  The combination of superconductivity and spin-momentum locking at the
interface between an s-wave superconductor and a three-dimensional topological
insulator (3D-TI) is predicted to generate exotic p-wave topological
superconducting phases that can host Majorana fermions. However, large bulk
conductivities of previously investigated 3D-TI samples and Fermi level
mismatches between 3D bulk superconductors and 2D topological surface states
have thwarted significant progress. Here we employ bulk insulating topological
insulators in proximity with two-dimensional superconductor NbSe$_2$ assembled
via Van der Waals epitaxy. Experimentally measured differential conductance
yields unusual features including a double-gap spectrum, an intrinsic asymmetry
that vanishes with small in-plane magnetic fields and differential conductance
ripples at biases significantly larger than the superconducting gap. We explain
our results on the basis of proximity induced superconductivity of topological
surface states, while also considering possibilities of topologically trivial
superconductivity arising from Rashba-type surface states. Our work
demonstrates the possibility of obtaining p-wave superconductors by proximity
effects on bulk insulating TIs.
