Topological insulators and superconductors: tenfold way and dimensional hierarchy
University of California, Berkeley · University of California, Santa Barbara · +2 more institutions
Abstract
It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on the case, by a Z or a Z_2 topological invariant. This is an exhaustive classification. Here we construct representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians. Using these representatives we demonstrate how topological insulators (superconductors) in different dimensions and different classes can be related via dimensional reduction by compactifying one or more spatial…
Citation impact
- FWCI
- 43.87
- Percentile
- 100%
- References
- 104
Authors
4Topics & keywords
- Physics
- Topological insulator
- Topology (electrical circuits)
- Topological entropy in physics
- Symmetry protected topological order
- Homogeneous space
- Superconductivity
- Invariant (physics)