The panels from left to right illustrate a phase transition through a vortex in a superconducting (doped) topological insulator as the chemical potential is raised. The leftmost panel shows Majorana bound states (red) trapped where the vortex line intersects the surface of the topological insulator. The second panel shows the development of a “mini-gap” region surrounding the vortex core across which the bound states can tunnel as the chemical potential increases. The third panel shows the critical point where a mode along the vortex line becomes gapless allowing the surface bound states to easily tunnel and hybridize with the state on the opposite surface. The final panel is tuned past the critical point where the vortex line is again gapped and the Majorana bound states are absent, leading to a trivial state.