Classification of topological insulators and superconductors in the presence of reflection symmetry

Ching Kai Chiu, Hong Yao, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

276 Scopus citations


We discuss a topological classification of insulators and superconductors in the presence of both (nonspatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using the structure of bulk Dirac Hamiltonians of minimal matrix dimensions and explicit constructions of topological invariants, we provide the complete classification, which still has the same dimensional periodicities with the original Altland-Zirnbauer classification. The classification of reflection-symmetry-protected topological insulators and superconductors depends crucially on the way reflection symmetry operation is realized. When a boundary is introduced, which is reflected into itself, these nontrivial topological insulators and superconductors support gapless modes localized at the boundary.

Original languageEnglish (US)
Article number075142
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number7
StatePublished - Aug 26 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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