RT Journal Article
SR Electronic
T1 Topological states from topological crystals
JF Science Advances
JO Sci Adv
FD American Association for the Advancement of Science
SP eaax2007
DO 10.1126/sciadv.aax2007
VO 5
IS 12
A1 Song, Zhida
A1 Huang, Sheng-Jie
A1 Qi, Yang
A1 Fang, Chen
A1 Hermele, Michael
YR 2019
UL http://advances.sciencemag.org/content/5/12/eaax2007.abstract
AB We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.