  We study a single vortex in a two-dimensional $p+ip$ Fermi superfluid interacting with a Bose-Einstein condensate. The Fermi superfluid is topologically non-trivial and hosts a zero-energy Majorana bound state at the vortex core. Assuming a repulsive $s$-wave contact interaction between fermions and bosons, we find that fermions are depleted from the vortex core when the bosonic density becomes sufficiently large. In this case, a dynamically-driven local interface emerges between fermions and bosons, along which chiral Majorana edge states should appear.We examine in detail the variation of vortex-core structures as well as the formation of chiral Majorana edge states with increasing bosonic density. In particular, when the angular momentum of the vortex matches the chirality of the Fermi superfluid, the Majorana zero mode and normal bound states within the core continuously evolve into chiral Majorana edge states. Otherwise, a first-order transition occurs in the lowest excited state within the core, due to the competition between counter-rotating normal bound states in forming chiral Majorana edge states. Such a transition is manifested as a sharp peak in the excitation gap above the Majorana zero mode, at which point the Majorana zero mode is protected by a large excitation gap.Our study presents an illuminating example on how topological defects can be dynamically controlled in the context of cold atomic gases. 
Chiral Majorana edge states in the vortex core of a $p+ip$ Fermi   superfluid