2014/03/31 by Ken Shiozaki, Masatoshi Sato · 5 citations
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.supr-con #hep-th
paper · pdf · doi:10.1103/physrevb.90.165114
published as Phys. Rev. B 90, 165114 (2014) · 58 pages, final version
arxiv created 2014/10/14 · arxiv updated 2014/10/15
We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by non-interacting Bloch and Bogoliubov de Gennes Hamiltonians that support additional order-two spatial symmetry, besides any of ten classes of symmetries defined by time-reversal symmetry and particle-hole symmetry. The additional order-two spatial symmetry we consider is general and it includes Z2 global symmetry, mirror reflection, two-fold rotation, inversion, and their magnetic point group symmetries. We find that the topological periodic table shows a novel periodicity in the number of flipped coordinates under the order-two spatial symmetry, in addition to the Bott-periodicity in the space dimensions. Various symmetry protected topological phases and gapless modes will be identified and discussed in a unified framework. We also present topological classification of symmetry protected Fermi points. The bulk classification and the surface Fermi point classification provide a novel realization of the bulk-boundary correspondence in terms of the K-theory.