  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, 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. To address this issue, 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.
