Novel axisymmetric coherent vortex state in arrays of Josephson junctions far from equilibrium

Abstract

We present a numerical study of a topologically disordered, overdamped, array of Josephson junctions subjected to dc and ac currents. We find that vortices are nucleated by the ac current, apart from the ones produced at defects. After a complex transient, these vortices settle into a parity-broken timeperiodic, axisymmetric coherent vortex state characterized by rows of vortices lying along a tilted axis. This locked-in state leads to giant half-integer pseudosteps in the I-V characteristics that are hysteretic in nature. Possible connections of these results to recent experiments are discussed. PACS numbers: 74.50.+r, 74.60.Jg, 85.25.Dq Arrays of Josephson junctions (AJJ) have been the subject of considerable recent interest, both theoretically and experimentally [1]. Many of the early studies in AJJ were aimed at testing the predictions of the equilibrium long-range phase-coherent transitions expected to take place in these systems [2]. More recently, novel phenomena have been discovered in the dynamic responses of the arrays subject to time-dependent periodic probes. Giant Shapiro steps (GSS) in the I-V characteristics of periodic proximity-effect AJJ have been measured in zero [3] and rational frustration magnetic fields [4]. These results have led to a series of numerical and analytic analyses that have for the most part been successful in explaining the GSS results [5,6]. One exception is the recent report of half-integer pseudosteps seen in Nb-Au-Nb AJJ [7].In this paper we present results that yield half-integer pseudosteps that may be related to these experiments.Here we study the dynamics of defect and currentnucleated vortices as a result of a current / a = /dc + /ac xsin(2>rw), applied uniformly from the bottom of the AJJ along the y direction. The formation of vortex pairs by defects in a dc current at zero temperature was studied recently by Leath and Xia [8]. These authors emphasize the formation of these excitations as an example of breakdown phenomena. The new element in our investigation is that of adding an ac current to the study of the dynamics of the defect-generated vortices in AJJ. It turns out that adding an ac current changes the physics in a fundamental way as we shall discuss below. We have studied the dynamics of the AJJ when we have one, two, three, or all the lattice sites randomly displaced from their periodic positions. We have found that after a transient time that depends on the number of defects, the dynamics tends to a nonequilibrium time-periodic state with a well-defined vortex geometric structure that is qualitatively and to some extent quantitatively independent of the nature and number of defects in the system. This novel state leads to half-integer giant pseudosteps in the I-V characteristic. This state is in many respects different in nature from the GSS mentioned above and we shall call it an axisymmetric coherent vortex state (ACVS). Since the existence of the ACVS does not appear to depend qualitatively on the number of defects in the lattice, most of our discussion...

Paramagnetic Meissner effect and related dynamical phenomena

“…The system of differential equations (7.5) is integrated numerically by a second order Runge-Kutta-HelfandGreenside algorithm for stochastic differential equations [287]. The time step is chosen to depend onL and is equal to ∆t = 0.1τ J and ∆t = 0.1τ J ×L forL > 1 and L < 1, respectively.…”

Current-voltage characteristics of diluted Josephson-junction arrays: Scaling behavior at current and percolation threshold

“…The nodes are located at r = mx + nŷ with unit lattice constant. The current I µ (r) flowing between r and r +μ, is modeled as 6,19,20 …”

Mode-locking transitions and vortex flows in current-driven Josephson-junction arrays

“…However, using the special properties of G 0 Ϫ1 , faster algorithms have been evolved wherein the above multiplication is carried out in O(N lnN) steps or faster. 31,32 Fast algorithms have also been developed for the case of busbars and defects in the form of missing bonds. 33 For small arrays with only a few plaquettes, we use the direct O(N 2 ) algorithm.…”