  We theoretically consider transport properties of a normal metal (N)-
superconducting semiconductor nanowire (S)-normal metal (N) structure (NSN) in
the context of the possible existence of Majorana bound states in disordered
semiconductor-superconductor hybrid systems in the presence of spin-orbit
coupling and Zeeman splitting induced by an external magnetic field. We study
in details the transport signatures of the topological quantum phase transition
as well as the existence of the Majorana bound states in the electrical
transport properties of the NSN structure. Our theory includes the realistic
nonperturbative effects of disorder, which is detrimental to the topological
phase (eventually suppressing the superconducting gap completely), and the
effects of the tunneling barriers (or the transparency at the tunneling NS
contacts), which affect (and suppress) the zero bias conductance peak
associated with the zero energy Majorana bound states. We show that in the
presence of generic disorder and barrier transparency the interpretation of the
zero bias peak as being associated with the Majorana bound state is problematic
since the nonlocal correlations between the two NS contacts at two ends may not
manifest themselves in the tunneling conductance through the whole NSN
structure. We establish that a simple modification of the standard transport
measurements using conductance differences (rather than the conductance itself
as in a single NS junction) as the measured quantity can allow direct
observation of the nonlocal correlations inherent in the Majorana bound states
and enables the mapping out of the topological phase diagram (even in the
presence of considerable disorder) by precisely detecting the topological
quantum phase transition point.
