Spin-Orbit-free topological insulators without time-reversal symmetry

A. Alexandradinata, Chen Fang, Matthew J. Gilbert, B. Andrei Bernevig

Research output: Contribution to journalArticlepeer-review

114 Scopus citations


We explore the 32 crystallographic point groups and identify topological phases of matter with robust surface modes. For n=3,4, and 6 of the Cnv groups, we find the first-known 3D topological insulators without spin-orbit coupling, and with surface modes that are protected only by point groups; i.e., the relevant symmetries are purely crystalline and do not include time reversal. To describe these Cnv systems, we introduce the notions of (a) a halved mirror chirality, an integer invariant which characterizes half-mirror-planes in the 3D Brillouin zone, and (b) a bent Chern number, the traditional Thouless-Kohmoto-Nightingale-den Nijs invariant generalized to bent 2D manifolds. We find that a Weyl semimetallic phase intermediates two gapped phases with distinct halved chiralities. In addition to electronic systems without spin-orbit coupling, our findings also apply to intrinsically spinless systems such as photonic crystals and ultracold atoms.

Original languageEnglish (US)
Article number116403
JournalPhysical review letters
Issue number11
StatePublished - Sep 12 2014

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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