronic materials discovery in nonmagnetic crystalline solids from the prediction of the first 2D and 3D TIs to the recently introduced methods that have facilitated large-scale searches for topological materials. We also discuss future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices., Comment: Final version, 27 pages, 7 figures