Zurek-Kibble Mechanism for the Spontaneous Vortex Formation in $Nb-Al/Al_{ox}/Nb$ Josephson Tunnel Junctions: New Theory and Experiment

TL;DR

This paper presents a new theoretical and experimental study of the Zurek-Kibble mechanism in Josephson tunnel junctions, demonstrating a scaling law for fluxon formation with a specific exponent, confirming theoretical predictions.

Contribution

The paper introduces a refined theory and provides the first reliable experimental measurement of the scaling exponent in fluxon formation during phase transitions in Josephson junctions.

Findings

Confirmed the scaling exponent $\sigma = 0.5$ experimentally.

Replaced earlier idealized model with realistic strong-coupling predictions.

First reliable measurement of fluxon formation scaling in condensed matter.

Abstract

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched $Nb-Al/Al_{ox}/Nb$ annular Josephson tunnel junctions as a function of the quench time, $\tau_{Q}$. The probability $f_{1}$ to trap a single defect during the N-S phase transition clearly follows an allometric dependence on $\tau_{Q}$ with a scaling exponent $\sigma = 0.5$, as predicted from the Zurek-Kibble mechanism for {\it realistic} JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealised model was used that predicted $\sigma = 0.25$, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability.