讲座摘要：Inspired by recent experiments, we theoretically study the single-vortex state of a Bose-Fermi mixture. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. In presence of p-wave Fermi-Fermi interaction, this gives rise to a dynamically driven local interface that 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, where the circulation of the vortex plays an important role. In particular, we find the Majorana zero mode in the vortex core becomes isolated by tuning the Bose density when the vortex circulation mismatches the chirality of the p-wave interaction. Our study may provide a paradigm for the dynamical control of vortex.