Majorana modes and transport in a system with three $p$-wave superconductors and normal metal leads

Oindrila Deb, Manisha Thakurathi, Diptiman Sen

Published 2015-08-04Version 1

We study Majorana modes and transport in a one-dimensional system with three $p$-wave superconductors (SCs) which are connected to normal metal leads. We consider a model where there are junctions with barriers between the leads and the SCs; there is also a junction between the three SCs which is described by a Hermitian matrix. If the SCs are sufficiently long, there will be a Majorana mode at each of the barriers with the leads. In addition, depending on the relative signs of the $p$-wave pairings in the three SCs, there can be one or three Majorana modes at the junction of the three SCs. We study the effects of all these Majorana modes on the sub-gap conductances of the system. We show that the conductances between the leads and the Cooper pair conductance between the leads and the SC have peaks which occur at the energies of the Majorana modes; we therefore get a rich pattern of conductance peaks as a function of the energy and lengths of the SCs. Using a renormalization group approach which is valid for weak density-density interactions between the electrons, we study the scattering matrix of the system at energies far from the gap. The fixed points of the renormalization group flows and their stabilities are studied; we discuss the implications of these for the conductances at large wire lengths and low temperatures. Finally we propose an experimental realization of this system which can realize different signs of the $p$-wave pairing in the different SCs.