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(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.