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If superconductivity is induced in the metallic surface states of topologicalinsulators via proximity, Majorana modes will be trapped on the vortex cores.The same effects hold for doped topological insulators which become bulk s-wavesuperconductors as long as the doping does not exceed a critical values $\mu^{\pm}_c.$ It is this critical chemical potential at which the materialforgets it arose from a band-inverted topological insulator; it loses itstopological \emph{imprint.} For the most common classes of topologicalinsulators, which can be modeled with a minimal 4-band Dirac model the valuesof $\mu^{\pm}_c$ can be easily calculated, but for materials with morecomplicated electronic structures such as HgTe or ScPtBi the result is unknown.We show that due to the hybridization with an additional Kramers' pair oftopologically trivial bands the topological imprint of HgTe-like electronicstructures (which includes the ternary Heusler compounds) can be widelyextended for p-doping. As a practical consequence we consider the effects ofsuch hybridization on the range of doping over which Majorana modes will bebound to vortices in superconducting topological insulators and show that therange is strongly extended for p-doping, and reduced for n-doping. This leavesopen the possibility that other topological phenomena may be stabilized over awider range of doping.

Stabilization of Majorana modes in vortices in the superconducting phase of topological insulators using topologically trivial bands