  Rashba spin-orbit coupled semiconductor-superconductor hybrid structures in
the presence of Zeeman splitting have emerged as the first experimentally
realizable topological superconductor supporting zero-energy Majorana bound
states. However, recent experimental studies in these hybrid structures are not
in complete agreement with the theoretical predictions, for example, the
observed height of the zero-bias conductance peak (ZBCP) associated with the
Majorana bound states is less than 10% of the predicted quantized value 2e^2/h.
We try to understand the sources of various discrepancies between the recent
experiments and the earlier theories by starting from a microscopic theory and
studying non-equilibrium transport in these systems at arbitrary temperatures
and applied bias voltages. Our approach involves quantum Langevin equations and
non-equilibrium Green's functions. Here we are able to model the tunnel
coupling between the one-dimensional semiconductor-superconductor hybrid
structure and the metallic leads realistically; study the role of tunnel
coupling on the height of the ZBCP and the subgap conductance; predict the
nature of the splitting of the ZBCP with an increasing magnetic field beyond
the critical field; show the behavior of the ZBCP with an increasing
gate-controlled onsite potential; and study the evolution of the full
differential conductance across the topological quantum phase transition. When
the applied magnetic field is quite large compared to the Rashba splitting and
the bulk energy gap is much reduced, we find the ZBCP even for an onsite
potential much larger than the applied magnetic field. The height of the
corresponding ZBCP depends on the tunnel coupling even at zero temperature and
can be much smaller than 2e^2/h.
