Topological quantum chemistry

• Published in: Nature (London) Vol. 547; no. 7663; pp. 298 - 305
• Main Authors: Bradlyn, Barry, Elcoro, L., Cano, Jennifer, Vergniory, M. G., Wang, Zhijun, Felser, C., Aroyo, M. I., Bernevig, B. Andrei
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 20-07-2017; Nature Publishing Group
• Subjects: 119/118; 639/766/119/2792; 639/766/119/995; Analysis; Atomic structure; Band theory; Band theory (Physics); Chemical bonds; Chemical properties; Chemical research; Chemistry; Crystal structure; Electrical insulators; Electron states; Group theory; Humanities and Social Sciences; Iron; Materials; Metalloids; Methods; multidisciplinary; Orbitals; Polarization; Quantum chemistry; Science; Science & Technology - Other Topics; Solitons; Symmetry; Topological groups; Topology; France
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/nature23268

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.
A complete electronic band theory is presented that describes the global properties of all possible band structures and materials, and can be used to predict new topological insulators and semimetals.
A quantum chemistry theory of electron bands
Chemists and physicists have traditionally fostered very different perspectives on energy band theory. Barry Bradlyn
et al
. have developed a new and complete theory to calculate electronic band structure with the unique feature that it can be used to determine for any material whether it is topologically trivial or not. The theory consists of several parts, joining up the conventional band structure approach, which considers electron properties in non-local, momentum space, with a local viewpoint of chemical bonding and interactions. The authors classify the band structures for all 230 symmetry groups and show how this can be used to search for previously undiscovered materials with interesting topological properties.