Josephson junction with magnetic-field tunable current-phase relation

TL;DR

This paper analyzes a Josephson junction with asymmetric regions, demonstrating how its current-phase relation can be tuned by magnetic field, including a negative second harmonic and a field-dependent term, leading to an electronically tunable junction.

Contribution

It introduces a model for a magnetic-field tunable current-phase relation in asymmetric 0-$ extpi$ Josephson junctions, including a novel field-dependent term.

Findings

Effective current-phase relation includes sin(ψ), sin(2ψ), and H cos(ψ) terms.

Magnetic field H can tune the current-phase relation.

At H=0, the junction behaves as a φ Josephson junction.

Abstract

We consider a 0-$\pi$ Josephson junction consisting of asymmetric 0 and $\pi$ regions of different lengths $L_0$ and $L_\pi$ having different critical current densities $j_{c,0}$ and $j_{c,\pi}$. If both segments are rather short, the whole junction can be described by an \emph{effective} current-phase relation for the spatially averaged phase $\psi$, which includes the usual term $\propto\sin(\psi)$, a \emph{negative} second harmonic term $\propto\sin(2\psi)$ as well as the unusual term $\propto H \cos\psi$ tunable by magnetic field $H$. Thus one obtains an electronically tunable current-phase relation. At H=0 this corresponds to the $\varphi$ Josephson junction.