Search

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_{nv} 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_{nv} 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.

We study a new type of three-dimensional topological superconductor that exhibits Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from Z2 to Z, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Especially, we show that a vortex binding two MZMs can be realized on the (001) surface of a topological crystalline insulator SnTe with proximity induced BCS Cooper pairing, or in bulk superconductor InxSn1-xTe.

We theoretically predict that thin-film topological crystalline insulators can host various quantum anomalous Hall phases when doped by ferromagnetically ordered dopants. Any Chern number between ±4 can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through the proximity effect, and (c) the thickness of the thin film. We propose a heterostructure to realize quantum anomalous Hall phases with Chern numbers that can be tuned by electric fields.

We perform a complete classification of two-band k·p theories at band crossing points in 3D semimetals with n-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by C(4,6)-protected double-Weyl nodes with quadratic in-plane (along k(x,y)) dispersion or C(6)-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr(2)Se(4) and confirm it is a double-Weyl metal protected by C(4) symmetry. Furthermore, if the direction of the ferromagnetism is shifted away from the [001] axis to the [111] axis, the double-Weyl node splits into four single Weyl nodes, as dictated by the point group S(6) of that phase. Finally, we discuss experimentally relevant effects including the splitting of multi-Weyl nodes by applying a C(n) breaking strain and the surface Fermi arcs in these new semimetals.