Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry

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,C-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 HgCr2Se4 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.