  We study multiband semiconducting nanowires proximity-coupled with an s-wave
superconductor and calculate the topological phase diagram as a function of the
chemical potential and magnetic field. The non-trivial topological state
corresponds to a superconducting phase supporting an odd number of pairs of
Majorana modes localized at the ends of the wire, whereas the non-topological
state corresponds to a superconducting phase with no Majoranas or with an even
number of pairs of Majorana modes. Our key finding is that multiband occupancy
not only lifts the stringent constraint of one-dimensionality, but also allows
having higher carrier density in the nanowire. Consequently, multiband
nanowires are better-suited for stabilizing the topological superconducting
phase and for observing the Majorana physics. We present a detailed study of
the parameter space for multiband semiconductor nanowires focusing on
understanding the key experimental conditions required for the realization and
detection of Majorana fermions in solid-state systems. We include various
sources of disorder and characterize their effects on the stability of the
topological phase. Finally, we calculate the local density of states as well as
the differential tunneling conductance as functions of external parameters and
predict the experimental signatures that would establish the existence of
emergent Majorana zero-energy modes in solid-state systems.
