  We theoretically consider the substrate-induced Majorana localization length
renormalization in nanowires in contact with a bulk superconductor in the
strong tunnel-coupled regime, showing explicitly that this renormalization
depends strongly on the transverse size of the one-dimensional nanowires. For
metallic (e.g. Fe on Pb) or semiconducting (e.g. InSb on Nb) nanowires, the
renormalization effect is found to be very strong and weak respectively because
the transverse confinement size in the two situations happens to be 0.5nm
(metallic nanowire) and 20nm (semiconducting nanowire). Thus, the Majorana
localization length could be very short (long) for metallic (semiconducting)
nanowires even for the same values of all other parameters (except for the
transverse wire size). We also show that any tunneling conductance measurements
in such nanowires, carried out at temperatures and/or energy resolutions
comparable to the induced superconducting energy gap, cannot distinguish
between the existence of the Majorana modes or ordinary subgap fermionic states
since both produce very similar broad and weak peaks in the subgap tunneling
conductance independent of the localization length involved. Only low
temperature (and high resolution) tunneling measurements manifesting sharp zero
bias peaks can be considered to be signatures of Majorana modes in topological
nanowires.
