  To guide experimental work on the search for Majorana zero-energy modes, we
calculate the superconducting pairing symmetry of a three-dimensional
topological insulator in combination with an s-wave superconductor. In analogy
to the case of nanowires with strong spin-orbit coupling we show how the
pairing symmetry changes across different topological regimes. We demonstrate
that a dominant p-wave pairing relation is not sufficient to realize a Majorana
zero-energy mode useful for quantum computation. Our main result of this paper
is the relation between odd-frequency pairing and Majorana zero energy modes by
using Green functions techniques in three-dimensional topological insulators in
the so-called Majorana regime. We discuss thereafter how the pairing relations
in the different regimes can be observed in the shape of the tunneling
conductance of an s-wave proximized three-dimensional topological insulator. We
will discuss the necessity to incorporate a ferromagnetic insulator to localize
the zero-energy bound state to the interface as a Majorana mode.
