Majorana Fermion in Superconducting Island on Top of Topological Insulator

We study the electron states localized at the edge of a superconducting island placed on the top of a topological insulator in a transverse magnetic field. In such systems, Majorana fermions emerge if an odd number of vortices is hosted by the island. Majorana states emerge in pairs: one state is localized near the vortex core, and another at the island edge. We analyze the robustness of Majorana fermions at the edge of the island threaded by a single vortex. If the system parameters are optimized, the energy gap between the Majorana fermion and the first excited state at the edge is of the order of the superconducting gap induced on the surface of the topological insulator. The stability of the Majorana fermion state against a variation of the gate voltage and its sensitivity to the magnetic field allows one to experimentally distinguish the edge Majorana fermion from conventional Dirac fermions.