Effect of inductive and capacitive coupling on the current–voltage characteristic and electromagnetic radiation from a system of Josephson junctions

We have studied the current–voltage characteristic of a system of long Josephson junctions taking into account the inductive and capacitive coupling. The dependence of the average time derivative of the phase difference on the bias current and spatiotemporal dependences of the phase difference and magnetic field in each junction are considered. The possibility of branching of the current–voltage characteristic in the region of zero field step, which is associated with different numbers of fluxons in individual Josephson junctions, is demonstrated. The current–voltage characteristic of the system of Josephson junctions is compared with the case of a single junction, and it is shown that the observed branching is due to coupling between the junctions. The intensity of electromagnetic radiation associated with motion of fluxons is calculated, and the effect of coupling between junctions on the radiation power is analyzed.     

Current mirror effect and correlated cooper-pair transport in coupled arrays of small Josephson junctions

We have measured the transport properties of capacitively coupled one-dimensional arrays of small aluminum Josephson junctions. Under suitable biasing conditions, the samples act as current mirrors; the currents in the two arrays couple to each other and become equally large. The coupling is found both for currents flowing in the same direction and in opposite directions. We have also measured the time dependent fluctuations of the currents in the two arrays, and we find a strong correlation or anticorrelation of the fluctuations depending on the relative direction of the two currents.     

Tunneling in superconducting structures

Here we review our results on the breakpoint features in the coupled system of IJJ obtained in the framework of the capacitively coupled Josephson junction model with diffusion current. A correspondence between the features in the current voltage characteristics (CVC) and the character of the charge oscillations in superconducting layers is demonstrated. Investigation of the correlations of superconducting currents in neighboring Josephson junctions and the charge correlations in neighboring superconducting layers reproduces the features in the CVC and gives a powerful method for the analysis of the CVC of coupled Josephson junctions. A new method for determination of the dissipation parameter is suggested.     

Diffusion current in a system of coupled Josephson junctions

The role of a diffusion current in the phase dynamics of a system of coupled Josephson junctions (JJs) has been analyzed. It is shown that, by studying the temporal dependences of the superconducting, quasi-particle, diffusion, and displacement currents and the dependences of average values of these currents on the total current, it is possible to explain the main features of the current-voltage characteristic (CVC) of the system. The effect of a diffusion current on the character of CVC branching in the vicinity of a critical current and in the region of hysteresis, as well as on the part of CVC branch corresponding to a parametric resonance in the system is demonstrated. A clear interpretation of the differences in the character of CVC branching in a model of capacitively coupled JJs (CCJJ model) and a model of capacitive coupling with diffusion current (CCJJ+DC model) is proposed. It is shown that a decrease in the diffusion current in a JJ leads to the switching of this junction to an oscillating state. The results of model calculations are qualitatively consistent with the experimental data.     

Staircase Structure of Shapiro Steps

We investigate IV-characteristics of coupled Josephson junctions which model the intrinsic Josephson junctions in high temperature superconductors under external electromagnetic radiation. A staircase structure of Shapiro steps is found in the branching region. Its origin is related to the coupling between junctions and their switching from rotating to oscillating states. This conclusion is tested by detailed analysis of the IV-characteristics as for total stack and for each junction in the stack. IV-curves of junctions in the stack are compared with the average of time derivative of phase difference. Experimental observation of this staircase structure would give us a proof of coupling between junctions and a way for precise measurement of its value. Such investigations would be also useful for a diagnostic of Josephson junctions in the stack.     

New features in collective dynamics of intrinsic Josephson junctions

We discuss the breakpoint phenomenon, which reflects a resonance between Josephson and plasma oscillations in the system of coupled Josephson junctions. The resonance leads to the creation of the longitudinal plasma waves (LPW) at the breakpoint and to the oscillation dependence of the breakpoint current as a function of the dissipation and coupling parameters. A group behavior of the current-voltage characteristics (IVC) of the stacks with different number of junctions is predicted. Particularly, in the materials with dissipation parameter β=0.35 and coupling parameter α=3, we expect four groups of the IVC, which demonstrate a different character of changing of the breakpoint current with the number of junctions in the stack. Using the k-αβ-method, we find the values of the wave numbers k of the LPW and explain this group behavior of the IVC.     

Macroscopic quantum interference effects in superconducting multiterminal microstructures

We review the macroscopic quantum phenomena in superconducting microstructures based on multiterminal junctions. The multiterminal Josephson junction presents a system in which the weak coupling takes place between several massive superconducting banks (terminals). Compared with the conventional (two-terminal) junctions such systems have additional degrees of freedom and a corresponding set of control parameters, preset transport currents and (or) applied magnetic fluxes. The general phenomenological theory of multiterminal Josephson junctions is presented. The specific multichannel interference effects (studied theoretically and experimentally) are described for two microstructures: the four-terminal SQUID and a system consisting of two weakly coupled superconducting rings.     

Effects of disorder on voltage coherence in a modified linear Josephson array

We report numerical simulations on the effect of disorder in parallel-biased series of arrays of overdamped Josephson junctions. Our arrays feature additional parallel-conected ‘shunt’ junctions which provide strong local coupling between pairs of junctions along the series-connected ‘backbone’. We find that series arrays of 20 junctions have phase-locked and phase-coherent dynamical modes which are tolerant of more than 50% spread in critical currents,I _C , and plaquette area, S. The arrays, however, show moderate tolerance to (10% spread) disorder in bias currents,I _B . This tolerance to disorder in array parameters implies that practical RF sources might be possible using these arrays.     

Kohärenz in linearen Anordungen von Josephsonverbindungen mit induktiver Kopplung

Coherence in Linear Arrays of Josephson Junctions with Inductive Coupling Using reduced equations for the phases of the voltage oscillations we investigate the synchronization in a linear array of Josephson junctions with inductive coupling. The examples under consideration are the coupling between next neighbours, the large range coupling and the SQUID coupling. Especially, we investigate the formation of coherent modes and their stability, the effect of the de conductivity on the phase locking and the tolerance of the junctions critical currents.     

The <Emphasis Type="Italic">c</Emphasis>-axis charge traveling wave in a coupled system of Josephson junctions

We demonstrate a manifestation of the charge traveling wave along the c axis (TW) in current voltage characteristics of coupled Josephson junctions in high-T _c superconductors. The branches related to the TW with different wavelengths are found for the stacks with different number of Josephson junctions at different values of system’s parameters. Transitions between the TW branches and the outermost branch are observed. The electric charge in the superconducting layers and charge-charge correlation functions for TW and outermost branches show different behavior with bias current. We propose an experimental testing of the TW branching by microwave irradiation.     

Topology-induced critical current enhancement in Josephson networks

We investigate the properties of Josephson junction networks with inhomogeneous architecture. The networks are shaped as “square comb” planar lattices on which Josephson junctions link superconducting islands arranged in the plane to generate the pertinent topology. Compared to the behavior of reference linear arrays, the temperature dependencies of the Josephson currents of the branches of the network exhibit relevant differences. The observed phenomena evidence new and surprising behavior of superconducting Josephson arrays.     

Self-radiation from arrays of niobium Josephson junctions embedded in the open resonator

This paper focuses on self-radiation from arrays of Josephson junctions embedded in a quasi-optical resonator. The mechanism of coupling this radiation to the principal mode of the open resonator is illustrated using experiments and simulations with CST microwave studio software. Comparing the microstrips and dielectric resonators used as the antennas of the series arrays of discrete Josephson junctions, we demonstrate that the dielectric resonator antennas are more effective than microstrips.     

Influence of the diffusion current on the hysteretic behavior in the system of coupled Josephson junctions

The detailed investigation of the phase dynamics and the I–V curves in the system of coupled Josephson junctions have been carried out. The superconducting, quasiparticle, diffusion, and displacement currents have been calculated as functions of the total current through the system. The role of the diffusion current in the formation of the I–V curves has been studied and the influence of this quantity on the I–V curve branching and the magnitude of the return current has been revealed. The calculation results agree qualitatively with the experimental data.     

d-Wave-induced Josephson current counterflow in YBa2Cu3O7/Nb zigzag junctions

Well-defined zigzag-shaped ramp-type Josephson junctions between YBa2Cu3O7 and Nb have been studied. The magnetic field dependencies of the critical currents provide evidence for d-wave--induced alternations in the direction of the Josephson current between neighboring sides of the zigzag structure. The arrays present controllable model systems to study the influences of pi facets in high-angle high- T(c) grain boundaries. From the characteristics, we estimate a possible imaginary s-wave admixture to the order parameter of the YBa2Cu3O7 to be below 1%.     

Josephson Currents and Gap Enhancement in Graph Arrays of Superconductive Islands

Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions.     

Nonlinear dynamics and resistive transition in intrinsic Josephson junctions

We study the dynamics of phase differences in intrinsic Josephson junctions by using numerical simulations. We especially pay attention to the dynamics of junctions with weak dissipation under an externally applied electric current, where nonlinear character of the system appears most significant. It is found that, when an electric current is applied, the spatially localized oscillations appear. These oscillations are similar to the so-called “breather modes”, which are well known in the dynamics of the sine-Gordon systems. We show that the development of these modes depends on the number of junctions, and the dynamics significantly differs between even and odd numbers. As a result, the critical current of the system also undergoes this even-odd effect.     

Synchronization of underdamped Josephson-junction arrays

Our recent experiments show that arrays of underdamped Josephson junctions radiate coherently only above a threshold number of junctions switched onto the radiating state. For each junction, the radiating state is a resonant step in the current-voltage characteristics due to the interaction between the junctions in the array and an electromagnetic cavity. Here we show that a model of a one-dimensional array of Josephson junctions coupled to a resonator can produce many features of the coherent be havior above threshold, including coherent radiation of power and the shape of the array current-voltage characteristic. The model also makes quantitative predictions about the degree of coherence of the junctions in the array. However, in this model there is no threshold; the experimental below-threshold region behavior could not be reproduced.Received: 11 April 2003, Published online: 23 July 2003PACS: 74.50.+r Tunneling phenomena; point contacts, weak links, Josephson effects - 85.25.-j Superconducting devices     

Aspects of stochastic resonance in Josephson junction,bimodal maps and coupled map lattice

We present the results of extensive numerical studies on stochastic resonance and its characteristic features in three model systems, namely, a model for Josephson tunnel junctions, the bistable cubic map and a coupled map lattice formed by coupling the cubic maps. Some interesting features regarding the mechanism including multisignal amplification and spatial stochastic resonance are shown.     

Dynamics of fluxons in Josephson junctions under the noise current action

The motion of magnetic flux quanta (fluxons) in long Josephson junctions (LJJ) under action of direct and random currents is under investigation. The velocity distribution function of fuxons is calculated which, even in the absence of the direct current component, is non-Gaussian. As a consequence, the current-voltage characteristic of a noise junction differs from that for a regular one. The dependence of the voltage difference on the current for junctions, both with and without the noisy current component, is shown to be non-monotonic. There is a good agreement between the calculation data and the numerical simulation results.