Topological quantum chemistry
Barry Bradlyn, L. Elcoro, Jennifer Cano, M. G. Vergniory, Zhijun Wang, C. Felser, M. I. Aroyo, B. Andrei Bernevig
Summary
The authors develop a complete framework linking the symmetry properties of electronic bands to topological character, merging group theory of crystallographic space groups with band structure analysis. By cataloguing how atomic orbitals at Wannier centers transform under crystal symmetries, they identify which band structures are topologically trivial (atomic limit) versus topologically nontrivial. This enabled systematic, predictive identification of topological materials from symmetry data alone.
Key findings
- Introduces the concept of 'topological quantum chemistry' connecting real-space orbital symmetry (band representations) to momentum-space band topology.
- Provides a complete mapping of elementary band representations for all 230 space groups, allowing topological materials to be flagged when bands cannot be expressed as an atomic limit.
- Lays the groundwork for high-throughput searches that subsequently catalogued thousands of topological materials.
Subjects & keywords
Cite this paper
Barry Bradlyn, L. Elcoro, Jennifer Cano, M. G. Vergniory, Zhijun Wang, C. Felser, M. I. Aroyo, & B. Andrei Bernevig (2017). Topological quantum chemistry. Nature. https://doi.org/10.1038/nature23268
@article{bradlyn2017topological,
author = {Barry Bradlyn and L. Elcoro and Jennifer Cano and M. G. Vergniory and Zhijun Wang and C. Felser and M. I. Aroyo and B. Andrei Bernevig},
title = {Topological quantum chemistry},
journal = {Nature},
year = {2017},
doi = {10.1038/nature23268},
url = {https://doi.org/10.1038/nature23268}
}