Spontaneous fluxon production in annular Josephson tunnel junctions in the presence of a magnetic field

We report on the spontaneous production of fluxons in annular Josephson tunnel junctions during a thermal quench in the presence of a symmetry-breaking magnetic field. The dependence on field intensity $B$ of the probability ${\overline{f}}_1$ to trap a single defect during the $N\text{−}S$ phase transition depends drastically on the sample circumferences. We show that this can be understood in the framework of the same picture of spontaneous defect formation that leads to the experimentally well attested scaling behavior of ${\overline{f}}_1$ with quench rate in the absence of an external field.

Figure 1

(Color online) Log-log plot of the frequency ${\overline{f}}_1$ of trapping single fluxons versus the quenching time ${\tau }_Q$ for an AJTJ of circumference $0.5\mathrm{mm}$ (closed circles) and for an AJTJ with circumference $1.5\mathrm{mm}$ (closed squares). The best fits through the data (solid and dashed lines) show that scaling with $\sigma =0.5$ is totally robust. Both samples had equal critical current density $J_c$.

Figure 2

(Color online) Dependence of the single fluxon trapping frequency ${\overline{f}}_1$ for quench time ${\tau }_Q=5\mathrm{s}$ for an AJTJ of circumference $C=0.5\mathrm{mm}$ in the presence of a magnetic field $B$ perpendicular to the barrier plane. The solid line corresponds to the case $N=1$ in ${\overline{f}}_1(N,\overline{n})$ of Fig. 5, as derived from Eq. (22).

Figure 3

(Color online) Dependence of ${\overline{f}}_1$ for quench time ${\tau }_Q=5\mathrm{s}$ for an AJTJ of circumference $C=2.0\mathrm{mm}$ in the presence of a magnetic field $B$ perpendicular to the barrier plane. The solid line corresponds to the case $N=16$ in ${\overline{f}}_1(N,\overline{n})$ of Fig. 5, as derived from Eq. (22).

Figure 4

(Color online) We display the probabilities ${\overline{f}}_1=f_1+f_{-1}$ as a function of $N$, as given by Eqs. (16, 17) (dashed and dotted lines), respectively; the dots are the values of ${\overline{f}}_1$ according to the independent sector model for some integer values of $N$ from Eq. (3). The maximum of ${\overline{f}}_1$ occurs at $N=N_c\approx 10.5$, for which value ${\overline{f}}_1\approx 49\%$. The inset shows the probability ${\overline{f}}_0$ as a function of $N$, as given by Eq. (6), essentially indistinguishable from that by Eq. (19) at this scale.

Figure 5

(Color online) The values of ${\overline{f}}_1(N,\overline{n})$ as a function of $\overline{n}$ for fixed $N$ for several values of $N$; $N=1$, 2, 4, 8, and 16, according to Eq. (22).