Vortices in a Monopole Superconducting Weyl Semi-metal*

A monopole 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 study the zero-energy vortex bound states in a model of a monopole superconductor based on a time-reversal broken Weyl semi-metal with proximity-induced superconductivity. 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.