  The helical electron states on the surface of topological insulators or
elemental Bismuth become unstable toward superconducting pairing formation when
coupled to the charge or magnetic fluctuations. The latter gives rise to
pairing instability in chiral channels $d_{xy}\pm i d_{x^2-y^2}$, as has been
observed recently in epitaxial Bi/Ni bilayer system at relatively high
temperature, while the former favors a pairing with zero total angular
momentum. Motivated by this observation we study the vortex bound states in
these superconducting states. We consider a minimal model describing the
superconductivity in the presence of a vortex in the superconducting order
parameter. We show that zero-energy states appear in the spectrum of the vortex
core for all pairing symmetries. Our findings may facilitate the observation of
Majorana modes bounded to the vortices in heterostructures with no need for a
proximity-induced superconductivity and relatively large value of $\Delta/E_F$.
