Benefits of weak disorder in one dimensional topological superconductors

TL;DR

This paper reveals that weak disorder can enhance the robustness of Majorana bound states in 1D topological superconductors by decreasing their localization length, contrary to typical disorder effects, with implications for Josephson junction systems.

Contribution

It demonstrates that weak disorder can reduce Majorana localization length, increasing topological phase stability, and identifies the disorder strength at which the phase transition occurs.

Findings

Weak disorder decreases Majorana localization length.

Topological phase becomes more robust under weak disorder.

Phase transition occurs at high localization length compared to mean-free path.

Abstract

Majorana bound states are zero-energy modes localized at the ends of a one-dimensional (1D) topological superconductor. Introducing disorder usually increases the Majorana localization length, until eventually inducing a topological phase transition to a trivial phase. In this work we show that in some cases weak disorder causes the Majorana localization length to decrease, making the topological phase more robust. Increasing the disorder further eventually leads to a change of trend and to a phase transition to a trivial phase. Interestingly the transition occurs at $\xi_0\gg l$, where $l$ is the disorder mean-free path and $\xi_0$ is the localization length in the clean limit. Our results are particularly relevant to a 1D topological superconductors formed in planar Josephson junctions.