• DOI:10.1063/1.3149495
• Corpus ID: 14320124

Periodic table for topological insulators and superconductors

@article{Kitaev2009PeriodicTF,
  title={Periodic table for topological insulators and superconductors},
  author={Alexei Y. Kitaev},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2009}
}

• A. Kitaev
• Published 18 January 2009
• Physics, Mathematics
• arXiv: Mesoscale and Nanoscale Physics

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_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.