Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

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.