A non-commutative framework for topological insulators

C. Bourne, A. L. Carey, A. Rennie

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of non-commutative index theory of operator algebras. In particular, we formulate the index problems using Kasparov theory, both complex and real. We show that the periodic table of topological insulators and superconductors can be realized as a real or complex index pairing of a Kasparov module capturing internal symmetries of the Hamiltonian with a spectral triple encoding the geometry of the sample's (possibly non-commutative) Brillouin zone.

Original languageEnglish
Article number1650004
JournalReviews in Mathematical Physics
Issue number2
Publication statusPublished - 2016 Mar 1
Externally publishedYes


  • K K -theory
  • Topological insulators
  • spectral triple

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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