Transmission Amplitude through a Coulomb blockaded Majorana Wire

We study coherent electronic transport through a Coulomb blockaded superconducting Rashba wire in the co-tunneling regime between conductance resonances. By varying an external Zeeman field the wire can be tuned into a topological regime, where non-local transport through Majorana zero modes is the dominant mechanism. We model coherent transport in the co-tunneling regime by using a scattering matrix formalism, and find that the transmission amplitude has a maximum as a function of Zeeman field, whose height is proportional to the wire length. We relate the transmission amplitude to the Majorana correlation length, and argue that the Zeeman field and length dependence of the transmission amplitude are unique signatures for the presence of Majorana zero modes.