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Applied Physics Letters

Phase coherence and disorder in Josephson-junction arrays

Miguel Octavio, C. B. Whan, Christopher J. Lobb

Published Feb 10, 1992• 41 citations
Publisher

Abstract

We present simulations of one- and two-dimensional Josephson-junction arrays to study the effects of disorder on the coherent oscillation of such arrays. For uniformity in the critical currents comparable to that which can be achieved with present technology, two-dimensional arrays are much more stable against disorder than one-dimensional arrays. Both systems are particularly sensitive to disorder when biased near the critical current, with stability increasing at currents farther above the critical current.

DOI
10.1063/1.106513

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We present simulations of one- and two-dimensional Josephson-junction arrays to study the effects of disorder on the coherent oscillation of such arrays. For uniformity in the critical currents comparable to that which can be achieved with present technology, two-dimensional arrays are much more stable against disorder than one-dimensional arrays. Both systems are particularly sensitive to disorder when biased near the critical current, with stability increasing at currents farther above the critical current.
Two-dimensional arrays of Josephson junctions have been shown to operate in a state in which the microwave oscillations of the junctions are phase-coherent. However, the performance of an array is strongly dependent on both the details of the load-coupling circuit and the characteristic parameters of the junctions. We have measured two-dimensional arrays of resistively shunted Josephson tunnel junctions which are capacitively coupled to a nearby detector junction. Changing the critical current of the junctions in our arrays, while keeping the junction parasitics and array coupling roughly the same, results in an unexpected change in device operation. We have also investigated variations of the coupling circuit. Numerical simulations of the detection circuit enable us to estimate the power output from the array and to optimize the parameters of the system.
We have investigated two-dimensional arrays of overdamped Josephson junctions that have been fabricated in Nb/Al/sub 2/O/sub 3//Nb-technology, together with microwave coupling structures. Different arrays have shown to emit coherent microwave radiation by using microwave-coupled on-chip detectors. Low-temperature scanning electron microscopy is used to study the coupling of the microwave radiation to an on-chip load. From the appearance of Shapiro steps in the current vs. voltage curves of detector junctions for different degrees of disorder in the array-junctions, margins of the spread in the critical currents of the Josephson junctions for coherent oscillation can be drawn.
The dynamics of the quasi-optical two-dimensional Josephson junction arrays for oscillators is investigated. Numerical time-domain simulations of small-scale parallel arrays were performed. It is found that the DC biasing circuit determines the states of these arrays. It is also found that other states exist in which parts of the array operate in phase. The authors investigate the sensitivity of in-phase states to variations in junction critical currents and to nonvanishing fluctuations. It is found that the DC self-field effects do not provide a stable phase-locking mechanism and that RF interactions are necessary for locking the array in phase.>
We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of EJ∕kB{E}_{J}∕{k}_{B}EJ​∕kB​ with the Josephson coupling strength EJ{E}_{J}EJ​), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent z=2.0z=2.0z=2.0 in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.
The results of numerical simulations of phase-locked 1D and 2D Josephson-junction arrays are reported. It is shown that the multi-junction structures with non-local junction interaction provide phase-locked oscillation state within wide critical current margins /spl Delta/I/sub c/ up to 40...50%. The effective non-local interaction in 2D structure based on 4-junction interferometer cell can be provided by the regular single flux quantum array flow across it. The wide tolerable spread in /spl Delta/I/sub c/ allows one to realize both (i) phase-locked 2D high-T/sub c/ Josephson-junction array with the oscillation frequency F close to characteristic value F/sub c/ and (ii) based on Nb tunnel Josephson-junction technology 1D array with the voltage-controlled phase-locked oscillation frequency within wide frequency band from 0.4 F/sub c/ to 1.2 F/sub c/.
The nonequilibrium phase transition of two-dimensional fully frustrated Josephson junction arrays driven by external currents is studied in the framework of the short-time dynamic scaling approach. Within the resistively shunted junction dynamics, besides the critical temperature Tc{T}_{c}Tc​, the static and dynamic critical exponents $2\ensuremath{\beta}∕\ensuremath{\nu}$, $\ensuremath{\nu}$, and zzz are obtained. The resulting values of Tc{T}_{c}Tc​ are consistent with previous steady-state simulations and decrease with the increase of currents. It is found that the values of the exponent $\ensuremath{\nu}$ are not sensitive to external currents, while the values of $2\ensuremath{\beta}∕\ensuremath{\nu}$ and zzz are strongly current dependent.