Monopole Superconductivity in Magnetically Doped Cd$_3$As$_2$

When magnetically doped, the Dirac semimetal Cd$_3$As$_2$ features Fermi pockets enclosing Weyl points with chiralities $\pm 1$ and $\pm 2$. The superconducting pairing between parity related Fermi pockets with opposite Chern numbers exhibits exotic pairing gap functions, which have nodes enforced by nonzero Cooper pair Berry phase. We show that for pairing between Fermi pockets with Chern numbers $\pm 1$ or $\pm 2$ in magnetically doped Cd$_3$As$_2$, the gap function exhibits monopole harmonic symmetry with monopole charge $1$ or $2$, depending on the chemical potential. The total vorticity of the gap function, i.e., the winding of the pairing phase over a Fermi surface, is independent of the form of the proximity pairing and is equal to twice the monopole charge of the Cooper pair.