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

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.