Vortices in a Monopole Superconducting Weyl Semi-metal

A monopole harmonic superconductor is a novel topological phase of matter with topologically protected gap nodes that result from the non-trivial Berry phase structure of Cooper pairs. In this work we propose to realize a monopole superconductor by the proximity effect between a time-reversal broken Weyl semi-metal and an $s$-wave superconductor. Furthermore, we study the zero-energy vortex bound states in this system by projection methods and by exact solutions. The zero modes exhibit a non-trivial phase winding in real space as a result of the non-trivial winding of the order parameter in momentum space. By mapping the Hamiltonian to the $(1+1)$d Dirac Hamiltonian, it is shown that the zero modes, analogous to the Jackiw-Rebbi mode, are protected by the index theorem. Finally, we propose possible experimental realizations.