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We study the effects of Majorana modes and interactions between electrons ontransport in a one-dimensional system with a junction of three p-wavesuperconductors (SCs) which are connected to normal metal leads. Forsufficiently long SCs, there are zero energy Majorana modes at the junctionsbetween the SCs and the leads,and, depending on the signs of the p-wavepairings in the three SCs, there can also be one or three Majorana modes at thejunction of the three SCs. We show that the various sub-gap conductances havepeaks occurring at the energies of all these modes; we therefore get a richpattern of conductance peaks. Next, we use a renormalization group approach tostudy the scattering matrix of the system at energies far from the SC gap. Thefixed points of the renormalization group flows and their stabilities arestudied; we find that the scattering matrix at the stable fixed point is highlysymmetric even when the microscopic scattering matrix and the interactionstrengths are not symmetric. We discuss the implications of this for theconductances. Finally we propose an experimental realization of this systemwhich can produce different signs of the p-wave pairings in the different SCs.

Transport across a system with three p-wave superconducting wires: effects of Majorana modes and interactions