Fractional Josephson effect in a quadruple quantum dot

TL;DR

This paper proposes a method to generate fractional Josephson effects with periods of 4-pi, 8-pi, and 12-pi using coupled double quantum dots hosting Majorana fermions, highlighting robustness against parameter perturbations.

Contribution

It introduces a novel setup of coupled double quantum dots to realize fractional Josephson effects with extended periods, advancing understanding of Majorana-based quantum phenomena.

Findings

Demonstrates 4-pi, 8-pi, and 12-pi Josephson effects in coupled double dots.

Shows robustness of fractional effects against parameter perturbations.

Provides a new platform for exploring Majorana fermion physics.

Abstract

A double quantum dot coupled to an s-wave superconductor and subject to an inhomogeneous magnetic field can host a pair of zero-energy Majorana fermions when the dot properties are tuned appropriately. Here, we demonstrate the possibility to generate a fractional 4-pi Josephson effect in two such double dots tunnel-coupled to each other. We discuss the robustness of this effect with respect to perturbations away from the special point in parameter space where the uncoupled double dots host Majorana fermions. We demonstrate the possibility to generate Josephson effects with a period of 8-pi and 12-pi in strongly-coupled double dots.