Correlated double-Weyl semimetals with Coulomb interactions: Possible applications to ${\mathrm{HgCr}}_2{\mathrm{Se}}_4$ and ${\mathrm{SrSi}}_2$

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 ${\mathrm{HgCr}}_2{\mathrm{Se}}_4$ and ${\mathrm{SrSi}}_2$, candidate materials of hosting double-Weyl fermions.

Figure 1

The schematic phase diagram of the microscopic lattice model in Eq. (1) as a function of the parameter $m$. Here, “3D Chern insulator” refers to a 3D insulator with finite Hall conductivity ${\sigma }_{xy}$. Quadratic band touching is realized at the transitions between the double-Weyl semimetal and the trial (or Chern) insulators.

Figure 2

(a) Feynman diagrams. (b) The RG flow in the parameter space of $\alpha =\frac{g^2}{8{\pi }^{2}v}$ and $\beta =\frac{g^{2}mv}{8\pi \mathrm{\Lambda }\eta }$. There are two fixed points. The fixed point at (0,0) represents noninteracting double-Weyl fermions which are not stable against long-range Coulomb interactions. The nontrivial fixed point is at $({\alpha }^{*},{\beta }^{*})=(0,1)$, where the Coulomb interactions at low energy are qualitatively different between the quadratic- and linear-dispersing directions.

Figure 3

The numerical values of the $G_i$ functions are plotted.

Figure 4

Schematic plot of specific heat in double-Weyl semimetals with and without Coulomb interactions. The dotted line is the specific heat from electronic contribution in noninteracting double-Weyl fermions. The solid line is plotted from Eq. (A39) [or Eq. (10)]. The dashed line is plotted from the same equation but without the exponential factor.