# Detecting Majorana modes through Josephson junction ring-quantum dot hybrid architectures

## TL;DR

This paper proposes a Josephson junction ring with a quantum dot as a sensitive probe for detecting Majorana zero modes, highlighting how flux periodicity changes reveal Majorana physics and parity effects.

## Contribution

It introduces a novel hybrid architecture combining Josephson junction rings and quantum dots to detect and manipulate Majorana modes through flux and parity control.

## Key findings

- Majorana modes induce $4 extpi$ periodicity in Josephson junction rings.
- Increasing the number of islands enhances the visibility of Majorana signatures.
- Quantum dot occupation tuning enables control over groundstate parity and flux periodicity.

## Abstract

Unequivocal signatures of Majorana zero energy modes in condensed matter systems and manipulation of the associated electron parity states are highly sought after for fundamental reasons as well as for the prospect of topological quantum computing. In this Letter, we demonstrate that a ring of Josephson coupled topological superconducting islands threaded by magnetic flux and attached to a quantum dot acts as an excellent parity-controlled probe of Majorana mode physics. As a function of flux threading through the ring, standard Josephson coupling yields a $\Phi_0=h/(2 e)$ periodic features corresponding to $2\pi$ phase difference periodicity. In contrast, Majorana mode assisted tunneling provides additional features with $2\Phi_0$ ($4\pi$ phase difference) periodicity, associated with single electron processes. We find that increasing the number of islands in the ring enhances the visibility of the desired $4\pi$ periodic components in the groundstate energy. Moreover as a unique characterization tool, tuning the occupation energy of the quantum dot allows controlled groundstate parity changes in the ring, enabling a toggling between $\Phi_0$ and $2\Phi_0$ periodicity.