Topological quantum chemistry

Bradlyn B, Elcoro L, Cano J, Vergniory MG, Wang Z, Felser C, Aroyo MI, Bernevig BA (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Nature Nature Research

Book Volume: 547

Pages Range: 298-305

Journal Issue: 7663

DOI: 10.1038/nature23268

Abstract

Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more.

Involved external institutions

Princeton University US United States (USA) (US) University of Basque Country / Universidad del Pais Vasco (UPV) / Euskal Herriko Unibersitatea (EHU) ES Spain (ES) Donostia International Physics Center (DIPC) ES Spain (ES) Max-Planck-Institut für Chemische Physik fester Stoffe (MPI CPfS) / Max Planck Institute for Chemical Physics of Solids DE Germany (DE)

How to cite

APA:

Bradlyn, B., Elcoro, L., Cano, J., Vergniory, M.G., Wang, Z., Felser, C.,... Bernevig, B.A. (2017). Topological quantum chemistry. Nature, 547(7663), 298-305. https://doi.org/10.1038/nature23268

MLA:

Bradlyn, Barry, et al. "Topological quantum chemistry." Nature 547.7663 (2017): 298-305.

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