Static Magnetic Flux Dynamics in One-Dimensional (1D) Josephson Lattices

We investigated static magnetic flux dynamical properties of one-dimensional lattices of Josephson junctions. The discretized wave equations of the Josephson junction lattice were solved using a generalized relaxation iteration algorithm. Numerical simulations indicated that transitions between periodic state and chaotic state will occur as the physical parameters and geometric parameters such as external current y _n, magnetic field h ₀, h, and the length of Josephson junction _n and d _n , varied. A shot length of the Josephson junction favors stable periodic states.     

Phase transition of frustrated two-dimensional Josephson junction arrays

We have investigated the resistive behavior of frustrated Josephson tunnel junction arrays. The transitions nearf=1/2, atf=1 and at a nonspecial value off=0.38 are studied in detail with linear and nonlinear resistance measurements. The parameterf is the frustration index, the applied flux per unit cell of the array normalized to the flux quantum ₀=h/2e. The transition atf=1/2 looks similar to the zero-field Kosterlitz-Thouless transition, including a universal jump in the nonlinear resistance exponent. Compared tof=0, the transition is shifted to much lower temperatures. Nearf=1/2, below the transition temperature, single vortex crossings dominate the resistance. The transition atf=1 is qualitively the same as thef=0 Kosterlitz-Thouless transition, but small deviations are found. Forf=0.38, there is no experimental evidence for a special phase transition; over the whole temperature range, the resistance decreases exponentially with an energy barrier close to two in units of the Josephson coupling energy.     

Theory of the AC Josephson effect in triplet superconducting junction

The quasiparticle and AC Josephson current in superconductor / insulator / superconductor (S/I/S) junctions including a triplet p-wave superconductor are calculated for arbitrary transmission of the junction. As a triplet pairing state we select one of the unitary pairing states which is a promising candidate for the superconducting state in Sr ₂ RuO ₄ . In p-wave superconductor / insulator /p-wave superconductor junction, both quasiparticle current and AC Josephson current are enhanced near zero-bias voltage due to the existence of zero energy state of p-wave superconductors. For the s-wave superconductor/ insulator / p-wave superconductor junction, the quasiparticle current at low voltage is suppressed due to the energy gap of s-wave superconductor. The first Fourier component of the AC Josephson current vanishes due to the difference of the parity between the two superconductors.     

Controlled Single-Cooper-Pair Charging Effects in a Small Josephson Junction Array

We report on measurements of single-Cooper-pair charging effects in small Josephson junction arrays, and the experimental techniques that were used. We succeeded in having complete control over the array's electrostatic parameters; offset charges were accurately compensated, and the poisoning of 2e-periodic effects by quasiparticles was circumvented. This allowed for a controlled study of the array's coherent ground state. A few measurements gave results which were not fully 2e-periodic due to interesting parity effects. The arrays are in the regime where the energy scales for the Josephson effect and single-charge effects are comparable.     

Cross-Whisker Intrinsic Josephson Junction as a Probe of Symmetry of the Superconducting Order Parameter

As a test of the superconducting order parameter, we have developed an intrinsic Josephson junction by the name of cross-whisker junction. This junction was made using two Bi₂Sr₂CaCu₂O_8+d single crystal whiskers. Two whiskers were connected at their c planes with various cross-angles. Angular dependence of the critical current densities shows d-wave-like fourfold-symmetry. However, the angular dependence is much stronger than that of the conventional d_x ^{2-y 2} wave. The Jc shows its smallest value around 45 deg, which suggests that the Josephson penetration depth becomes longer. We have successfully observed a Fraunhofer pattern in the cross-whisker junction with cross-angle 45 deg.     

Periodic Oscillations of Josephson-Vortex Flow Voltage in Stacked Intrinsic Josephson Junctions

Using the coupled sine-Gordon equations, we study the magnetic oscillation behavior of the Josephson-vortex flow voltage (JVFV) in stacked intrinsic Josephson junctions (IJJs). It is found that the periodic oscillations of the JVFV with the magnetic field are determined by the lattice structure. In narrow IJJs with a high density of vortices, the boundary interaction is favorable for forming a rectangular lattice structure and inducing H ₀ oscillations. The oscillation period is equal to the magnitude of the field needed to add one vortex quantum per one intrinsic Josephson junction. In wide IJJs, the shearing inter-layered interaction is favorable for forming a triangular lattice structure and inducing H ₀/2 oscillations. In this case, with increasing magnetic field, a transformation from the triangular (with period H ₀/2) to rectangular (with period H ₀) configurations is also obtained in a long lateral size. Besides, from the magnetic oscillation characteristics of the JVFV in wide IJJs, the oscillating inversions have also been obtained.     

Identification of parameters with different orders of magnitude in chaotic systems

The synchronization and parameter identification of six unknown parameters in a chaotic neuron model, which one parameter (about 0.006) is 3 orders of magnitude smaller than the others (about 1–5), is investigated by using Lyapunov stability theory and adaptive synchronization in detail. Two gain coefficients (δ₁,?δ₂) are introduced into the Lyapunov function to obtain certain optimized controllers and parameter observers. A selectable amplification factor k ₀ is presented using scale conversion and it is used to improve the accuracy of parameter estimation with the smallest order. The parameter space for gain coefficient (δ) versus amplification factor k ₀, and the parameter space δ₁ versus δ₂ at certain fixed amplification factor k ₀ are calculated numerically. It is found that the selection values of optimized gain coefficients and amplification factor are critical to estimate the six unknown parameters, particularly for the smallest unknown parameters with an order 0.001. The extensive numerical results show that it is more effective to estimate the smallest unknown parameter r when the two gain coefficients δ₁ and δ₂ are given the same value and a higher amplification factor k ₀ is used. It could be useful to estimate the unknown parameters with large deviation of order magnitude, such as a single chaotic Josephson junction coupled to a Resonant tank and other chaotic systems with potential application [Z.Y. Wang, H.Y. Liao, and S.P. Zhou, Study of the DC biased Josephson junction coupled to a Resonant tank, Acta. Phys. Sin. 50(10) (2001), pp. 1996–2000 (in Chinese)].     

Numerical Simulations of the Fluxon Dynamics of a Two-Dimensional Josephson Junction System

A direct perturbation method applied to a long Josephson junction molded by one-dimensional sine-Gordon equation is presented and the modulation of perturbations on fluxon velocity and stable state is studied. Simulations of a two-dimensional Josephson junction with dc bias current in an external magnetic field provide an I–V characteristic curve for the system and determine the various dynamic behaviors, including the periodic, quasiperiodic, and chaotic motions. Physical explanations for the behaviors are presented. The numerical results are in good agreement with the energetic analysis.     

Characterization of Submicron Sized Josephson Junction Fabricated in a Bi2Sr2Ca2Cu3O10+δ (Bi-2223) Single Crystal Whisker

To study the detailed characteristics of a nano-periodic Josephson junction array in a Bi₂Sr₂Ca₂Cu₃O_10+δ (Bi-2223) single crystal whisker without shunted grain boundaries, we fabricate a submicron stack with an area of 0.5 μm×0.5 μm and height of approximately 200 nm using a focused ion beam (FIB) etching technique. The stack has several hundreds of elementary Josephson junctions along the c-axis. We fabricate the stack by rotation and tilt of the sample stage in the FIB. The current–voltage (I–V) characteristics give a well-defined superconducting gap (V _g) and we notice suppression of the critical current in submicron junction with respect to big sized junction. We believe that the suppression of critical current in submicron junction is due to the normal resistance of the junction which belongs to the quantum resistance range.     

Dynamic reduction of the critical current in a Josephson junction

We have investigated the switching behavior of a Josephson tunnel junction driven by a signal with speed comparable to its plasma period _p . The Josephson junction is assumed initially to be in a static state so that the average voltage across it is zero. Application of a steplike current pulse of rise time _p is shown to induce switching to the finite voltage state even for values of currents much smaller than its critical current. A reduction of the critical current occurs due to the dynamic process. The approximate expressions derived show good agreement with the results obtained from simulations. The extent of dynamical reduction is limited to 27%. Shunting of the junction can eliminate this effect.     

Weak link between conventional and unconventional superconductors

In this paper we consider the Josephson coupling between a conventional and an unconventional superconductor through a constriction. It is demonstrated that a weak link is very different from a tunnel junction. In particular, in an orientation where the coupling in a tunnel junction vanishes because of symmetry, the Josephson current in the case of a weak link can nevertheless be finite, albeit with the distinctive characteristics of(i) a current phase relationship with a period of 2/n, (ii) the critical current near but below the transition temperature T ₁ of the lower transition temperature superconductor is proportional to (1–(T/T ₁)) ^n/2, where n is an integer determined by the symmetry.     

Superconducting Ladders and Kagomé Networks

We have used a remarkably simple and generally applicable method to determine the interaction between vortices and the ground state for both a ladder array of Josephson junctions and a ladder of thin superconducting wires. Applying a delta-star transformation we go on to show that much of the physics of Kagomé lattices (1D or 2D) should be the same as that of a corresponding simpler lattice.     

Radiation from Flux Flow in Josephson Junction Structures

We derive the radiation power from a single Josephson junction (JJ) and from layered superconductors in the flux-flow regime. For JJ case, we formulate the boundary conditions for the electric and magnetic fields at the edges of the superconducting leads using the Maxwell equations in the dielectric media and find dynamic boundary conditions for the phase difference in JJ which account for the radiation. We derive the fraction of the power fed into JJ transformed into the radiation. In a finite-length JJ this fraction is determined by the dissipation inside JJ and it tends to unity as dissipation vanishes independently of mismatch of the junction and dielectric media impedances. We formulate also the dynamic boundary conditions for the phase difference in intrinsic JJs in highly anisotropic layered superconductors of the Bi₂Sr₂CaCu₂O₈ type at the boundary with free space. Using these boundary conditions, we solve equations for the phase difference in the linear regime of Josephson oscillations for rectangular and triangular lattices of Josephson vortices. In the case of rectangular lattice for crystals with the thickness along the c-axis much larger than the radiation wavelength, we estimate the radiation power per unit length in the direction of magnetic field at the frequency 1 THz as ∼N μW/cm for Tl₂Ba₂CaCu₂O₈ and ∼0.04 N μW/cm for Bi₂Sr₂CaCu₂O₈. For crystals with thickness smaller than the radiation wavelength, we found that the radiation power in the resonance is independent on number of layers and can be estimated at 1 THz as 0.5 W/cm (Tl₂Ba₂CaCu₂O₈) and 24 mW/cm (Bi₂Sr₂CaCu₂O₈). For rectangular lattice, due to superradiation regime, up to half of power fed into the crystal may be converted into the radiation. In the case of triangular or random lattice in the direction perpendicular to the layers, the fraction of power converted into the radiation depends on the dissipation rate and is much lower than for rectangular lattice in the case of high-temperature superconductors with nodes in the gap.     

The Josephson Effect in Nanoscale Tunnel Junctions

In nanoscale Josephson junctions, the Josephson coupling energy is usually comparable with the charging energy of the junction and with the typical energy of thermal fluctuations. Under these circumstances, phase fluctuations imposed by the electromagnetic environment of the junction crucially affect the junction electrical behavior. In particular, they determine the maximum supercurrent the junction can sustain. We discuss this quantity in the case where the junction is not resistively shunted, so that the I V characteristics of the junction remains hysteretic. For a simple, yet realistic, unshunted junction model, we obtain detailed predictions of the shape of the supercurrent branch of the I V characteristic. Finally, we present experimental results supporting the theoretical analysis and which demonstrate that the supercurrent in an unshunted nanoscale Josephson junction can indeed be of the order of its critical current.     

THz Wave Emission from Intrinsic Josephson Junctions Controlled by Surface Impedance

Recently terahertz wave emission from intrinsic Josephson junctions without external magnetic fields has been intensively studied, and some emission states have been proposed numerically or theoretically. For the surface impedance Z=1, the McCumber-like state with small spatial dependence of the electric field in the junction becomes stable, while for large and complex Z, the π-phase kink state characterized by translational symmetry breaking along the layered structure becomes stable. In the present study, the relations between these two extreme cases are clarified numerically by solving the coupled equations of the Josephson relations and the Maxwell equations for an experimental width of the junction, 86 μm. The dynamical phase diagram in the surface impedance (Z)–current (J) plane and the optimal value of Z for the strongest emission are evaluated.     

A simple route for synthesis of a bi-epitaxial junction in thin films of YBa2Cu3O7 − x

A two-step fabrication process for the creation of a bi-epitaxial junction in thin films of YBa₂Cu₃O_{7 – x} is described. The junction has been fabricated on (100) SrTiO₃ substrate using a buffer layer of CeO₂. Polarized light optical microscopy indicates a regular basket-weave microstructure and a granular structure on either side of the junction. The junction shows Josephson critical currents at temperatures upto 74 K and the critical current increases linearly with decreasing temperature.     

DC and ac Josephson effects observed in high-temperature superconductor YBaCuO

We report the observation of the dc and ac Josephson effect and quasiparticle tunnelling in the high-temperature superconductor YBaCuO. The observation is made at 4.2 K. These effects were observed in a junction made by a niobium tip pressed against a high-T _c sample of YBaCuO ceramic. We observed a clean dc Josephson effect with a critical currentI _c 2 A and the ac effect with Shapiro steps corresponding toV=(hf/2e)n. The nature of the junction is not clear; however, we suggest that all observed effects can be explained by assuming a singlet pairing state in the ceramic. We have also observed a very peculiar noise behavior along theV-I characteristic.     

Josephson Bicrystal Junctions on Sapphire Substrates for THz Frequency Application

Thin film metal oxide superconducting bicrystal junctions on sapphire substrates with I _c R _N products up to 2.5 mV at 4.2 K for width 4 μm and normal-state junction resistance 10–60 Ω were fabricated and characterized at dc and THz frequency. Three types of samples—one with broadband log-periodic antenna, another with double-slot antenna for 300 GHz and third one with double-slot antenna for 400 GHz—have been investigated at THz frequency. New design of antenna coupling with Josephson junction was elaborated for minimization of THz frequency losses in superconducting film. For a particular case of f=320 GHz double-slot antenna, a ratio for bandwidth Q = f/Δf ≈ 10 was measured.     

Flicker (1/f) noise in tunnel junction dc SQUIDS

We have measured the spectral density of the 1/f voltage noise in current-biased resistively shunted Josephson tunnel junctions and dc SQUIDs. A theory in which fluctuations in the temperature give rise to fluctuations in the critical current and hence in the voltage predicts the magnitude of the noise quite accurately for junctions with areas of about 2 × 10⁴ µm², but significantly overestimates the noise for junctions with areas of about 6 µm². DC SQUIDs fabricated from these two types of junctions exhibit substantially more 1/f voltage noise than would be predicted from a model in which the noise arises from critical current fluctuations in the junctions. This result was confirmed by an experiment involving two different bias current and flux modulation schemes, which demonstrated that the predominant 1/f voltage noise arises not from critical current fluctuations, but from some unknown source that can be regarded as an apparent 1/f flux noise. Measurements on five different configurations of dc SQUIDs fabricated with thin-film tunnel junctions and with widely varying areas, inductances, and junction capacitances show that the spectral density of the 1/f equivalent flux noise is roughly constant, within a factor of three of (10^?10/f)? ₀ ² Hz^?1. It is emphasized that 1/f flux noise may not be the predominant source of 1/f noise in SQUIDS fabricated with other technologies.     

Dissipation in Superfluid 3He Weak Links

We suggest a new interpretation of the Berkeley data on the dissipation of superflow in Josephson junctions in superfluid ³He-B. The measurements are well described by the following relation between the current through a junction and the pressure head applied to it (current-pressure relation or CPR): $I = G_1 P + G_2 \sqrt P $ . The Berkeley group has proposed an explanation based on 1) ballistic removal of quasiparticles from the junction; 2) dissipative motion of the anisotropy axis of the order parameter inside the junction. We argue that part 1) of the model, which is responsible for the G ₂ part of the CPR, is invalid, since it presumes the existence, in the bulk, of quasiparticles with energies inside the superfluid gap. Part 2) which is responsible for the G ₁ term implies that the anisotropy axis of the order parameter strongly depends on the phase difference across the junction. Our agternative model is based on mechanisms well known in superconductors: dissipation due to time lag of inequilibrium order parameter and/or Andreev reflection of quasiparticles trapped inside the junction. For the parameters of the Berkeley experiment these models give the same order of magnitude for the G ₁ in the CPR, and are in rough agreement with the experiment. The nature of the G ₂ term remains mysterious. It could arise due to saturation of the current of Andreev-scattered quasiparticles if the quasiparticle relaxation time in the junction is considerably longer than in normal Fermi liquid.