Penetration of magnetic field into high-temperature superconductors

The penetration of a monotonically time-increasing magnetic field in high-temperature superconductors (HTSC) slabs with the power law dependencies of the critical current density and resistivity on the magnetic field is investigated theoretically. It is shown that the asymptotic solutions of the extended critical state model correspond to the cases of the classical critical state model and the model of viscous flux flow without pinning. The ranges of the applicability of these models and the conditions for the transition from one model to the other are determined. These theoretical conclusions explain experimental data presented in scientific literature     

The materials equation and scaling law of flux pinning in high Tc superconductors

In order to increase the critical current density and trapped magnetic field in high T_c superconducting materials, various kinds of inhomogeneities were introduced and used as pinning centers of flux lines. A universal scaling behavior of the pinning force is observed in different high T_c cuprates. We show that this scaling law is a natural result of a unified materials equation for type-II superconductors. This equation agrees reasonably well with recently observed phenomena.     

Induced current in a Bi2Sr2CaCu2Ox superconductor tube

Experiments were conducted to measure the induced current in a high-temperature Bi₂Sr₂CaCu₂O_x superconductor tube that was excited by an external coil driven by an AC sinusoidal voltage source. Experimental data were obtained for tests without and with an iron core inside the superconductor tube. All of the tests were conducted at 77 K and an excitation frequency of 60 Hz. The results showed that immediately after field penetration, the induced current (RMS value) decreased from the critical current, then began to recover, and eventually approached the critical current again at a high excitation current. Before field penetration, the induced current was mainly shielding current, which is 180 ° out of phase with the excitation current. After field penetration, the induced current consisted of two parts, a shielding current that led the excitation current by 180 ° and an inductive current (Faraday's law) that led the excitation current by 90 °. The presence of the iron core amplified the drop in induced current immediately after field penetration and delayed the growth of the inductive current after field penetration.     

Fluxon modes in stacked HTSC intrinsic Josephson junctions

Fluxon modes in stacked Josephson junctions (SJJ's) are studied both theoretically and experimentally. It is shown that the critical current J_c across the stack is multiple valued due to a possibility of having different fluxon configurations (modes), which is in good agreement with experiment on Bi₂Sr₂CaCu₂O_8+x, the temperature and magnetic field dependencies of the critical current were calculated for a stack with nonidentical junctions.     

Large Shapiro steps and wide junction behaviour in HTS Josephson junctions at nitrogen temperatures

We have fabricated bicrystal high-T_c superconductor (HTS) Josephson junctions which, under microwave radiation, exhibited first current steps (1. Shapiro steps) with an amplitude of 1 mA at 80 K. This was possible because of a considerable increase of the critical current I_c of the junctions by increasing the HTS film thickness up to 700 nm. However, above a certain I_c threshold, the junction behaviour deviated from the simple resistively shunted junction (RSJ) model. We show that the junctions can be described by the wide junction model. Both the static (dependence of I_c on magnetic field) and the dynamic characteristics (response to microwave radiation) of our junctions can be well fitted in the frame of the wide junction model. We present data of junctions with relative widths w/λ_j=5 and 7 (w-physical width of the junction, λ_j-Josephson penetration depth), i.e. with w/λ_j lying in the intermediate interval where the behavior of the junctions is most sensitive to changes in w/λ_j. This allowed us to fit experimental data with relatively good accuracy. We discuss the consequences of wide junction behavior on the maximal first Shapiro step and the impact on metrological applications of HTS Josephson junctions.     

AC losses in type-II superconductors induced by nonuniform fluctuations of external magnetic field

Magnetic field fluctuations are inevitable in practical applications of superconductors and it is often necessary to estimate the ac losses these fluctuations induce. If the fluctuation wavelength is greater than the size of a superconductor, known estimates for an alternating uniform external magnetic field can be employed. The authors consider the opposite case and analyze, using a model critical-state problem, penetration of spatially nonuniform fluctuations into type-II superconductors. Numerical simulation is based on a variational formulation of the Bean model. The analytical solutions, found in a weak penetration limit, are used to evaluate ac losses for two types of fluctuations: the running and standing waves. It is shown that for spatially nonuniform fluctuations the losses are better characterized by the fluctuation penetration depth than by the fluctuation amplitude. The results can be used to estimate the ac losses in flywheels, electric motors, magnetic shields, etc.     

Low noise “ohmic” contacts on n-type silicon

A technique is given for preparation of low noise ohmic contacts on n-type silicon using silver-silicon eutectic. It allows reaching electric fields up to 20 kV cm¹ in a wide range of resistivities and lattice temperatures (300–6°K). Interface chemical composition and structure is studied using scanning electron microscopy and X-ray analysis. Contact resistivity ?_c is studied versus bulk resistivity ? and lattice temperature T. High field conductivity shows that ?_c is not sufficient to characterize ohmic contacts. It is shown that the contact noise (j²/f) law is valid up to 500 MHz and that noise measurements are much more sensitive to contact behavior than first order coefficients. Contact noise may be important at intermediate bias but is proved to be negligible both at very low and very high bias. Moreover it has been possible to define a contact quality factor which provides a quantitative characterization of contact behavior.     

Ballistic mobility and saturation velocity in low-dimensional nanostructures

Ohm's law, a linear drift velocity response to the applied electric field, has been and continues to be the basis for characterizing, evaluating performance, and designing integrated circuits, but is shown not to hold its supremacy as channel lengths are being scaled down. In the high electric field, the collision-free ballistic transport is predicted, while in low electric field the transport remains predominantly scattering-limited in a long-channel. In a micro/nano-circuit, even a low logic voltage of 1 V gives an electric field that is above its critical value ε_c (ε?ε_c) triggering non-ohmic behavior that results in ballistic velocity saturation. The saturation velocity is an appropriate thermal velocity for a non-degenerate and Fermi velocity for a degenerate system with given dimensionality. A quantum emission may lower this ballistic velocity. The collision-free ballistic mobility in the ohmic domain arises when the channel length is smaller than the mean free path. The results presented will have a profound influence in interpreting the data on a variety of low-dimensional nanostructures.     

Low temperature magnetic penetration depth in d-wave superconductors

We briefly review the experimental results of the low temperature magnetic penetration depth λ(T) of d-wave superconductors. In very clean high-T_c superconductors (HTSC) the low temperature in-plane penetration depth λ_‖(T) varies linearly with T. A weaker power law temperature dependence is found for the out-of-plane penetration depth λ_⊥(T) in most of HTSC. In the organic superconductors κ-(BEDT-TTF)₂X [X=Cu(NCS)₂, Cu[N(CN)₂]Br] and slightly dirty HTSC λ_‖∝bT²/(T*+T), where is deduced from an impurity scattering model. In clean CeCoIn₅ a crossover from linear to quadratic temperature behavior at low T was interpreted as the first evidence for nonlocal effects in a d-wave superconductor.     

Analytical model of superconducting to normal transition of bulk high Tc superconductor BSCCO-2212

A comprehensive theoretical expression for the superconducting-to-normal transition of high-temperature superconducting (HTS) materials is derived. The electric field and resistivity of bulk melt-cast processed BSCCO-2212 are derived from the superconducting, flux creep, flux flow, and resistive properties of high critical temperature superconductors (HTS). An asymptotic function is used to model the Bean and Ohmic limits of the E(B,T,J) characteristics. Comparison is made with the experimental results of Elschner et al. The new model may be used in simulating the operation of HTS power equipment, and may be applicable to other HTS materials.     

A.c. loss measurements in high-tc superconductors

Low a.c. loss is a key issue for electrical engineering applications of high-T_c superconductors at industrial frequencies. Different material options are characterized by three different a.c. loss measurement techniques which approach as much as possible the application conditions of the conductors. Melt-textured-growth YBa₂Cu₃O_7−x bulk samples, suitable for magnetic bearings, are characterized in an external a.c. field by magnetization measurements. Melt-casted Bi₂Sr₂Ca₂Cu₃O_8−x samples and powder-in-tube Bi₂Sr₂Ca₂Cu₃O_10−x tapes are suitable for current leads or power cables. In these applications the conductors are exposed to a.c. transport currents. The associated losses in self field are measured by a very sensitive electrical measurement technique. Finally, a calorimetric method is necessary when larger conductors (for instance Bi₂Sr₂Ca₂Cu₃O_8−x tubes) are tested under transport currents I_t, generating a transverse magnetic field H α I_t, as encountered in magnet windings for SMES, transformers or generators. The results show that the a.c. losses are sufficiently low for self field applications at industrial frequencies and a comparison of the different high T_c superconductors is given. The results show further that the a.c. losses are essentially hysteretic and can be modeled using the Bean model.     

Geometrical magnetoresistance and negative differential mobility in semiconductor devices

The tensors of differential and static mobilities of hot electrons in a magnetic field are calculated in the frame of a model assuming electron energy-dependent relaxation times. It is shown that an N-type curve for ν(E) (drift velocity versus electric field) should become of an S-type in a strong enough magnetic field if the Hall field is short-circuited due to the sample configuration. An S-type (in the absence of a magnetic field) curve for ν(E) may become N-type in similar conditions. These effects are due to the peculiarities of geometrical magnetoresistance (GMR) in high electric and magnetic fields. Numerical calculations are performed for Si, GaAs, InP and Ga_0.3In_0.7Sb. For GaAs at room temperature the critical value of a magnetic field which is necessary for the turnover of the curve for ν(E) is about 30 kOe. It is demonstrated that for a conventional Hall sample the differential Hall mobility in high magnetic and electric fields should be strongly frequency-dependent on frequencies about and higher than an inverse differential dielectric relaxation time. It may diverge at these frequencies if the differential mobility in the absence of a magnetic field is negative. It is shown how the measurements of GMR for hot electrons can be used to estimate the maximal value of the negative differential mobility.     

Fabrication and Characterization of Bi(Pb)-Sr-Ca-Cu-O/Ag2O Superconducting Tubes

Superconducting magnetic shields of Bi_1.7Pb_0.4Sr_1.6Ca_2.4Cu_3.6O_y with or without Ag₂O superconductor were fabricated in tubular form with one end closed by using a cold isostatic pressing method. It was found that the addition of Ag₂O in the BPSCCO samples resulted in no significant effect on T_c when sample were treated at 835‡C in air. However, the critical current density and the shielding magnetic flux density (at 77K) were found to be decreased, compared to the pure BPSCCO sample. The correlations of superconducting properties with micro-structure of these materials are discussed in this paper.     

Mechanism of current flow in a Au-Ti-Al-Ti-n +-GaN ohmic contact in the temperature range of 4.2–300 K

The temperature dependence of the contact resistivity ρ _c (T) of Au-Ti-Al-Ti-n ⁺-GaN ohmic contacts is studied experimentally and substantiated theoretically in the temperature range T = 4.2–300 K. It is shown that the saturation portion of ρ _c (T) is observed in the low-temperature measurement region (4.2–50 K). As the temperature increases, ρ _c decreases by the exponential law. The experimental and calculated dependences ρ _c (T) are in agreement. The obtained results make it possible to conclude the field nature of the current transfer for the saturation region of ρ _c (T) and the thermal-field one, for the exponential region.     

Long lengths of silver-clad Bi2223 superconducting tapes with high current-carrying capacity

Long lengths of silver-clad (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀ (Bi2223) high-T_c multifilamentary tapes were produced using the powder-in-tube (PIT) technique followed by a thermomechanical process. The relationships between microstructure and electrical, magnetic and mechanical properties of the heat treated tape were evaluated from the critical current density measurements, irreversibility magnetic field determination and mechanical bending tests. Emphasis was stressed on the J_c behavior in magnetic fields at different temperatures. A J_c of 10,000 A/cm² at 77 K in a zero field for a 10 m tape and 75,000 A/cm² at 23 K in a field of 3 T for a short tape was achieved. The results obtained showed that Bi2223/Ag high-T_c composite tapes are a potential alternative to conventional low-T_c superconductors in magnetic levitation (MAGLEV) applications.     

Flux trapping in a ring-shaped YBCO bulk by pulsed fieldmagnetization

A pulsed magnetic field can be applied using small coils to generate a strong magnetic field for the magnetization of the high-Tc superconductors (HTS) to be used as quasi-permanent magnets in flywheels and motors. The dynamic electromagnetic behavior of two melt-processed ring-shaped Y-Ba-Cu-O bulks using the pulsed field magnetization (PFM) process has been experimentally investigated and analyzed. The flux trapped in the bulk by PFM process was compared to the flux trapped by field cooling process. Both cases then have been analyzed with a numerical model based on the finite-element method (FEM). The power-law model was utilized to relate the electric field to the current density inside the superconductor. The dependence of the critical current density on the magnetic field density was taken into account. Measured and calculated results are compared and discussed     

Development of needle-shaped grains from Bi2Sr2CaCu2O8+x with high critical current density suitable for making superconducting wires

We present a grain microstructure for Bi(2212) consisting of only giant needle-shaped grains of around 1.5 mm length and 100 μm diameter. We study the structural and chemical changes suffered by a conventional ceramic Bi(2212) sample in the course of the thermal treatment used to obtain those giant needle-shaped grains. For that, different samples of the same batch were treated with incomplete thermal treatments, and the resulting samples were analysed by using scanning electron microscopy (SEM), optical microscopy, energy dispersed spectroscopy (EDS), inductively coupled plasma (ICP) and X-ray diffraction (XRD). To verify the superconducting nature of the needle-shaped grains, we have performed magnetization, resistivity, and critical current measurements on the original ceramic sample, and on that formed as giant needle-like grains. The critical temperature of these last grains is nearly the same as that of the ceramic sample (T_c∼90 K), which is a high value for the Bi(2212) compound. The critical current density (J_c) of the needle-shaped grains is around 2500 A/cm² at 77 K and in absence of applied magnetic field, a value comparable with that presented for the best wires and thick films. Not only are the shape and the size of these grains very suitable for making superconducting wires, but also the superconducting properties, T_c and J_c, are both high enough to be confident about the possibility of improving the actual Bi(2212) superconducting wires for high current applications.     

A numerical study of field-aided diffusion

A numerical method for determining the effect of the internal electric field on the diffusion of impurity ions in semiconductors is described. The model of the diffusion process is defined by the flux equations, the continuity equations and Gauss' law. Due to the complexity of this model, there is no known analytical solution. However, the system of nonlinear equations is solved numerically using an iteration technique.Diffusion profiles are presented for boron diffusing in silicon at 1100°C for various values of surface concentration C₀. These profiles are compared to the complementary error function which is the correct solution neglecting the internal electric field. The impurity profiles are also compared to those obtained by solving an approximate diffusion equation derived by using the concept of a concentration dependent “effective” diffusion coefficient.It is shown that the influence of the electric field on the motion of the impurities is a strong function of the surface concentration. For high values of C₀, the impurity profile becomes exponential. The accuracy of the solutions obtained by solving the approximate diffusion equation depends on both the value of C₀ and the diffusion time.     

Microstructure-critical current relationships in hard superconductors

The pinning of the flux line lattice (FLL) by crystal lattice defects gives rise to a critical current density J_c for hard superconductors. The volume pinning force density F_p = ‖BXJ_c‖ however, depends both on the elementary interaction force f_p between a single defect and the FLL and on the nature of the summation of these many f_p’s. The latter will depend on the spatial arrangement of defects and on the elastic and plastic deformation properties of the FLL. For localized defects the f_p is a strong function of defect “size”, reaching a maximum when the size is approximately the coherence length, and is approximately proportional to H_c ²(T) (1−h) where H_c is the thermodynamic critical field and h is the reduced magnetic field H/H_c2. The summation model must give a F_p which obeys the following empirical rules: 1) F_p has a maximum at a reduced field h_p which decreases with increasing defect density ρ and f . 2) F_p at h > h_p is structure insensitive while F_p at h < h_p is structure sensitive. 3) A scaling law is obeyed if T is changed, i.e., F_p = H_c2(T)_m .f(h), where m is ∿2.5 andf(h) is only a function of reduced field and microstructure. Experimental evidence for these generalizations is presented and a model which predicts these results is outlined and quantitatively tested. Work supported by the U. S. Energy Research and Development Administration.     

Ferrite-dielectric resonators made of uniaxial ferrites in before-the-resonance region

Theeffect of splitting resonant frequencies of azimuthally heterogeneousHE _±11δ oscillations of a disc ferrite-dielectric resonator made of barium hexaferrite is studied in external magnetic field on frequencies below 47 GHz. Applicability of the developed earlier analytical theory of electromagnetic oscillations in magneto-gyrotropic resonators to mode identification and calculation of field dependencies of magnetic oscillations’ resonant frequencies in the before-the-resonance region is demonstrated. Hysteresis effect is discovered in the field dependencies of magneto-dynamic oscillations’ eigenfrequencies in resonators made of uniaxial ferrite. The influence of dielectric layer between the resonator and the metal screen on frequency splitting of HE _±11δ oscillations is studied. The possibility of using ferrite-dielectric resonators in the self-magnetization mode is discussed.