Correlated double-Weyl semimetals with Coulomb interactions: possible applications to HgCr2Se4 and SrSi2

We study the fate of double-Weyl fermions in three-dimensional systems in the presence of long-range Coulomb interactions. By employing the momentum-shell renormalization group approach, we find that the fixed point of noninteracting double-Weyl fermions is unstable against Coulomb interactions and flows to a nontrivial stable fixed point with anisotropic screening effect. Moreover, experimentally measurable quantities such as specific heat obtain unusual logarithmic corrections. We also discuss implications of our results to three-dimensional materials HgCr2Se4 and SrSi2, candidate materials of hosting double-Weyl fermions.