CPT theorem and classification of topological insulators and superconductors

Chang Tse Hsieh, Takahiro Morimoto, Shinsei Ryu

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38 Scopus citations


We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of K-theory classification of gapped quadratic fermion theories with symmetries, and the other in terms of the K-matrix theory description of the edge theory of (2+1)-dimensional bulk theories. The first approach is specific to free fermion theories in general spatial dimensions while the second approach is limited to two spatial dimensions but incorporates effects of interactions. We also clarify the role of the CPT theorem in the classification of symmetry-protected topological phases, and show, in particular, that the topological superconductors discussed before are related by the CPT theorem.

Original languageEnglish (US)
Article number245111
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number24
StatePublished - Dec 3 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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