Refined Majorana phase diagram in a topological insulator–superconductor hybrid system

The edge state of the topological insulator coupled to a superconductor system is able to simulate the Majorana fermion in zero-energy mode since the Kitaev-type pairing is induced by exchanging quasi-excitations in electron tunneling. However, this is not always the case. The present study has revealed that this physical simulation is not valid for a larger surface gap, which is the energy gap of the insulator's surface states. A refined pairing term that depends on the surface gap has been obtained as a second-order effect of the proximity effect, whereas the lowest order produces a constant pairing strength. By carefully considering the dependence of pairing strength on the surface gap, the Majorana phase diagram is re-achieved and a significant difference from previous work is observed, where the pairing strength was assumed to be independent of the surface gap and resulted in a conical phase boundary.