  Tunneling experiment is a key technique for detecting Majorana fermion in
solid state systems. We use Keldysh non-equilibrium Green function method to
study multi-lead tunneling in superconducting nanowire with Rashba and
Dresselhaus spin-orbit couplings. A zero-bias \textit{dc} conductance peak
appears in our setup which signifies the existence of Majorana fermion and is
in accordance with previous experimental results on InSb nanowire.
Interestingly, due to the exotic property of Majorana fermion, there exists a
hole transmission channel which makes the currents asymmetric at the left and
right leads. The \textit{ac} current response mediated by Majorana fermion is
also studied here. To discuss the impacts of Coulomb interaction and disorder
on the transport property of Majorana nanowire, we use the renormalization
group method to study the phase diagram of the wire. It is found that there is
a topological phase transition under the interplay of superconductivity and
disorder. We find that the Majorana transport is preserved in the
superconducting-dominated topological phase and destroyed in the
disorder-dominated non-topological insulator phase.
