Disorder effects on Majorana zero modes: Kitaev chain versus semiconductor nanowire

TL;DR

This paper compares how disorder impacts Majorana zero modes in the Kitaev chain and semiconductor nanowires, revealing that disorder effects are system-dependent and more pronounced in nanowires, especially at weak to intermediate levels.

Contribution

It provides a comparative analysis of disorder effects on Majorana modes in the Kitaev chain and nanowires, highlighting nonuniversal behavior in intermediate disorder regimes.

Findings

Disorder affects nanowires more strongly than Kitaev chains.

Strong disorder leads to universal Anderson localization in both systems.

Intermediate disorder regimes are nonuniversal and system-dependent.

Abstract

Majorana zero modes in a superconductor-semiconductor nanowire have been extensively studied during the past decade. Disorder remains a serious problem, preventing the definitive observation of topological Majorana bound states. Thus, it is worthwhile to revisit the simple model, the Kitaev chain, and study the effects of weak and strong disorder on the Kitaev chain. By comparing the role of disorder in a Kitaev chain with that in a nanowire, we find that disorder affects both systems but in a nonuniversal manner. In general, disorder has a much stronger effect on the nanowire than the Kitaev chain, particularly for weak to intermediate disorder. For strong disorder, both the Kitaev chain and nanowire manifest random featureless behavior due to universal Anderson localization. Only the vanishing and strong disorder regimes are thus universal, manifesting respectively topological superconductivity and Anderson localization, but the experimentally relevant intermediate disorder regime is nonuniversal with the details dependent on the disorder realization in the system.