Abstract
In this article, we review the framework of topological quantum chemistry and its applications to understanding topological materials. We review the construction of band representations, which encode the symmetry properties of topologically trivial electronic bands. We show how this enables the classification and identification of topologically nontrivial bands by comparing constraints on band structures in both position and momentum space. Finally, we discuss the application of topological quantum chemistry to materials discovery.
| Original language | English (US) |
|---|---|
| Title of host publication | Encyclopedia of Mathematical Physics, Second Edition |
| Subtitle of host publication | Volumes 1-5 |
| Publisher | Elsevier |
| Pages | V1:46-V1:55 |
| Volume | 1-5 |
| ISBN (Electronic) | 9780323957069 |
| ISBN (Print) | 9780323957038 |
| DOIs | |
| State | Published - Jan 1 2024 |
| Externally published | Yes |
Keywords
- Band representations
- Band topology
- Crystal symmetry groups
- Topological materials
- Wannier functions
ASJC Scopus subject areas
- General Mathematics