2014/10/05 by Ching‐Kai Chiu, Chiu, Ching-Kai
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #FOS: Physical sciences #Graphene research and applications #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Superconductivity (cond-mat.supr-con) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.1410.1117
openalex publication_date 2014/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well known to possess a half quantum Hall effect. Furthermore, it has been known that the surface of a weak 3D topological insulator gapped by a charge density wave exhibits a half quantum spin Hall effect. To generalize these results to all Altland-Zirnbauer symmetry classes of topological insulators and superconductors, we reproduce the classification table for the ten symmetry classes by using the representation theory of Clifford algebras and construct minimal-size Dirac Hamiltonians. We find that if the surface dimension and symmetry class possesses a ℤ or ℤ2 topological invariant, then the resulting surface state with a gapped symmetry breaking term may have a nontrivial topological phase.