Manipulating the topological spin of Majoranas

TL;DR

This paper explores how the topological spin of Majorana zero modes, related to their Abelian exchange phase, can be manipulated via device geometry, offering new control methods for topological quantum computing.

Contribution

It demonstrates that the fractional charge and topological spin of Majoranas can be controlled by device geometry, introducing a new knob for quantum manipulation.

Findings

Fractional charge can be manipulated through device geometry.

Vortex interference experiments can detect shifts due to fractional charge.

Topological spin is tunable via device design.

Abstract

The non-Abelian exchange statistics of Majorana zero modes make them interesting for both technological applications and fundamental research. Unlike their non-Abelian counterpart, the Abelian contribution, $e^{i\theta}$, where $\theta$ is directly related to the Majorana's topological spin, is often neglected. However, the Abelian exchange phase and hence the topological spin can differ from system to system. For vortices in topological superconductors, the Abelian exchange phase is interpreted as an Aharonov-Casher phase arising from a vortex encircling a $e/4$ charge. In this work, we show how this fractional charge, and hence the topological spin, can be manipulated through the control of device geometry, introducing an additional control knob for topological quantum computing. To probe this effect, we propose a vortex interference experiment that reveals the presence of this fractional charge through shifts in the critical current.