Experiments on spontaneous vortex formation in Josephson tunnel junctions

It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss an improved experiment for measuring the scaling exponent $\sigma$ for the production of single fluxons in annular symmetric Josephson tunnel junctions. We find $\sigma \simeq 0.5$ and show how this can arise from the Kibble-Zurek scenario. Further, we report accurate measurements of the temperature dependence of the junction gap voltage, which allow for precise monitoring of the fast temperature variations during the quench.

Figure 1

Layout of the $4.2\times 3{\mathrm{mm}}^2$ Si chip containing four series-biased $\mathrm{Nb}\text{−}\mathrm{Al}∕{\mathrm{AlO}}_x∕\mathrm{Nb}$ Josephson tunnel junctions. It integrates three ring-shaped junctions having a mean circumference $C=500\mathrm{\mu }\mathrm{m}$ and a width $\mathrm{\Delta }r=4\mathrm{\mu }\mathrm{m}$, one $4\times 500\mathrm{\mu }{\mathrm{m}}^2$ overlap-type linear junction, and two meander line resistive Mo strips used for heating.

Figure 2

Sketch (not in scale) of two geometries for the annular Josephson tunnel junctions used for the Kibble-Zurek experiment. The junction base and top electrodes are shown in dark and light gray, respectively. In (a) the annular junction is obtained by the superposition of two superconducting rings, while in (b) it is realized by the superposition of a ring-shaped superconducting top electrode over a superconducting plane base electrode.

Figure 3

The temperature dependence of gap voltage $V_g$. The open circles are the experimental data with the junction biased at 25% of the total current jump at the gap voltage; the solid line is the prediction that follows from Eq. (4). The fit yields $T_C=9.12\pm 0.04\mathrm{K}$ and $V_g(T=0)=2.89\pm 0.02\mathrm{mV}$.

Figure 4

Log-log plot (base 10) of the measured frequency $f_1$ of trapping single fluxons versus the quenching time ${\tau }_Q$. Each point corresponds to many thermal cycles, closed squares for sample 22-4, closed triangles for sample 08-3, and closed circles for sample 08-4. The vertical error bars give the statistical error while the relative error bars in ${\tau }_Q$ amounting to $\pm 10\%$ are as large as the dots’ width. The solid line is the fit of all data to an allometric relationship $f_1=a{\tau }_Q^{-b}$ which yields $a=0.01\pm 10\%$ (taking ${\tau }_Q$ in seconds) and $b=0.51\pm 5\%$. The open stars represent the data obtained in a previous experiment (Refs. 1, 2).