Effect of impurities and disorder on the braiding dynamics of Majorana zero modes

TL;DR

This paper investigates how impurities and disorder influence the braiding dynamics of Majorana zero modes, revealing that under certain conditions, disorder can unexpectedly enhance braiding performance despite generally causing errors.

Contribution

It provides a quantitative analysis of the effects of single impurities and random disorder on MZM braiding, highlighting scenarios where disorder can improve braiding outcomes.

Findings

Impurities generally increase hybridization, reducing braiding fidelity.

A disorder window exists where braiding energy decreases, improving outcomes.

Disorder can sometimes beneficially affect braiding despite increased diabatic effects.

Abstract

Impurities and random disorder are known to affect topological superconducting phases and their Majorana zero modes (MZMs). In particular, it is a common assumption that disorder negatively influences the braiding dynamics of MZMs. Recently, it was shown, however, that random disorder can also stabilize or even increase topological phases. Here, we investigate quantitatively how a single impurity can lead to braiding errors. We show that the impurity increases, in most scenarios, the dynamical hybridization of the MZMs, reducing the braiding performance. In addition, we show how random disorder, i.e., impurities on all lattice sites but with different strengths, affects braiding. As for the static case, we observe a window of opportunity where random disorder decreases the average energy of a braid, and thus improves braiding outcomes. This window of opportunity is, however, limited due to an increase of diabatic effects in the presence of disorder. Nevertheless and contrary to physical intuition, disorder can in certain situations be beneficial and improve braiding outcomes.