# Disorder robustness and protection of Majorana bound states in ferromagnetic chains on conventional superconductors

## TL;DR

This paper demonstrates that Majorana bound states in ferromagnetic chains on superconductors are highly robust against disorder, especially in longer chains, with implications for quantum computing stability.

## Contribution

The study provides a self-consistent analysis showing the robustness of MBS against disorder and how chain length and material parameters influence their stability.

## Key findings

- MBS are protected against disorder in homogeneous superconductors.
- Longer chains enhance MBS stability despite a decreasing minigap.
- Increased spin-orbit coupling and superconductivity reduce the minigap.

## Abstract

Majorana bound states (MBS) are well-established in the clean limit in chains of ferromagnetically aligned impurities deposited on conventional superconductors with finite spin-orbit coupling. Here we show that these MBS are very robust against disorder. By performing self-consistent calculations we find that the MBS are protected as long as the surrounding superconductor show no large signs of inhomogeneity. We find that longer chains offer more stability against disorder for the MBS, albeit the minigap decreases, as do increasing strengths of spin-orbit coupling and superconductivity.