Breakdown of the escape dynamics in Josephson junctions

D. Massarotti, D. Stornaiuolo, P. Lucignano, L. Galletti, D. Born, G. Rotoli, F. Lombardi, L. Longobardi, A. Tagliacozzo, and F. Tafuri

Phys. Rev. B 92, 054501 – Published 3 August 2015

Abstract

We have identified anomalous behavior of the escape rate out of the zero-voltage state in Josephson junctions with a high critical current density $J_{c}$ . For this study we have employed ${YBa}_{2} {Cu}_{3} O_{7 - x}$ grain boundary junctions, which span a wide range of $J_{c}$ and have appropriate electrodynamical parameters. Such high $J_{c}$ junctions, when hysteretic, do not switch from the superconducting to the normal state following the expected stochastic Josephson distribution, despite having standard Josephson properties such as a Fraunhofer magnetic field pattern. The switching current distributions (SCDs) are consistent with nonequilibrium dynamics taking place on a local rather than a global scale. This means that macroscopic quantum phenomena seem to be practically unattainable for high $J_{c}$ junctions. We argue that SCDs are an accurate means to measure nonequilibrium effects. This transition from global to local dynamics is of relevance for all kinds of weak links, including the emergent family of nanohybrid Josephson junctions. Therefore caution should be applied in the use of such junctions in, for instance, the search for Majorana fermions.

Received 13 November 2014
Revised 29 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.054501

Authors & Affiliations

D. Massarotti^1,2,*, D. Stornaiuolo^1,2, P. Lucignano², L. Galletti^1,2, D. Born³, G. Rotoli⁴, F. Lombardi⁵, L. Longobardi^4,6, A. Tagliacozzo^1,2, and F. Tafuri^2,4

¹Universitá degli Studi di Napoli ”Federico II,” Dipartimento di Fisica, via Cinthia, 80126 Napoli, Italy
²CNR-SPIN UOS Napoli, Complesso Universitario di Monte Sant'Angelo, via Cinthia, 80126 Napoli, Italy
³Leibniz Institute of Photonic Technology e.V., P.O. Box 100239, D-07702 Jena, Germany
⁴Seconda Universitá di Napoli, Dipartimento di Ingegneria Industriale e dell'Informazione, via Roma 29, 81031 Aversa (Ce), Italy
⁵Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, S-41296 Göteborg, Sweden
⁶American Physical Society, 1 Research Road, Ridge, New York 11961, USA

^*dmassarotti@na.infn.it

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Vol. 92, Iss. 5 — 1 August 2015

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Images

Figure 1
(a) Three-dimensional representation of the SCDs measured for various temperatures on three GB YBCO JJs. (b) At low $J_{c}$ values ( $5 \times 10^{2} A / {cm}^{2}$ ), the SCDs of JCT A are confined to a small range of currents, with $σ$ of the order of 10 nA. With increasing $J_{c}$ the histograms progressively cover a larger interval of currents, both absolutely and relatively [JCTs B and C in (c) and (d) respectively]. In (e) the escape rate curves $Γ (I)$ computed from the SCDs of JCT C have been shown for the same temperature range as in (d).
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Figure 2
(a) Temperature dependence of $σ$ measured on GB JCTs A (blue squares), B (red triangles), and C (black points) respectively. The blue and red solid lines are Monte Carlo simulations of the phase dynamics, according to multiple escape and retrapping processes in the washboard potential [shown in (b)], with $Q = 1.30$ and 1.17 for JCTs A and B respectively. Some data from sample A have been presented in Ref. [40] previously. (c) Simulations of the thermal dependence of $σ$ as a function of $J_{c}$ for different values of the $Q$ damping parameter (full color lines), confined to the moderately damped regime, are compared with experimental data of JCT C (black points). Keeping all the other junction parameters fixed, an enhancement of $J_{c}$ leads to an increase of $I_{c}$ and $Q$ . An increase in $Q$ produces steeper $σ$ tails above $T^{*}$ and cannot reproduce the broadened experimental data of JCT C. This is even more evident in the two-dimensional ( $σ - T$ ) projection. For completeness, in the ( $σ - T$ ) projection the color points referred to the results of Monte Carlo simulations have been reported for $Q$ values ranging 1–10, and compared with the data of JCT C (black points). The colored lines are guides for the eye. At high $J_{c}$ the Langevin approach does not hold anymore and nonequilibrium concepts apply. Simulations fitting the SCDs of JCT C (see Fig. 4) are consistent with multiple heating events as reported pictorially in (d). As explained in the text, $T_{b}$ is the bath temperature and $T_{th}$ is the threshold temperature above which the transition to the resistive state occurs. In (d) the arrows qualitatively sketch the temperature jump due to a single heating event and the number of events necessary to induce the switching to the resistive state.
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Figure 3
Temperature dependence of the skewness $γ$ of the SCDs measured on JCTs B (red triangles) and C (black circles) respectively. Retrapping processes in the PD regime cause a progressive symmetrization of the SCDs of JCT B, signaled by the thermal dependence of $γ$ , which is almost 0 above the transition temperature $T^{*}$ . Asymmetric SCDs, as the histogram measured at $T = 0.1 K < T^{*}$ (shown in the top left corner of the figure), become Gaussian-like distributions above $T^{*}$ (see the histogram measured at $T = 4 K > T^{*}$ in the top right corner). The histograms of JCT C are asymmetric over the whole temperature range, including for temperatures above $T^{* *}$ (as shown by the SCD measured at $T = 7$ K reported in the lower right corner of the figure). The black dashed line indicates the mean value of the skewness ( $γ ≃ - 0.8$ ).
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Figure 4
(a) SCDs measured on JCT C (black circles) along with the fit (red solid lines) resulting from numerical simulations of heat-diffusion-like dynamics, according to Eq. (1). (b) Fitting procedure above $T^{* *}$ : single heating event dynamics does not reproduce the experimental histogram, signaling a multiple PSE process. Dissipation due to heat relaxation plays a relevant role. (c) Temperature dependence of $T_{eff}$ estimated from numerical simulations of Eq. (1). Below $T^{* *}$ , a single heating event induces the switching and $T_{eff} > T_{b}$ . Above $T^{* *}, T_{eff}$ and $T_{b}$ coincide since the system is able to thermalize in the time interval between well separated heating events, and multiple PSEs are needed to overcome $T_{th}$ .
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