Adiabatic nonabelian braiding of imperfect Majoranas

TL;DR

This paper investigates how nonabelian braiding of Majorana bound states is affected by imperfections like disorder, proposing a compensation method that preserves nonabelian statistics in realistic, imperfect systems.

Contribution

It introduces a protocol to compensate for splitting in imperfect Majorana bound states, maintaining their nonabelian braiding properties despite system imperfections.

Findings

Braiding outcomes depend on MBS isolation degree

The protocol remains robust against imperfections

Nonabelian statistics are preserved except in the perfect fermion limit

Abstract

Demonstration of a nontrivial result of quasiparticle exchange (or braiding) is usually considered the definitive proof of a topological phase with nonabelian excitations, such as Majorana bound states (MBSs). However, in finite systems with disorder and smooth potential variations, the MBSs are imperfect in the sense that they are not fully isolated in space and can, to a varying degree, resemble conventional fermions. Here, we study the braiding properties of isolated MBSs, regular fermions, and anything in between. We find a way to compensate for the undesired splitting of the ground-state degeneracy which occurs during the protocol for imperfect MBS. This leads to a braiding outcome that depends on the degree of MBS isolation but remains robust and nonabelian except in the perfect fermion limit. Our protocol could be implemented in different platforms with nonabelian excitations, including quantum-dot-based minimal Kitaev chains.