Topological Monopole Superconductivity in Magnetically Doped Cd₃As₂

We explore the monopole superconductivity arising from the proximity induced Cooper pairing in magnetically doped Dirac semimetal Cd₃As₂. Regardless of the details of proximity pairing, the zero-momentum inter-Fermi-surface pairing gap function is always nodal and described by monopole harmonic functions. It exhibits rich monopole pairing structure that depends on whether the Cooper pairing occurs between Fermi pockets with Chern numbers ±1 or ±2 at different chemical potentials. When Cooper pairing occurs between the Fermi pockets with Chern numbers ±1, the low-energy quasiparticle spectrum consists of linear BdG Weyl nodes, while for the pairing between Chern number ±2 Fermi pockets, the low-energy quasiparticle spectrum can exhibit quadratic BdG Weyl nodes near the Fermi surface along the four-fold rotation axis or linear BdG Weyl nodes away from the rotation axis. The total phase winding around all gap nodes on a Fermi pocket is a topological invariant proportional to the pair monopole charge.