Fusion rules in a Majorana single-charge transistor

TL;DR

This paper proposes a simplified method to demonstrate Majorana bound state fusion rules in a single-charge transistor, enabling experimental verification of non-abelian anyons through charge pumping and DC current measurement.

Contribution

It introduces a more efficient device design and protocol for observing MBS fusion rules, reducing complexity and operational steps compared to previous approaches.

Findings

Fusion rules can be demonstrated via charge pumping in a simplified device.

The protocol's timescales and signals are experimentally feasible.

Numerical and analytical analysis confirms the protocol's effectiveness.

Abstract

A demonstration of the theoretically predicted non-abelian properties of Majorana bound states (MBSs) would constitute a definite proof of a topological superconducting phase. Alongside the nontrivial braiding statistics, the fusion rules are fundamental properties of all non-abelian anyons. In this work, we propose and theoretically analyze a way to demonstrate MBS fusion rules in a Majorana single-charge transistor. Our proposal reduces both the number of operations and the device complexity compared to previous designs. Furthermore, we show that the fusion protocol can be adapted to pump a quantized amount of charge in each cycle, providing a straightforward method to detect fusion rules through a DC current measurement. We analyze the protocol numerically and analytically and show that the required operational timescales and expected measurement signals are within experimental capabilities in various superconductor-semiconductor hybrid platforms.