Dynamical Properties of Weakly Coupled Josephson Systems
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DYNAMICAL PROPERTIES OF WEAKLY COUPLED JOSEPHSON SYSTEMS K. H. LEE, T.-K. XIA, AND D. STROUD Department of Physics, Ohio State University, Columbus, OH 43210, U. S. A. ABSTRACT We review recent work on the dynamical behavior of coupled resistively-shunted Josephson junctions, with emphasis on our own calculations. We present a model which allows for the inclusion of finite temperature, disorder, d.c. and a. c. applied currents, and applied magnetic fields. We discuss applications to (a) calculations of critical currents and IV characteristics; (b) harmonic generation and microwave absorption by finite clusters of Josephson junctions; (c) critical energies for vortex depinning; and (d) quantized voltage plateaus in arrays subjected to combined d.c. and a. c. currents. Possible connections to the behavior of granular high-temperature superconductors are briefly discussed. INTRODUCTION The physical properties of granular superconductors have been of interest since the pioneering work of B. Abeles and his collaborators in the early 1970's[1]. Interest has grown in recent years for a variety of reasons. First, it has been realized that many nominally homogeneous superconductors in fact show many attributes of granularity. In particular, there is considerable evidence that even nominally single crystal samples of the high-Tc superconductors discovered by Bednorz and Miller are often studded with grain and twin boundaries which behave very much like superconducting weak links[2]. These weak links may have something to do with the strange time-dependent magnetization of high-temperature superconductors, which has been variously attributed to glassy behavior[3], giant flux creep[4], and flux lattice melting[5]. Secondly, with recent advances in microfabrication technology, it has been possible to make artificial "granular materials," with controlled particle sizes, disorder, etc., which permit one to study systematically the physical properties of such disordered materials. In this paper, we will briefly review the dynamical response of granular superconductors viewed as collections of coupled weak links. Many of the calculations have been published before, some by members of our group and some by other groups[6,7,8], but several calculations are quite new. MODEL We consider a possibly disordered collection of N superconducting grains. The ith grain is assumed to be coupled to the jth by a Josephson junction in parallel with a shunt resistance. The current from grain i to grain j is thus given by Iii
ii Ic.,ij siin(q, -- b) + +R•-.(1)
where 4i is the time-dependent phase of the superconducting order parameter on the i'h grain, I.;ij is the critical current of the junction between grains i and j, Vi - Vi- Vj is the
Mat. Res. Soc. Symp. Proc. Vol. 195. 01990 Materials Research Society
348
voltage drop between grains i and j, and Rij is the shunt resistance between these grains. The voltage drop across the junction is related to the phase difference by the Josephson relation
d
2e(Vi--V)
(2)
These equations are to be
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