Evolution of the Transmission Phase Through a Coulomb-blockaded Majorana Wire

We present a study of the transmission of electrons through a Coulomb-blockaded semiconductor wire with strong spin-orbit coupling in proximity to an s-wave superconductor. Such systems support Majorana bound states in the presence of an external magnetic field and are of interest both due to recent experimental progress and as candidates for realizations of quantum computing. While phase lapses in the transmission phase are expected to occur in the absence of superconductivity we find that they vanish completely in the topological regime. Our calculation is based on a model which expresses tunnelling through the wire, through effective matrix elements which depend on both the fermion parity of the wire and the overlap with Bogoliubov-de-Gennes wave functions. Together with a modified scattering matrix formalism this allows us to study the transmission including electron-electron interactions. We finally discuss the role of spin polarization and breaking of effective time-reversal symmetry.