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 _4,6-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 ₂Se 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.