Topological quantum chemistry

By Barry Bradlyn, L. Elcoro, Jennifer Cano, M. Vergniory, Zhijun Wang, Claudia Felser, M. Aroyo, Bogdan Andrei Bernevig. Nature, 2017

1,517 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/e5a0fff54abb5eca5e61f2b8d73a5f2acaad6c3a

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

Topological Semimetals from First Principles (2018, background): “These attempts have led to a set of recent ideas centered around the notion of symmetry indicators (162, 163, 164, 165, 140).”
Quantization of fractional corner charge in Cn -symmetric higher-order topological crystalline insulators (2018, background): “More generically, we can distinguish nontrivial topological classes arising from the Cn symmetry through the symmetry representations that the occupied energy bands take at the high symmetry points of the BZ (HSPs)[2, 44, 46, 47, 51, 56, 57].”
Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators (2017, background): “Furthermore, the presence of crystalline symmetries leads to a plethora of topological distinctions even when the band insulators admit atomic descriptions and are therefore individually trivial [24,25].”