Robustness of vortex-bound Majorana zero modes against correlated disorder

TL;DR

This paper studies how correlated disorder impacts Majorana zero modes in 2D topological superconductors, revealing that disorder correlation length significantly influences the stability of these modes.

Contribution

It provides a detailed analysis of the effects of correlated disorder on MZMs, including perturbative and numerical methods, highlighting the importance of disorder correlation length.

Findings

Correlated disorder strongly affects MZMs compared to uncorrelated disorder.

MZMs are more resilient when disorder correlation length is much smaller than the coherence length.

MZMs can survive strong disorder if the disorder correlation length exceeds the coherence length.

Abstract

We investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a $p_x \pm i p_y$ superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length $\ell$ is on the same order as the superconducting coherence length $\xi$. In contrast, MZMs can survive stronger disorder for $\ell \ll \xi$ as random variations cancel each other within the length scale of $\xi$, while an MZM may survive up to very strong disorder for $\ell \gg \xi$ if it is located in a favorable domain of the given disorder realization.