Fusion rules in a Majorana single-charge transistor

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.

14+10 pages, 4+3 figures

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Cited by in corpus (3)

• Progress in superconductor-semiconductor topological Josephson junctions
• Full counting statistics in a Majorana single-charge transistor
• Creating and detecting poor man's Majorana bound states in interacting quantum dots