Two-dimensional Josephson Junction Research Articles

Magnetic properties of two-dimensional SNS-type Josephson junction arrays

The field dependence of the magnetic moment of square (100×100) SNS-type Josephson junction arrays was studied by a SQUID magnetometer. A considerable difference in the behavior of this dependence was revealed for the cases of the entry of magnetic flux into the array and its exit from it. The branches of the curve obtained with increasing field strength had the form of regular periodic dependences with peaks corresponding to integer and half-integer numbers of flux quanta per cell. The curves obtained with decreasing field strength had no noticeable features and, in particular, no periodic structure. Magnetic flux avalanches were not observed in the SNS-type arrays, although the critical parameter of the system was sufficiently great (LIC/Φ0≫1) to satisfy the necessary condition of the self-organized criticality. The quasi-hydrodynamic flux motion in the array was explained by the considerable viscosity characterizing the vortex motion through the Josephson junctions.

Critical behavior of frustrated Josephson junction arrays with bond disorder.

The scaling behavior of the current-voltage (IV) characteristics of a two-dimensional proximity-coupled Josephson junction array (JJA) with quenched bond disorder was investigated for frustrations f = 1/5, 1/3, 2/5, and 1/2. For all these frustrations including 1/5 and 2/5 where a strongly first-order phase transition is expected in the absence of disorder, the IV characteristics exhibited a good scaling behavior. The critical exponent nu indicates that bond disorder may drive the phase transitions to be continuous but not into the Ising universality class, contrary to what was observed in Monte Carlo simulations. The dynamic critical exponent z for JJA's was found to be only 0.60-0.77.

Phase locking dynamics in 2D Josephson junction arrays with external load

Phase locking in a basic two-dimensional hybrid Josephson junction array consisting of two rows and four columns shunted by an external load is investigated, exploiting an approximation combining the ideas of harmonic balance with that of the slowly varying phase procedure. Using small ring inductances, the junction voltages within the same row oscillate nearly in-phase unless the external magnetic flux in the loops is near a multiple of a quarter of the flux quantum. Without external load we have found a stable antiphase regime where both rows carry out uniform interferometer oscillations. A stable in-phase regime, favored in an optimized radiation source, can be reached by means of an external inductive shunt for small external fields only.

Investigation of vortex dynamics in Josephson junction arrays with magnetic flux noise measurements

We have measured the magnetic flux noise in a two-dimensional Josephson junction array in nominally zero magnetic field, in the vicinity of the superconducting transition. This transition is of the Berezinski–Kosterlitz–Thouless (BKT) type, driven by the unbinding of thermally excited vortex–antivortex pairs. At temperatures just above the BKT transition temperature T c, the flux-noise power spectrum S( ω) is white up to a temperature dependent cross-over frequency ω ξ ( T). We identify ω ξ with the characteristic time related to the scale at which the cross-over from free vortex response to a response dominated by bound pairs occurs. The signature of free vortices is thus white noise while bound vortex pairs give rise to a 1/ ω dependence.

Spatiotemporal intermittency in the critical dynamics of dc-driven two-dimensional frustrated Josephson arrays

We report the numerical observation of spatiotemporal intermittency in the critical dynamics of two-dimensional frustrated underdamped dc-driven Josephson junction arrays. This intermittency is due to the hopping of the system among the different subcritical metastable states, which are characterized by domain walls separating regions with the symmetry of the ground state. Turbulentlike domains correspond to the regions surrounding the nucleation and decay of these domain walls, or equivalently, to the regions where vortex motion takes place. This intermittency is further signaled by the observation of $1/f$ noise in the high-frequency tail of the power spectrum of the voltage fluctuations, and by the scaling of the characteristic time scale for front propagation with the current. A study of the ground and metastable states of the system is also presented.

Mutual-inductance route to the paramagnetic Meissner effect in two-dimensional Josephson-junction arrays

We simulate two-dimensional Josephson junction arrays, including full mutual- inductance effects, as they are cooled below the transition temperature in a magnetic field. We show numerical simulations of the array magnetization as a function of position, as detected by a scanning SQUID which is placed at a fixed height above the array. The calculated magnetization images show striking agreement with the experimental images obtained by A. Nielsen et al. The average array magnetization is found to be paramagnetic for many values of the applied field, confirming that paramagnetism can arise from magnetic screening in multiply-connected superconductors without the presence of d-wave superconductivity.

Finite-size effects and dynamical scaling in two-dimensional Josephson junction arrays

In recent years many groups have used Fisher, Fisher, and Huse (FFH) dynamical scaling to investigate and demonstrate details of the superconducting phase transition. Some attention has been focused on two dimensions where the phase transition is of the Kosterlitz-Thouless-Berezinskii (KTB) type. Pierson et al. used FFH dynamical scaling almost exclusively to suggest that the dynamics of the two-dimensional superconducting phase transition may be other than KTB-like. In this work we investigate the ability of scaling behavior by itself to yield useful information on the nature of the transition. We simulate current-voltage (IV) curves for two-dimensional Josephson junction arrays with and without finite-size-induced resistive tails. We find that, for the finite-size effect data, the values of the scaling parameters, specifically the transition temperature and the dynamical scaling exponent z, depend critically on the magnitude of the contribution that the resistive tails make to the IV curves. In effect, the values of the scaling parameters depend on the noise floor of the measuring system.

Nonequilibrium photoresponse of YBa2Cu3O7−x granular films to 8 mm microwave radiation

Nonequilibrium photoresponse behavior has been investigated for YBa2Cu3O7−x (YBCO) granular films to 8 mm microwave radiation under various bias currents and magnetic fields. The measurements reveal that the nonequilibrium photoresponse mode occurs only in the tail region of the resistance transition curve R(T) from the normal to the superconducting state, where transportation behavior of the granular superconducting film is found to be characterized by the Kosterlitz–Thouless (KT) phase transition model. Based on the KT model, the photoresponse mechanism has been interpreted in terms of the depinning process of the unbinding vortices, which are generated from the decoupling process of the vortex–antivortex pairs by current, and are held at the intrinsic pinning sites of the granular high-Tc superconducting films at low temperature. Under the co-action of the bias current and the incident microwave photons, these unbinding vortices will be driven out of the pinning center, creating viscous motion in the Josephson junction array system. An analytical result of the unbinding vortices density n(T,I) induced by applied current has been worked out based on the model of two-dimensional Josephson junction arrays that is employed as a model system for the YBCO granular films. The distribution of the n(T,I) is found to be analogous to that of the photoresponse measured in the temperature region of 2/3TKT<T<TKT. Additionally, the measurements reveal that the magnitude of the photoresponse is linearly increased with an increase of the incident microwave power. These results imply that the nonequilibrium photoresponse induced by microwave irradiation may be intrinsically related to the decoupling process of the vortex–antivortex pairs, as well as to the depinning dynamics of the unbinding vortices in the granular high-Tc superconducting films.

Some properties of Eck-like steps in 2D underdamped Josephson junctions arrays

Two-dimensional (2D) Josephson Junctions arrays have been studied largely in the overdamped case. Only recently some experimental, numerical and theoretical results have been obtained in the underdamped case. The nature of dynamical states of an array when placed in a magnetic field is again not fully explained and only approximate (linear) models have been proposed. On the other hand, the comprehension of such dynamics is of great importance for understanding the behavior of such arrays. In this work, we study numerically some of the dynamical states in 2D arrays using a full inductance matrix in the array equations. The results show that the response of the array to the magnetic field is governed at large by the parameter /spl beta//sub L/. Moreover we study the underlying dynamics which is dominated by so-called checkerboard solutions. The properties of such arrays are investigated in view of applications.

Two-dimensional Josephson junction arrays coupled through a high-Q cavity

The problem of disordered two-dimensional arrays of underdamped Josephson junctions is addressed. Our simulations show that when coupled to a high-Q cavity, the array exhibits synchronized behavior, and the power emitted can be considerably increased once enough junctions are activated to pump the cavity. The highly resonant cavity induces synchronized behavior, which is qualitatively different than what is familiar from other studies on nonlinear oscillator arrays, for example the Kuramoto model. We also address the effects of disorder, as well as the role of detuning between the spontaneous emission frequency of the junctions and the cavity resonant frequency. We show with a simple argument that we can predict the scaling behavior of disorder with the size of the array. The consequences for the design of microwave oscillators in the Gigahertz region are discussed.

Two-Dimensional Josephson Junction Array at an Irrational Frustration

Two-Dimensional Josephson Junction Array at an Irrational Frustration

Fiske resonances in annular Josephson junctions

The resonances in two-dimensional annular Josephson junctions have been investigated from both a theoretical and experimental point of view. We obtained the analytical expression for the amplitude modulation of the Fiske resonances in the case of an externally applied magnetic field and the determination of the voltage positions of the Fiske steps as a function of the junction geometrical parameters (inner and outer radius). The experiments have been carried out on Nb-based annular junctions with finite ring width. The dependence of the maximum amplitude of the first and second Fiske step as a function of the external magnetic field is investigated in detail for a wide range of ring widths. The agreement found between experiments and the theoretical model is excellent.

Dynamic scaling of I– V data for the neutral 2D Coulomb gas

The value of the dynamic critical exponent z has been studied for experimental two-dimensional superconducting and Josephson junction array systems in zero magnetic field via the Fisher–Fisher–Huse dynamic scaling analysis. We found z≃5.6±0.3, a relatively large value indicative of non-diffusive dynamics. We extend this work here to simulational I– V curves that are also found to be characterized by the same large value of z.

Phase-locking of disordered two-dimensional Josephson junction arrays to microwave radiation

A connection between the disorder in the critical currents of two-dimensional arrays of Josephson junctions and the amount of phase-locking of a row to an external microwave signal is proposed. We have computed the probability of phase-locking as a function of the spread of the critical currents of the individual junctions. The analytic results are in good agreement with numerical simulations. The predictions can be also qualitatively compared to the experiments.

Broken Symmetry of Row Switching in 2D Josephson Junction Arrays

We present an experimental and theoretical study of row switching in two-dimensional Josephson junction arrays. We have observed novel dynamic states with peculiar percolative patterns of the voltage drop inside the arrays. These states were directly visualized using laser scanning microscopy and manifested by fine branching in the current-voltage characteristics of the arrays. Numerical simulations show that such percolative patterns have an intrinsic origin and occur independently of positional disorder. We argue that the appearance of these dynamic states is due to the presence of various metastable superconducting states in arrays.

Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films

The dynamical vortex response of a two-dimensional array of the resistively shunted Josephson junctions in a perpendicular magnetic field is inferred from simulations. It is found that, as the magnetic field is increased at a fixed temperature, the response crosses over from normal to anomalous, and that this crossover can be characterized by a single dimensionless parameter. It is described how this crossover should be reflected in measurements of the complex impedance for Josephson junction arrays and superconducting films.

Dynamic scaling for two-dimensional superconductors, Josephson-junction arrays, and superfluids

The value of the dynamic critical exponent $z$ is studied for two-dimensional superconducting, superfluid, and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find $z\simeq5.6\pm0.3$, a relatively large value indicative of non-diffusive dynamics. Universality of the scaling function is tested and confirmed for the thinnest samples. We discuss the validity of the dynamic scaling analysis as well as the previous studies of the Kosterlitz-Thouless-Berezinskii transition in these systems, the results of which seem to be consistent with simple diffusion ($z=2$). Further studies are discussed and encouraged.

Giant Shapiro steps for two-dimensional Josephson-junction arrays with time-dependent Ginzburg-Landau dynamics

Two-dimensional Josephson junction arrays at zero temperature are investigated numerically within the resistively shunted junction (RSJ) model and the time-dependent Ginzburg-Landau (TDGL) model with global conservation of current implemented through the fluctuating twist boundary condition (FTBC). Fractional giant Shapiro steps are found for {\em both} the RSJ and TDGL cases. This implies that the local current conservation, on which the RSJ model is based, can be relaxed to the TDGL dynamics with only global current conservation, without changing the sequence of Shapiro steps. However, when the maximum widths of the steps are compared for the two models some qualitative differences are found at higher frequencies. The critical current is also calculated and comparisons with earlier results are made. It is found that the FTBC is a more adequate boundary condition than the conventional uniform current injection method because it minimizes the influence of the boundary.

Two-dimensional Josephson junction network architectures for maximum microwave radiation emission

We have investigated experimentally a novel type of self-synchronizing two-dimensional Josephson junction array based on special symmetry breaking network architectures. The measurements confirm the theoretical prediction that in such Josephson networks the Josephson oscillators mutually synchronize into a coherent in-phase state and that such arrays are capable of emitting maximum coherent microwave power in the entire theoretically expected frequency range. The DC biased oscillator array operates coherently even without a reinjection of the generated microwave by an external load or by a resonator cavity. The selector network possesses a much higher tolerance against imperfections, perturbations and load parameter variations than conventional regular two-dimensional or one-dimensional arrays. The experimental sample has been fabricated in an industrial process using Nb-technology, in effect providing relatively large spreads in the array junction parameters. The measured frequency range goes from 85 GHz up to 380 GHz with a maximum microwave power of 0.16 /spl mu/W matched to a coupled load for an array with only 100 active Nb-AlO/sub x/-Nb junctions.

Phase locking dynamics in 2D Josephson junction arrays with small inductances

Phase locking in a basic two-dimensional hybrid Josephson junction array consisting of two rows and four columns is investigated exploiting the small inductance approximation. The general synchronization dynamics agrees with that of simpler systems. Especially, the junction voltages within the same row oscillate practically in phase unless the external magnetic flux in the loops is near to multiples of a quarter of the flux quantum. In case of a finite flux we have found a stable antiphase regime of both uniform interferometer oscillations whereas in the zero-field limit this locking regime is neutrally stable.