Abstract
Topology has driven the prediction and classification of quantum states of matter in the last several decades. Here we review its basic formulation from the perspective of band theory, space group symmetry, and quantum geometry. Our aim is to convey the conceptual development of the field from the current vantage point of topological materials, along with practical formulae, example models, and an overview of ongoing research.
| Original language | English (US) |
|---|---|
| Title of host publication | Encyclopedia of Mathematical Physics, Second Edition |
| Subtitle of host publication | Volumes 1-5 |
| Publisher | Elsevier |
| Pages | V1:1-V1:16 |
| Volume | 1-5 |
| ISBN (Electronic) | 9780323957069 |
| ISBN (Print) | 9780323957038 |
| DOIs | |
| State | Published - Jan 1 2024 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Band theory
- Classification
- Fractional chern insulators.
- Many-body topology
- Quantum geometry
- Space group symmetry
- Topological materials
- Topological quantum field theory
- Topology
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