1303.1843 (Ching-Kai Chiu et al.)

Classification of topological insulators and superconductors in the
presence of reflection symmetry    [PDF]

Ching-Kai Chiu, Hong Yao, Shinsei Ryu

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.

View original: http://arxiv.org/abs/1303.1843