It is straightforward to compute this integral, and by doing so one finds $$\label{eq:7}
  \partial_\mu \mathcal{B}^\mu(\vec{p}) = \pm 2 \delta(\vec{p}).$$ Thus each band touching is a source of [*two*]{} quanta of Berry flux, and can be therefore considered a [*double Weyl point*]{}. The net Berry flux of both double Weyl points added together vanishes, which is required as the Brillouin zone is a closed manifold without any boundary through which a net flux may escape.

The Berry flux of each double Weyl point is directly related to the Hall conductivity. Indeed, one can show quite generally that the Hall conductivity is proportional to separation of the points,[@anton] $$\begin{aligned}
\sigma_{xy} = &=&2\times \frac{e^2 }{h} \times \frac{2K}{2\pi} \ , \nonumber \end{aligned}$$ where the first factor of $2$ is due to the doubled nature of the Weyl points. This is valid at zero temperature when the Fermi level is at the energy of the double Weyl points. Neglecting the small corrections to the exponent due to Coulomb interactions, we have $K
\sim \sqrt{m H}$, which explains the estimate in Eq.  of the main text.

RG equations
------------

Here we describe the renormalization of the fermionic propagator, which was not presented in the main 