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.     

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.     

The kosterlitz-thouless transition and vortex dynamics

The physics of the Kosterlitz-Thouless vortex-unbinding transition in two-dimensional superfluids is discussed, and theN ×N Josephson junction array is considered as a prototype system. Dynamical behaviour is considered in two cases: (a) the complex impedance shows structure at a frequency-dependent transition temperature, similar to the dynamic susceptibility of a spin glass; (b) with a perpendicular non-uniform magnetic field, of a particular ‘self-similar’ hierarchical pattern, a scaling argument gives non-exponential relaxational dynamics of a prepared non-equilibrium vortex distribution.     

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.     

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.     

Josephson Current Through Planar Pb–Cu–Pb Nanobridges

We report on the fabrication and characterization of coplanar Pb–Cu–Pb nanobridges. In such superconductor (S) – normal metal (N) – superconductor junctions the Josephson coupling is mediated via the proximity effect at the S–N interface. For a junction in the dirty limit (ℓ≪ ξ _N where ℓ is the mean free path and ξ _N is the coherence length in N) the Josephson current I _c is proportional to L/ξ _N ·exp(−L/ξ _N ). The relation defines an upper limit for the length L of the normal-metal bridge in order to observe Josephson coupling. A Josephson current of up to 750 μA at 1.5 K was observed in junctions with L/ξ _N = 0.82 which is only 1/8 of the theoretically expected value. The reduction might originate from oxide layers at the normal metal – superconductor interfaces.     

S-N-S Josephson Weak Links in Superluid 3He-B

The Josephson current is calculated for an SNS junction consisting of two reservoirs of superfluid ³ He-B connected via thin cylindrical channels. The current-phase relations and maximal Josephson currents are calculated for channels of different diameter and length.     

Angular Dependence of the Radiation Power of a Josephson STAR-emitter

We calculate the angular dependence of the power of stimulated terahertz amplified radiation (STAR) emitted from a dc voltage applied across a stack of intrinsic Josephson junctions. During coherent emission, we assume that a spatially uniform ac Josephson current density in the stack acts as a surface electric current density antenna source, and the cavity features of the stack are contained in a magnetic surface current density source. A superconducting substrate acts as a perfect magnetic conductor with H _||,ac=0 on its surface. The combined results agree very well with recent experimental observations. Existing Bi₂Sr₂CaCu₂O_8+δ crystals atop perfect electric conductors could have Josephson STAR-emitter power in excess of 5 mW, acceptable for many device applications.     

Impedance spectroscopy analysis of double perovskite Ho<Subscript>2</Subscript>NiTiO<Subscript>6</Subscript>

The electrical properties of double perovskite Ho₂NiTiO₆ (HNT) are investigated by impedance spectroscopy in the temperature range 30–420 °C and frequency range 100 Hz to 1 MHz. The X-ray diffraction analysis reveals that the compound crystallizes in monoclinic phase. The imaginary part of impedance (Z″) as a function of frequency shows Debye type relaxation. The frequency dependence of Z″ peak is found to obey an Arrhenius law with an activation energy of 0.129 eV. Impedance data presented in the Nyquist plot (Z″ vs. Z′) are used to identify an equivalent circuit and to know the bulk and interface contributions. The complex impedance analysis of HNT exhibits the appearance of both the grain and grain-boundary contribution. The results of bulk ac conductivity as a function of temperature and frequency are presented. The activation energy (0.129 eV), calculated from the slope of log τ versus 10³/T plot, is found to be the nearly same as calculated (0.130 eV) from dc conductivity. The frequency dependent conductivity spectra obey the power law.     

Vortex Lattices in Rotating Bose-Einstein Condensate in an Optical Lattice: Analogy to Uniformly Frustrated Josephson-Junction Arrays

We investigate the effect of rotation for two-dimensional Josephson junction arrays consisting of atomic Bose-Einstein condensates trapped by both a harmonic trap and an optical lattice. This system is analogous to the superconducting Josephson junction array to which a transverse magnetic field is applied, being described by the uniformly frustrated XY model. The frustration parameter f, defined by the rotation frequency of the condensate and the lattice constant of the optical lattice, is an important parameter to determine the ground state. The numerical simulations of the Gross-Pitaevskii equation reveal that for f=1/2 the ground state possesses the checkerboard pattern of vortices, and for f<1/2 the vortex configuration is characterized by the staircase form.      

A Numerical Treatment of the rf SQUID: I. General Properties and Noise Energy

We investigate the characteristics and noise performance of rf Superconducting Quantum Interference Devices (SQUIDs) by solving the corresponding Langevin equations numerically and optimizing the model parameters with respect to noise energy. After introducing the basic concepts of the numerical simulations, we give a detailed discussion of the performance of the SQUID as a function of all relevant parameters. The best performance is obtained in the crossover region between the dispersive and dissipative regimes, characterized by an inductance parameter β′ _L ≡2π LI ₀/Φ ₀≈1; L is the loop inductance, I ₀ the critical current of the Josephson junction, and Φ ₀ the flux quantum. In this regime, the lowest (intrinsic) values of noise energy are a factor of about 2 above previous estimates based on analytical approaches. However, several other analytical predictions, such as the inverse proportionality of the noise energy on the tank circuit quality factor and the square of the coupling coefficient between the tank circuit and the SQUID loop, could not be well reproduced. The optimized intrinsic noise energy of the rf SQUID is superior to that of the dc SQUID at all temperatures. Although for technologically achievable parameters this advantage shrinks, particularly at low thermal fluctuation levels, we give examples for realistic parameters that lead to a noise energy comparable to that of the dc SQUID even in this regime.      

Evolution of Two-Band Superfluidity from Weak to Strong Coupling

We analyze the evolution of two-band superfluidity from the weak to the strong coupling (Bardeen–Cooper–Schrieffer to Bose–Einstein condensation) limit. We find that population imbalances between the two bands can be created by tuning the intraband or interband (Josephson) interactions. In addition, when the Josephson interband interaction is tuned from negative to positive values, a quantum phase transition occurs from a 0-phase to a π-phase state, depending on the relative phase of the two order parameters. We also find two undamped low energy collective excitations corresponding to in-phase phonon (Goldstone) and out-of-phase exciton (finite frequency) modes. Lastly, we derive the coupled Ginzburg–Landau equations, and show that they reduce to coupled Gross–Pitaevskii equations for two types of weakly interacting bosons (tightly bound fermions) in the BEC limit.      

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.     

Experimental evaluation of the nonlinear surface resistance of YBa2Cu3O7?x step-edge grain boundary Josephson junctions

The temperature, microwave current, and dc magnetic field dependencies of the effective surface resistanceR _s of YBa₂Cu₃O_7–x grain boundary Josephson junctions have been investigated at 6 GHz. The junctions were prepared on stepped LaAlO₃ substrates and incorporated into tapered linear half-wavelength microstrip resonators. The characteristic parameters of the heterogeneous resonator were analyzed theoretically considering the junction as a lumped element of complex impedance. The microwave properties of the junction could then be extracted and related to their characteristic dc transport properties. The critical currentI _c of the junction was found to limit the linear power dissipation in the superconducting strip. At microwave currents aboveI _c , highly nonlinear microwave losses occurred, which displayed a characteristic magnetic field modulation. At even higher currents,R _s saturated at a level corresponding to the normal resistanceR _n of the junction.     

Mathematical Model for Transitional Processes in Josephson Cryotrons Based on Tunnel Junctions

In this work, we consider controlling of logical states of Josephson memory cells (cryotrons) based on superconductor-insulator-superconductor (SIS) Josephson tunnel junctions by external current impulses. A mathematical model for the transitional processes that take place during direct logical transitions “0” → “1” and inverse logical transitions “1” → “0” is proposed. By means of mathematical modeling, we investigate transitional processes in cryotrons during the change of their logical state and obtain their transitional characteristics for operational temperatures T ₁=11.6 K and T ₂=81.2 K, close to the boiling temperatures of helium and nitrogen, respectively. It is shown that such memory cells can efficiently operate under the temperature T ₂=81.2 K. The behavior of the Josephson cryotrons as well as their operational stability is explored.     

Power handling capabilities of superconducting YBCO thin films: Thermally induced nonlinearity effects

We have measured the microwave power dependence of the surface impedance Z_s of YBa₂Cu₃O_x thin films up to very high microwave power levels. Films with different crystal qualities, including one with a bicrystal Josephson junction, were investigated. The experiments included both frequency-domain and pulsed time-domain measurements using a 14 GHz TE₀₁₁ dielectric cavity. Our results demonstrate that the dissipation of heat, generated by rf currents in the superconducting film, contributes to the observed nonlinearities in the surface resistance. The relative extent of this contribution is determined primarily by the film quality. A simple Fabry-Perot resonator model, combined with a cavity heat transfer model, was used to analyze the effects of such nonlinearities on the electromagnetic response of the dielectric cavity to a pulsed input signal.     

Electrical impedance of ethylene-carbon monoxide/propylene-carbon monoxide (<Emphasis Type="Italic">EPEC</Emphasis>-<Emphasis Type="Italic">69</Emphasis>) thermoplastic polyketone

Electrical impedance technique was employed to investigate the electrical properties of ethylene-carbon monoxide/propylene-carbon monoxide terpolymer (EPEC-69). The measurements were performed in the frequency range 0.1–10⁵ Hz and in the temperature range 30–110 °C. The results reveal that the dielectric constant, loss factor, modulus, and ac conductivity are dependent of frequency and temperature. A Debye relaxation peak was detected in the plot of Z″ versus frequency where the activation energy was determined and found to be 1.26 eV. When the surface phenomenon effects were separated using the imaginary part of the complex admittance a second dielectric dispersion was observed in the low frequency region. Two models were proposed from the impedance measurements depending on temperature range.     

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.     

A Superconducting Cold-Electron Bolometer with SIS’ and Josephson Tunnel Junctions

A novel concept of a Superconducting Cold-Electron Bolometer (SCEB) with Superconductor-Insulator-Weak Superconductor (SIS’) Tunnel Junction and Josephson Junction has been proposed. The main innovation of this concept is utilizing the Josephson Junction for DC and HF contacts, and for thermal isolation. The SIS’ junction is used also for electron cooling and dc readout of the signal. The SIS’ junction is designed in loop geometry for suppression of the critical current by a weak magnetic field. The key moment of this concept is that the critical current of the Josephson junction is not suppressed by this weak magnetic field and can be used for dc contact. Due to this innovation, a robust two layer technology can be used for fabrication of reliable structures. A direct connection of SCEBs to a 4-probe antenna has been proposed for effective RF coupling.      

Electrical properties of the DGEBA/PANI-Ag composites

The metallopolymer polyaniline-silver (PANI-Ag) was synthesized and used as conductive filler in crosslinked diglycidyl ether of bisphenol A (DGEBA) epoxy network. The hybrid organic/inorganic PANI-Ag powders were successfully synthesized via in situ chemical oxidation of polyaniline-emeraldine base (PANI-EB) by the capped Ag⁺ on the polyaniline-emeraldine base (PANI-EB) surface. The UV–Vis and FT-IR spectra confirmed the pernigraniline structure (PN) of PANI in the hybrid PANI-Ag. The PANI-Ag dispersion in epoxidic matrix was analyzed by optical microscopy (OM). The images analysis from OM showed that the particle agglomerate size of the metallopolymer increased with increasing PANI-Ag concentration in the DGEBA composite, owing to the aggregation effect. The dc conductivity and impedance spectroscopy of the DGEBA/PANI-Ag composite was measured at different PANI-Ag concentrations in the DGEBA network. The electrical dc conductivity of the PANI-Ag was 35.1 S cm⁻¹ and was dependent of the PANI-Ag concentration in DGEBA matrix. The real and imaginary part of impedance complex measurements indicates a strong interfacial polarization at low frequency for both PANI-Ag and DGEBA/PANI-Ag, respectively. The imaginary part of impedance complex Im(Z) data decrease with the PANI-Ag hybrid concentration in the frequencies range of 10²–10⁶ Hz. The dependence of the Im(Z) on the frequency exhibited a relaxation process in both, PANI-Ag and DGEBA/PANI-Ag composite with 10 phr of PANI-Ag powder.