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

2013/03/12 by Ching-Kai Chiu, Hong Yao, Shinsei Ryu · 3 citations
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.88.075142

published as Phys. Rev. B 88, 075142 (2013) · 25 pages, 3 figures, 7 tables (reference corrections in v.2)

arxiv created 2013/03/12 · arxiv updated 2013/08/27

Abstract

We discuss a topological classification of insulators and superconductors in the presence of both (non-spatial) 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 non-trivial topological insulators and superconductors support gapless modes localized at the boundary.

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