A Model for Topological p-wave Superconducting Wires with Disorder and Interactions

TL;DR

This paper provides a detailed theoretical analysis of topological phases in coupled Kitaev wires with disorder and interactions, revealing the stability of novel fractional Majorana phases and their transition to protected topological states.

Contribution

It introduces new analytical and numerical methods to study disordered, interacting topological wires and identifies the stabilization of a fractional Majorana liquid by strong interactions.

Findings

The DCI phase is stabilized by strong interactions against disorder.

Disorder effects near quantum phase transitions are quantified.

The DCI phase becomes a protected topological phase with a bulk gap when inter-wire hopping is introduced.

Abstract

We present a comprehensive theoretical study of interacting and disordered topological phases of coupled Kitaev wires, which may support further realistic applications of Majorana fermions. We develop a variety of analytical, mathematical and numerical methods for one and two-coupled wires, associated with a topological marker accessible from real-space correlation functions on the wire(s). We verify the stability of the topological superconducting phase and quantify disorder effects close to the quantum phase transitions, e.g. through two-point correlation functions or using a renormalization group (RG) analysis of disorder. We show for the first time that the double critical Ising (DCI) phase -- a fractional Majorana liquid characterized by a pair of half central charges and topological numbers -- is stabilized by strong interactions against disorder which respects the inversion symmetry between the wires (ie. parity conservation on each wire). In the presence of an inter-wire hopping term, the DCI phase turns into a protected topological phase with a bulk gap. We study the localization physics developing along the critical line for weaker interactions.