Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry

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 C₍ₕ 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 C₍ₕ 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.