Classification of topological insulators and superconductors

Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki, Andreas W.W. Ludwig

Research output: Chapter in Book/Report/Conference proceedingConference contribution

313 Scopus citations


An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a topologically trivial and a topologically non-trivial state. Our approach consists in reducing the problem of classifying topological insulators (superconductors) in d spatial dimensions to the problem of Anderson localization at a {d - 1) dimensional boundary of the system. We find that in each spatial dimension there are precisely five distinct classes of topological insulators (superconductors). The different topological sectors within a given topological insulator (superconductor) can be labeled by an integer winding number or a Z2 quantity. One of the five topological insulators is the "quantum spin Hall" (or: Z2 topological) insulator in d = 2, and its generalization ind = 3 dimensions. For each dimension d, the five topological insulators correspond to a certain subset of five of the ten generic symmetry classes of Hamiltonians introduced more than a decade ago by Altland and Zirnbauer in the context of disordered systems (which generalizes the three well known "Wigner and Dyson" symmetry classes).

Original languageEnglish (US)
Title of host publicationAdvances in Theoretical Physics - Landau Memorial Conference
Number of pages12
StatePublished - 2009
Externally publishedYes
EventLandau Memorial Conference on Advances in Theoretical Physics - Chernogolovka, Russian Federation
Duration: Jun 22 2008Jun 22 2008

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


ConferenceLandau Memorial Conference on Advances in Theoretical Physics
Country/TerritoryRussian Federation

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Anderson localization
  • Quantum hall effects
  • Topological phase


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