  We study the effect of a non-Abelian SU(2) gauge potential on the topological
semimetal induced by a magnetic field having {\pi}-flux per plaquette and
acting on fermions in a cubic lattice. The Abelian {\pi}-flux term gives rise
to a spectrum characterized by Weyl points. When the non-Abelian part is turned
on, due to the presence of a C4 rotation symmetry, the Weyl points assume a
quadratic dispersion along two directions and constitute double monopoles for
the Berry curvature. We examine both analytically and numerically the main
features of this system, focusing on its gapless surface modes, the so-called
Fermi arcs. We discuss the stability of the system under confining hard-wall
and harmonic potentials, relevant for the implementation in ultracold atom
settings, and the effect of rotation symmetry breaking.

Quantum Gases;Strongly Correlated Electrons;Superconductivity;High Energy Physics - Theory