Majorana modes in smooth normal-superconductor nanowire junctions

TL;DR

This paper introduces a numerical method to analyze Majorana zero modes in smooth nanowire junctions, revealing how interface softness affects their protection and the potential for extended Majorana states under certain conditions.

Contribution

A novel numerical approach for spectrum calculation in smooth normal-superconductor nanowire junctions, highlighting the effects of interface softness on Majorana mode protection and state extension possibilities.

Findings

Soft potential interfaces hinder Majorana protection.

Soft superconductor gap transitions enhance Majorana protection.

Extended Majorana states may occur with active propagating modes.

Abstract

A numerical method to obtain the spectrum of smooth normal-superconductor junctions in nanowires, able to host Majorana zero modes, is presented. Softness in the potential and superconductor interfaces yields opposite effects on the protection of Majorana modes. While a soft potential is a hindrance for protection, a soft superconductor gap transition greatly favors it. Our method also points out the possibility of extended Majorana states when propagating modes are active far from the junction, although this requires equal incident fluxes in all open channels.