Topological quantum chemistry

Barry Bradlyn, L. Elcoro, Jennifer Cano, M. G. Vergniory, Zhijun Wang, C. Felser, M. I. Aroyo and B. Andrei Bernevig ()
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Barry Bradlyn: Princeton Center for Theoretical Science, Princeton University
L. Elcoro: University of the Basque Country UPV/EHU
Jennifer Cano: Princeton Center for Theoretical Science, Princeton University
M. G. Vergniory: Donostia International Physics Center
Zhijun Wang: Princeton University
C. Felser: Max Planck Institute for Chemical Physics of Solids
M. I. Aroyo: University of the Basque Country UPV/EHU
B. Andrei Bernevig: Donostia International Physics Center

Nature, 2017, vol. 547, issue 7663, 298-305

Abstract: 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.

Date: 2017
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DOI: 10.1038/nature23268

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