Disorder Protected and Induced Local Zero-Modes in Longer-Range Kitaev Chains

TL;DR

This paper investigates how disorder affects longer-range Kitaev chains, revealing stability regions, disorder-induced zero-modes, and phase transitions, with implications for local qubit coherence in disordered topological systems.

Contribution

It introduces a semi-analytic and numerical analysis of disorder effects on longer-range Kitaev chains, highlighting disorder-induced zero-modes and phase boundary modifications.

Findings

2 MZM region is stable under moderate disorder

Disorder can induce local zero-modes absent in clean systems

Disorder destroys direct phase transitions, creating a tricritical point

Abstract

We study the effects of disorder on a Kitaev chain with longer-range hopping and pairing terms which is capable of forming local zero energy excitations and, hence, serves as a minimal model for localization-protected edge qubits. The clean phase diagram hosts regions with 0, 1, and 2 Majorana zero-modes (MZMs) per edge. Using a semi-analytic approach corroborated by numerical calculations of the entanglement degeneracy, we show how phase boundaries evolve under the influence of disorder. While in general the 2 MZM region is stable with respect to moderate disorder, stronger values drive transition towards the topologically trivial phase. We uncover regions where the addition of disorder induces local zero-modes absent for the corresponding clean system. Interestingly, we discover that disorder destroys any direct transition between phases with zero and two MZMs by creating a tricritical point at the 2-0 MZM boundary of the clean system. Finally, motivated by recent experiments, we calculate the characteristic signatures of the disorder phase diagram as measured in dynamical local and non-local qubit correlation functions. Our work provides a minimal starting point to investigate the coherence properties of local qubits in the presence of disorder.