  We prove that a system of non-interacting electrons proximity coupled to a
conventional s-wave superconductor cannot realize a time reversal invariant
topological phase. This is done by showing that for such a system, in either
one or two dimensions, the topological invariant of the corresponding symmetry
class (DIII) is always trivial. Our results suggest that the pursuit of
Majorana bound states in time-reversal invariant systems should be aimed at
interacting systems or at proximity to unconventional superconductors.
