Periodic table for topological insulators and superconductors
- California Institute of Technology, Pasadena, CA 91125 (United States)
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z{sub 2}. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.
- OSTI ID:
- 21304870
- Journal Information:
- AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1134; ISSN APCPCS; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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