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Tunneling transport in NSN junctions made of Majorana nanowires across the topological quantum phase transition

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.