  With the recent achievement of extremely high-quality epitaxial interfaces
between InAs nanowires and superconducting Al shells with strong
superconductor-semiconductor tunnel coupling, a new regime of proximity-induced
superconductivity in semiconductors can be explored where the induced gap may
be similar in value to the bulk Al gap (large gap) with negligible subgap
conductance (hard gap). We propose several experimentally relevant consequences
of this large-gap strong-coupling regime for tunneling experiments, and we
comment on the prospects of this regime for topological superconductivity. In
particular, we show that the advantages of having a strong spin-orbit coupling
and a large spin g-factor in the semiconductor nanowire may both be compromised
in this strongly coupled limit, and somewhat weaker interface tunneling may be
necessary for achieving optimal proximity superconductivity in the
semiconductor nanowire. We derive a minimal, generic theory for the
strong-coupling hard-gap regime obtaining good qualitative agreement with the
experiment and pointing out future directions for further progress toward
Majorana nanowires in hybrid semiconductor-superconductor structures.
