Exotic Chiral Anomaly of Double-Weyl Fermions

Double-Weyl points in a 3D topological semimetal are protected by crystallographic point-group symmetries, as predicted in Hg$_{2}$Cr$_{2}$Se$_{4}$. The dispersion of fermions around double-Weyl points is highly anisotropic in momentum space, namely quadratic along $x$- and $y$-directions but linear in $z$-direction in the low energy effective Hamiltonian, which has intriguing physical consequences. For instances, we show that the double-Weyl fermions give rise to anisotropic chiral anomaly, qualitatively different from the usual chiral anomaly of (linear) Weyl fermions. We also discuss how the anisotropic dispersions of double-Weyl fermions affect their transport behaviors.