# Stability of Disordered Topological Superconducting Phases in Magnet--Superconductor Hybrid Systems

## TL;DR

This paper studies how different types of disorder affect the stability of topological superconducting phases in magnet-superconductor hybrid systems, revealing varying degrees of robustness and the impact on topological invariants.

## Contribution

It provides a comprehensive analysis of the effects of potential and magnetic disorder on topological phases, including the correlation between disorder structure and topological properties.

## Key findings

- Potential disorder weakly suppresses topological phases.
- Percolation disorder strongly suppresses topological phases.
- Disorder affects the spatial distribution of the Chern number density.

## Abstract

Magnet-superconductor hybrid heterostructures constitute a promising candidate system for the quantum engineering of chiral topological superconductivity. Here, we investigate the stability of their topological phases in the presence of various types of potential and magnetic disorder. In particular we consider magnetic disorder in the coupling strength and spin-orientation, as well as percolation type disorder representing missing magnetic moments. We show that potential disorder leads to the weakest suppression of topological phases, while percolation disorder leads to their strongest suppression. In addition, we demonstrate that in the case of correlated potential disorder, the spatial structure of the disorder potential is correlated not only with the particle number density, but also the Chern number density. Finally, we demonstrate how the disorder-induced destruction of topological superconductivity is reflected in the spatial structure and distribution of the Chern number density.