# Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor

## TL;DR

This paper proposes an electrical measurement scheme to observe the non-Abelian fusion rule of Majorana zero-modes in a topological superconductor using chiral edge vortices and Josephson junctions, revealing fusion statistics through charge transfer noise correlations.

## Contribution

It introduces a novel electrical detection method for the Majorana fusion rule via chiral edge vortices and Josephson junctions, linking topological qubit states to measurable current noise.

## Key findings

- Fusion results in correlated charge transfer with zero or one electron per cycle.
- Current difference between junctions is nearly noiseless, indicating fusion statistics.
- The scheme provides a practical way to detect Majorana fusion rules electrically.

## Abstract

Majorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they may not produce an unpaired fermion with equal probability. Building on a recent proposal to inject edge vortices in a chiral mode by means of a Josephson junction, we show how the fusion rule manifests itself in an electrical measurement. A $2\pi$ phase shift at a pair of Josephson junctions creates a topological qubit in a state of even-even fermion parity, which is transformed by the chiral motion of the edge vortices into an equal-weight superposition of even-even and odd-odd fermion parity. Fusion of the edge vortices at a second pair of Josephson junctions results in a correlated charge transfer of zero or one electron per cycle, such that the current at each junction exhibits shot noise, but the difference of the currents is nearly noiseless.