3914 (1972).

A. A. Burkov and L. Balents, Phys. Rev. Lett. [**107**]{}, 127205 (2011). L. Zhu, [*et al.*]{}, Phys. Rev. Lett. [**91**]{}, 066404 (2003). P. Gegenwart [*et al.*]{}, J. Low Temp. Phys. [**161**]{}, 117 (2010). P. Gegenwart, private communication.

Supplementary material
======================

Representations of the Hamiltonian
----------------------------------

In this section, we provide more information about the different representations used in the main text. The Hamiltonian reads $$\begin{aligned}
\mathcal{H}_0(k)&=&\alpha_1 k^2 + \alpha_2 (\vec{k} \cdot \vec{J})^2 + \alpha_3 (k_x^2 J_x^2 + k_y^2 J_y^2 +k_z^2 J_z^2) \nonumber \\
&=& \frac{k^2}{2 \tilde{M}_0} + \frac{ (\frac{5}{4}k^2-\vec{k} \cdot \vec{J})^2}{2m} - \frac{ (k_x^2 J_x^2 + k_y^2 J_y^2 +k_z^2 J_z^2)}{2 M_c} \nonumber \\
&=&\frac{d_a(k)}{2m} \Gamma^a + \frac{k^2}{2M_0} + \frac{d_4(k) \Gamma^4 + d_5(k) \Gamma^5}{2M_c} .\end{aligned}$$ The first line uses the conventional Luttinger parameters ($\alpha_{1,2,3}$) in the $j=3/2$ matrix representation, and the second line is the form used in the main text. For the purpose of computations, it is convenient to introduce the Clifford gamma matrices ($\Gamma_{a}$) in the third line as in the paper by Murakami [*et al.*]{} [@murakami]. $$\begin{aligned}
&&\epsilon_a(k)= \frac{d_a(k)}{2m} , \nonumber \\
&& d_1(k)= -\sqrt{3}k_y k_z \, , \,\,  d_2(k)= -\sqrt{3}k_x k_z \,, \,\, d_3(k)= -\sqrt{3}k_x k_y  , \nonumber \\
&& d_4(k) = \frac{-\sqrt{3}}{2}(k_x^2 -k_y^2) \,, 