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

TL;DR

This paper investigates how Majorana modes and electron interactions influence transport in a three-wire p-wave superconductor system, revealing complex conductance patterns and stable symmetric scattering states.

Contribution

It provides a detailed analysis of Majorana-induced conductance features and the stability of symmetric scattering matrices in a multi-wire p-wave superconductor junction.

Findings

Conductance peaks at energies of Majorana modes.

Stable fixed points exhibit highly symmetric scattering matrices.

Different signs of p-wave pairing can be experimentally realized.

Abstract

We study the effects of Majorana modes and interactions between electrons on transport in a one-dimensional system with a junction of three p-wave superconductors (SCs) which are connected to normal metal leads. For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads,and, depending on the signs of the p-wave pairings in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various sub-gap conductances have peaks occurring at the energies of all these modes; we therefore get a rich pattern of conductance peaks. Next, we use a renormalization group approach to study the scattering matrix of the system at energies far from the SC gap. The fixed points of the renormalization group flows and their stabilities are studied; we find that the scattering matrix at the stable fixed point is highly symmetric even when the microscopic scattering matrix and the interaction strengths are not symmetric. We discuss the implications of this for the conductances. Finally we propose an experimental realization of this system which can produce different signs of the p-wave pairings in the different SCs.