Topological Phase Transitions of Superconducting Vortex Bound States Driven by Impurities

We show that standard impurities, magnetic or nonmagnetic, weak or strong, can cause topological phase transitions inside the vortex cores of a conventional s-wave superconductor. Because of the nonzero angular momentum of Cooper pairs in the vortex cores, the vortex bound states in a two dimensional superconductor are sensitive to impurities in a way similar to the Yu-Shiba-Rusinov bound states induced by magnetic impurities. In three dimensional cases, the vortex bound states can be driven into topologically nontrivial phases by an impurity chain inside the vortex core. The system can host Majorana modes including the Majorana zero modes localized at the end of the vortex line and the propagating Majorana modes along the vortex line. These results suggest that the superconducting vortex can be the simplest platform to realize Majorana modes.