Two-dimensional Josephson Junction Arrays Research Articles

Simulation of the intergranular magnetization of (Bi,Pb) 2Sr 2Ca 2Cu 3O 10+ x superconductors by using Josephson junction arrays

In this paper we present a numerical simulation study of the intergranular magnetization of (Bi,Pb) 2Sr 2Ca 2Cu 3O 10+ x superconductors. The intergranular-current system was modelled as a two-dimensional Josephson junction array, which consists of superconducting grains connected via overdamped, narrow Josephson weak links. The simulations cover magnetic-flux distribution and magnetic-hysteresis studies, including relaxation effects due to thermal fluctuations in the junctions. Special attention was paid to the influence of intergranular defects on the array magnetization and intergranular flux pinning, with the motivation to find model parameters which fit to the experimental behavior of (Bi,Pb) 2Sr 2Ca 2Cu 3O 10+ x . A correspondence with the experimental results [Paasi et al., Physica C 259 (1996) 1) (previous paper)] required that there was an intergranular defect of the μm order located in the middle of the four grains of an array mesh. Such a defect could act as a strong pinning center for intergranular flux.

Two row switching regimes in two-dimensional Nb-Pb Josephson-junction array

A crossover in the two-dimensional Nb-Pb Josephson-junction array from the coherent phase slip line regime to quasiparticle row switching regime has been observed as temperature decreased. The boundary between these regimes corresponds to the temperature when the fluxon mass vanishes (β c ≃ 35)

Magnetic hysteresis of the critical current density in ceramic superconductors modelled as two-dimensional series-parallel Josephson junction array within the intragranular flux-trapping model

A model which takes into account a two-dimensional series-parallel array of Josephson junctions and the magnetic flux trapped in the grains, has been employed to obtain a better agreement between theory and experimental data than in the case of a classical single parallel Josephson junctions array for HTC ceramics. It was found that the theoretical J( B a) dependences both series-parallel and parallel array Josephson junctions in increasing applied magnetic field (virgin curve) are very similar, but there is an sizable difference in decreasing applied magnetic field (returning curve). The normalized critical current density J c( B a)/ J c(0) of a series-parallel array is smaller than in a parallel array. This effect is interpreted in terms of a proper hysteretic behavior of the series parallel array of Josephson junctions just when the intragranular flux-trapping model is considered.

Square-law Josephson detection of far-infrared radiation with current-biased granular Tl2Ba2CaCu2O8 thin films

The far-infrared photoresponse of granular thin film Tl2Ba2CaCu2O8 has been investigated at relatively low optical powers obtained from a c.w. laser source. Both bolometric and Josephson detection has been observed at wavelengths between 214 mu m and 1011 mu m. In contrast to measurements made with higher-power pulsed radiation, a Josephson photosignal proportional to incident power is obtained in this spectral range. The responsivity is found to increase strongly with wavelength, approximately proportionally to lambda 2.5, with a measured sensitivity of 12 V W-1 at 1011 mu m and a corresponding NEP of 2*10-8 W Hz- 12 /. The photoresponse dependences on wavelength and power are compared with recent numerical predictions of the behaviour of two-dimensional Josephson junction arrays with random defects (Cai et al. 1994 Phys. Rev. B 49 4015). The observed square-law response and strongly increased responsivity at longer wavelengths indicate the potential of utilizing such films as rugged, fast, large-area video detectors for the sub-mm/microwave spectral range.

Self-field effects in two-dimensional Nb Josephson-junction arrays

We have measured two-dimensional niobium Josephson junction arrays in which self induced fields are important. We find an increase of the depinning current when /spl lambda//sub /spl perp//, the penetration depth in the array, is of the order of one. There is evidence for a destruction of commensurate vortex states in the arrays as the depinning current becomes almost independent of the applied magnetic field. Our data also show that self-field effects change the array flux-flow dynamics and decrease the effective array viscosity. >

Scaling behavior of the magnetic-field-tuned superconductor-insulator transition in two-dimensional Josephson-junction arrays.

We have studied the superconductor-insulator (SI) phase transition for two-dimensional (2D) arrays of small Josephson junctions in a weak magnetic field. The data were analyzed within the context of the theory of the magnetic-field-tuned SI transition in 2D superconductors. We show resistance scaling curves over several orders of magnitude for the 2D arrays. The critical exponent ${\mathit{z}}_{\mathit{B}}$ is determined to be 1.05, in good agreement with the theory. Moreover, the transverse (Hall) resistance at the critical field is found to be very small in comparison to the longitudinal resistance.

Direct observation of vortex dynamics in two-dimensional Josephson-junction arrays

Spatially resolved images of the dynamic states of current-biased overdamped two-dimensional arrays of Nb/AlO/sub x//Nb Josephson junctions were obtained using low-temperature scanning electron microscopy. We present two-dimensional imaging results describing various vortex dynamic regimes in zero applied magnetic field. The nucleation of current-induced vortices at the array boundaries and their subsequent motion into the array interior are observed for bias currents slightly above the array critical current. With increasing bias current, vortex-vortex interaction becomes important. Discussions on the coherent microwave radiation emission are presented. >

The electron-beam irradiation on the high temperature superconducting thin films

Low-temperature scanning electron microscopy (LTSEM) is a promising measuring technique for probing the spatial distribution of the superconducting properties of the high-temperature superconducting (HTS) thin films. A theoretical analysis of the electron-beam irradiation on the HTS thin films in the LTSEM has been carried out. An inhomogeneously distributed grain array model has been applied in the analysis, and some numerical simulations have been carried out on the electron-beam induced voltage (EIV) signals in the LTSEM experiments. The comparisons of our numerical results with the LTSEM experimental data indicate that it is quite reasonable to use a two-dimensional Josephson junction array for stimulating the inhomogeneous HTS thin film sample. Our numerical results also show that the EIV signals are influenced by the electron-beam power used in the LTSEM, and a reduction of the electron-beam power is suggested in order to eliminate the errors in estimating the local values of critical temperature Tc and critical current Ic by the sample temperature and the bias current at which the first EIV signal occurs.

Coherent states of two-dimensional Josephson-junction networks

We have investigated numerically the phase-locking behavior of two-dimensional Josephson-junction arrays, taking into account a finite inductance (l≳1) of the unit cell and external magnetic fields. Within this model we demonstrate the existence of multivalued I-V curves of the network. Different branches of the I-V curve correspond to in-phase and anti-phase coherent states with high and low levels of output power, respectively. The arrays show hysteretic transitions between these states in external magnetic fields.

Observation of vortex dynamics in two-dimensional Josephson-junction arrays.

Spatially resolved images of the dynamic states of curent-biased two-dimensional arrays of Nb/${\mathrm{AlO}}_{\mathit{x}}$/Nb Josephson junctions were obtained using low-temperature scanning electron microscopy. The arrays were square or rectangular and the maximum size was 20 junctions \ifmmode\times\else\texttimes\fi{}20 junctions. In overdamped arrays our images at zero or small applied perpendicular magnetic field together with model calculations confirm the nucleation of a vortex at one sample edge (or an antivortex at the opposite edge) and its subsequent motion into the array interior. Vortex annihilation due to vortex-antivortex collision was observed to take place in the middle of the array or at the edge opposite to the nucleation edge. These dynamics and the underlying model considerations are similar to that for Abrikosov vortices in the current-induced resistive state of thin film type-II superconductors. The phenomenon of ``row switching'' is directly confirmed in images of underdamped arrays. The specific rows experiencing this process change randomly when the same bias point on the current-voltage characteristic is established many times, starting each time from zero current.

Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays.

When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity, $\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.

Low-field diamagnetic response of granular superconductors at finite temperatures.

We study the low-field diamagnetic response of granular superconductors at finite temperatures by means of a simple two-dimensional Josephson-junction array. The temperature effects are taken into account by inserting white-noise current sources in parallel to the resistively shunted junction circuit models of the Josephson junctions of the network. By this analysis we argue that a simplified one-dimensional description of the equivalent circuit, proposed by the authors for cylindrical granular superconductors, is still valid even in the presence of thermally activated flux jumps. A flux-creep picture for intergranular flux motion follows.

Dynamics of quasioptical Josephson junction arrays for submillimeter coherent sources

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. >

Rf power dependence of subharmonic voltage spectra of two-dimensional Josephson-junction arrays.

We have measured the rf-bias-current dependence of the \ensuremath{\nu}/2 subharmonic spectral response of planar 300\ifmmode\times\else\texttimes\fi{}300 Nb-Au-Nb proximity-coupled Josephson-junction arrays. The \ensuremath{\nu}/2 subharmonic voltage spectrum was examined at two rf-bias frequencies, \ensuremath{\nu}/${\ensuremath{\nu}}_{\mathit{c}}$\ensuremath{\approxeq}1.4, 2.0 (${\ensuremath{\nu}}_{\mathit{c}}$\ensuremath{\approxeq}120 MHz), and in applied magnetic fields corresponding to f=0,1/2 flux quantum per plaquette. The measurements were compared to analytical predictions for an rf-biased asymmetric superconducting quantum interference device with non-negligble loop inductance and large rf-bias-current amplitudes, based on the resistively shunted Josephson-junction model. Reasonable agreement was found between experiment and theory, suggesting that a possible origin for the observed subharmonic behavior in arrays involves an interplay between array plaquette inductances and junction critical-current variations.

Mesoscopic phenomena in two-dimensional condensed matter systems

Advances in nonlinear, nonequilibrium concepts and large-scale computation are described which make it possible to systematically study mesoscopic space-time phenomena - the crucial bridge between microscopic and macroscopic descriptions. Two simple examples are discussed as illustrations: spiral surface growth; and flux relaxation in two-dimensional Josephson junction arrays.

Vortex dynamics in two-dimensional underdamped, classical Josephson-junction arrays.

We present a systematic experimental study on vortex dynamics in two-dimensional Josephson-junction arrays built of underdamped single junctions in which charging effects can be neglected. Arrays in both square and triangular geometries are measured in small magnetic fields at low temperatures. We find that the whole picture of the spatial dynamics of vortices in two-dimensional arrays is analogous to the dynamics of the phase in a single junction. We study in detail the depinning current, the flux-flow resistance, and the maximum velocity of propagating vortices. Our data show that vortices in underdamped arrays, when driven with a current, experience more damping than can be explained by Ohmic-dissipation alone. A simple semiquantitative model, in which the energy lost to junctions in the wake of the moving vortices is taken into account, explains our data very well. The model shows that vortices will always experience damping no matter how underdamped the single junctions are.

Dynamics of voltage-driven Josephson junction arrays

The authors discuss the dynamics of voltage-driven Josephson junction arrays with negligible capacitances. The array dynamics shows a sensitive dependence on initial phases, leading to current-spike structures in the time-averaged I-V relations. They demonstrate this effect explicitly for the simple system of a two-junction chain, which they also use to illustrate the main features of current response to external driving voltages. They then show that a class of simplified ansatz solutions of two-dimensional voltage-driven Josephson junction arrays under a perpendicular magnetic field can be reduced to two-junction dynamics. In both cases, they find that coherent phase-slip processes can lead to subharmonic lockings with an external RF field.

Dynamics of capacitive Josephson-junction arrays subjected to electromagnetic radiation

We have studied the dynamics of regular two-dimensional Josephson-junction arrays subjected to electromagnetic radiation at frequencies comparable to the individual junction's characteristic frequency. The junctions are described using the resistively-shunted-junction model including capacitance with the plasma frequency also comparable to the characteristic frequency. The dynamical behavior falls into several different general classes, namely, periodic, quasiperiodic, and chaotic, depending on the particular characteristics of the junctions, the input currents, and the amplitude and frequency of the radiation. Detailed examples of each of these types of behavior are given. Current-voltage characteristics are examined and related to the dynamical behavior and the junction's properties. The effect of finite temperatures, included by means of a Langevin noise current, is also discussed, as is the stability of various types of dynamical states.

Phase coherence and disorder in Josephson-junction arrays

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.

Simulations and interpretation of fractional giant Shapiro steps in two-dimensional Josephson-junction arrays.

We present simulations of two-dimensional Josephson-junction arrays to study giant Shapiro steps in these arrays. The amplitude and frequency dependence of the step widths is found to be more complex than in single junctions. The fractional step widths are found to decrease more rapidly with increasing frequency or rf current than conventional steps in single junctions. The washboard model of single junctions is extended to arrays to explain these differences between arrays and single junctions.