Interplay of disorder and interaction in Majorana quantum wires

TL;DR

This paper investigates how disorder and electron interactions influence the stability and phase transitions of Majorana modes in one-dimensional topological superconductors, providing a phase diagram and stability criteria.

Contribution

It introduces a combined bosonization and RG approach to map the phase diagram and identify critical points in disordered interacting Majorana wires.

Findings

Quantum phase transition from topological to localized phase.

Phase boundary as a function of interaction and disorder.

Large stability regime for Majorana modes under disorder.

Abstract

We study the interplay between disorder and interaction in one-dimensional topological superconductors which carry localized Majorana zero-energy states. Using Abelian bosonization and the perturbative renormalization group (RG) approach, we obtain the RG-flow and the associated scaling dimensions of the parameters and identify the critical points of the low-energy theory. We predict a quantum phase transition from a topological superconducting phase to a non-topological localized phase, and obtain the phase boundary between these two phases as a function of the electron-electron interaction and the disorder strength in the nanowire. Based on an instanton analysis which incorporates the effect of disorder, we also identify a large regime of stability of the Majorana-carrying topological phase in the parameter space of the model.