Effect of Disorder on the Conductance of (non-) Topological SN Junctions

TL;DR

This paper investigates how disorder affects conductance in multi-channel SN junctions, highlighting differences between topological classes with and without Majorana modes using scattering matrix and field theory approaches.

Contribution

It introduces two complementary methods to analyze topological properties and disorder effects in SN junctions, including effects of Ohmic contacts and interactions.

Findings

Disorder impacts conductance differently depending on topological class.

Majorana modes lead to robust conductance features despite disorder.

Scattering matrix and field theory approaches provide complementary insights.

Abstract

General multi-channel SN junctions fall into two topological classes depending on whether or not there is a Majorana mode localized at the junction. This is known to lead to different behaviour of the conductance in the presence of arbitrary disorder near the junction. We discuss these topological properties from two perspectives, one based on representing the disorder by a scattering matrix in series with that of a clean SN junction and one based on low energy field theory methods. The first approach is used to discuss the effect of an Ohmic contact between a quantum wire and a three dimensional metal far from the junction. The second is useful for treating interactions.