Transient relaxation of the normal state resistance of tin microstrips in the presence of current bias

The transient relaxation of the normal state resistance in tin microstrips has been measured. The microstrips were current-biased below their dc critical current and excited into the normal state with electro optically produced current pulses, with durations as short as 600 psec, by temporarily exceeding the critical current. The effective relaxation time was measured by directly observing the voltage across the microstrip during the normal-superconducting transient. A region was observed in which the relaxation time decreased with increasing current pulse height. The relaxation time was found to be independent of temperature over the range 0.95T/T _c 0.77.     

Theory of the Andreev reflection and the density of states in proximity contact normal-superconducting infinite double-layer

Proximity contact N-S double-layer with infinite layer widths is studied in the clean limit. The finite reflection at the interface is taken into account. Starting from a recent theory of finite width double-layer by Ashida et al., we obtain explicit expressions for the quasi-classical Green's function which already satisfy the boundary condition and include no exploding terms at infinities. The self-consistent pair potentials are obtained numerically with sufficient accuracy. The Andreev reflection at the N-S interface is discussed on the basis of the self-consistent pair potential. It is shown that there exists a resonance state in a potential valley formed between the depressed pair potential and the partially reflecting interface, which leads to a peak of the Andreev reflection coefficient with the height unity slightly below the bulk superconductor energy gap. We also find general relationship between the Andreev reflection coefficient and the local density of states of the superconductor just at the interface.     

Phase-slip centers in superconducting indium microbridges

Measurement is made of the transition to the resistive state of nearly one-dimensional superconducting microbridges of indium. The length of the microbridges ranged from 30 to 130 µm. The experiments concentrated in particular on the onset and temperature dependence of the hysteresis of the voltage-current characteristic, the temperature dependence of the excess current, and the equivalent normal length of the phase-slip centers generated during the resistive transition. The results are in good agreement with the dynamic model of a phase-slip center proposed by Kadin, Smith, and Skocpol.     

Phase-slip centers in superconducting aluminum strips

Phase-slip centers in aluminum strips are analyzed in detail. Measurements have been performed on the spatial dependence of the electrochemical potential and the energy gap. Exponential decay of the quasiparticle potential is found, with a diffusion length that follows a (T _c ?T)^?0.25temperature dependence. The relaxation rate is higher than expected, corresponding to an inelastic scattering time of 4 ns. This is likely due to enhanced electron-electron scattering in two-dimensional metals. Gap measurements show depression of the gap in a region of more than 20 µm. Longitudinal nonequilibrium of the quasiparticles is probably responsible. For the time-averaged supercurrent divided by the critical current a value of 0.3 is found in the neighborhood ofT _c ,lower than observed in tin and indium.     

The proximity effect of the normal-superconducting superlattice

We propose an iterative procedure to solve the linearized Gorkov equation and calculate the superconducting critical temperature of superconductor-normal metal superlattice in the whole region of layer thickness. We also give a discussion of the validity range of the local approximation made on the proximity effect of SN superlattice.     

Nonlinear current-voltage characteristics of normal-superconducting boundaries

The voltage drop at a normal-superconducting boundary is considered in the case when the current flowing across the boundary is of the order of the critical current of the superconductor. The finite supercurrent decreases the distance the electric field penetrates into the superconductor, and leads to a nonlinear current-voltage characteristic. Explicit calculations are carried out for a dirty superconductor close to the transition temperature.Supported in part by National Science Foundation Grant DMR 78-21068.     

Phase-slip centers in long superconducting filaments

The behavior of phase slip centers and their interactions via exchange of ac and dc quasiparticles in long superconducting filaments are studied with samples fabricated by using an electron beam lithography technique. The data show that the ac decay length of quasiparticles is shorter than the dc decay length in indium at temperatures nearT _c . The interactions among phase slip centers in the long filament are interpreted on the basis of critical current variations due to quasiparticle exchange, from which a dc decay length 5.0 µm for indium atT/T _c =0.992 has been obtained. The results indicate that a phase slip center can be used as a quasiparticle detector to obtain information about other phase slip centers and their mutual interactions.Supported in part by the National Science Foundation.     

Microscopic theory of the current-voltage relationship across a normal-superconducting interface

Measurements by Pippardet al. have shown the existence of an extra resistance due to the penetration of an electrical potential into a superconductor. Previous theories of this effect are unable to explain the full temperature dependence of the extra resistance because they use oversimplified models of the normal superconducting interface. We show that the microscopic theory for dirty superconductors leads to a good agreement with experiment over the whole temperature range.This work was supported by the Science Research Council under grants B/RG/68265 and GR/A65218.     

Mechanism of the effect of the normal-superconducting transition on the amplitude-dependent damping and modulus defect in lead

Measurements of the amplitude-dependent damping and modulus defect in lead of various purities in the normal and superconducting states were carried out at frequencies of 100 kHz and 5 MHz. It is found that the effect of the normal-superconducting (N-S) transition is different for the amplitude-dependent damping and the modulus defect, this difference being dependent on the purity of the specimens used and the frequency of the measurements. Two cases are observed. In the first the ratio of the amplitude-dependent damping to the corresponding modulus defect is the same in both the N and S states, and in the second the ratio is changed significantly at the N-S transition. It is shown that in the first case the damping is due to hysteretic loss alone and the N-S transition only changes the conditions of dislocation breakaway from the pinning points. In the second the dynamic loss contribution determined by the viscous drag of the dislocations to the total loss is essential and the N-S transition changes the magnitude of that contribution. A model is proposed to take into account the influence of viscous drag of the dislocations upon the amplitude-dependent damping and modulus defect. A method of evaluating of the dynamic contribution in the total loss is suggested. The results obtained are discussed in terms of existing models of the effect of the N-S transition on the conditions of dislocation breakaway and of the present model.     

Phase-slip resistivity in high-temperature superconductors: a manifestation of intrinsic nano-granularity

Several critical experiments have shown that the so-called background magnetoresistance which occurs with no Lorentz force activation is isotropic in thea-b plane. This isotropic resistivity is linked to paradoxical behavior of vortices which cannot be changed by pinning, a result which may imply intrinsic pinning. Nevertheless, a number of flux-flow observations indicate that vortices may also behave as if they were unpinned. An explanation is proposed which states that this behavior arises as a consequence of defects in oxygen ordering in the Cu-O planes of HTSC crystals; this explanation involves segmentation of the Cu-O planes, and Josephson coupling between adjacent segments. The effective junction areas are seen to be very small, with dimensions characteristic of the size of the unit cell. Thermal motion of nano-scale weak links resolves the pinning paradox by inducing phase-slip resistive dissipation. The resulting phase-slip resistivity is shown to have axial symmetry, that is, the resistivity is independent of the angle between the current and the applied field, with both in thea-b plane.     

Energy relaxation during inelastic electron scattering on localized states

A mechanism which can be responsible for the phase relaxation in polycrystalline semiconductors and metals is proposed. This mechanism is related to the inelastic scattering of electrons on localized states with energies near the Fermi level.     

Phase-slip centers of superconducting indium bridges with variable thickness in a magnetic field

We have measured current-voltage (I–V) curves in magnetic fieldsH, for indium variable-thickness bridges whose strips were quasi-one-dimensional superconductors. TheI–V curves take three different types depending on theH regions. One has hysteresis due to phase-slip centers. The others have no hysteresis. The critical current againstH shows hysteresis owing to the surface currents induced byH. The modification of the pair-breaking time was introduced to treat theH dependence of the hysteresis ofI–V curves.     

Phase-slip centers in superconducting whiskers of Pb with small concentrations of In and Bi

The current-induced transition from the superconducting to the normal state in whiskers from Pb,Pb-In andPb-Bi has been investigated. Very close to the critical temperatureT _c0 the voltage-current(V-I) characteristics show linear portions that are not separated by voltage jumps. For lower temperatures a voltage-step structure occurs. The temperature region over which the step structure extends is shifted towardsT _c0 for decreasing mean free path l of the conduction electrons. The differential resistance of the first linear part of the characteristics in most cases does not depend on temperature like the related normal-like length that is proportional to l^1/2 in agreement with the phase-slip model of Skocpol, Beasley, and Tinkham. Very close toT _c0 the time-averaged supercurrent still flowing above the critical current is about the critical current itself. The shape and the characteristic properties of theV–I characteristics are compared with theoretical predictions.     

Investigation of electric field penetration into superconducting tantalum near a normal-superconducting interface

The temperature dependence of the excess resistance of Ta-Cu-Ta sandwiches was investigated. The samples were prepared by the mutual rolling of the bulk materials, with the thickness of the superconducting plates (0.1 cm) much greater than the penetration length of the electric field into the superconductorl _E up to temperatures very close toT _c. The penetration of the electric field through the clean NS interface into a superconductor with a relatively long electronic mean path (1 ₀) was studied. We used an rf SQUID voltmeter to measure the resistance, 10^–9 , at currents not exceeding 1 mA. The experimental data were compared with the Artemenko-Volkov and Hsiang-Clarke theories. The electron-phonon relaxation time for our tantalum sample was estimated to be 1×10^–10 sec.     

Research on relaxation modulus of viscoelastic materials under unsteady temperature states based on TTSP

The main goal of this work is to obtain relaxation curves of Hydroxyl-Terminated Polybutadiene (HTPB) propellant under unsteady temperature states. A series of relaxation tests of HTPB were carried out, with the strain level ε ₀ of the tests being applied with a ramp time of strain rate $\dot{\varepsilon}_{0}$ . A method is proposed to compensate for stress relaxation during the period of strain rate loading. The proposed method is compared to a numerical method and a general method in terms of accuracy of determination of relaxation modulus. The results show that the relaxation moduli obtained by the proposed method and the numerical method are more accurate than those from the general method; in addition, the proposed method is more convenient in data processing. The relaxation modulus values under unsteady temperature states were obtained from a series of relaxation curves under constant temperature, and at different temperatures according to Time-Temperature Superposition Principle (TTSP). In this work, reduced time is defined as a function of time-temperature shift factor a _T and a variable ψ(T) called ‘zero time’ which depends on temperature. A comparison of test results showed that the values of relaxation modulus that take ‘zero time’ into account are more accurate than those without ‘zero time’.     

Carrier relaxation through localized states in metallic and insulating YBa2Cu3O7−δ

The temperature dependence of photoexcited carrier relaxation in insulating and metallic YBa₂Cu₃O_7-δ and La_1.85Sr_0.15CuO₄ suggests that carriers relax towards equilibrium by hopping between localized states. The implication is that in the optimally doped superconducting phase, localized states and extended states co-exist. The findings confirm the polaronic interpretation of the MIR band in the optical conductivity.     

Thermometry with a nearly temperature independent sensitivity using a normal-superconducting tunnel diode biased close to the superconducting gap

We analyze the temperature dependence of the tunneling current in a normal-insulator–superconductor (NIS) tunnel junction and find that such a junction can serve as a primary thermometer below the superconducting critical temperature T_c with a nearly temperature independent sensitivity, provided the junction is suitably biased close to the superconducting gap. Deviations from expected behavior when the superconducting electrode does not follow most simple s-wave BCS density of states, and possible applications are briefly discussed.     

Compositional effects on microstructure evolution and microwave properties of silver–palladium based thick film microstrips

Recent improvements in materials and processing technologies have dramatically increased the frequency range where ceramic thick film circuits can be utilized. Coupled with inherent advantages of thick film technology viz. low manufacturing cost, multilayering capability and relative insensitivity to substrate surface characteristics, such improvements have resulted in circuits that are penetrating the domain which was previously reserved to thin film technology. In view of newer developments in modern electronics, there is still ample scope for the development of new materials and processes especially in thick film technology. In thick films, conductors play a major role and silver–palladium is one of the important conductor materials in microelectronic circuits. Efforts are made in this work towards the development of suitable silver–palladium thick film conductors from the standpoint of microwave applications. The properties such as surface microstructure, sheet resistance, adhesion and microwave performance of the indigenously developed silver–palladium paste compositions is reported here. Highly porous surface structure, low adhesion and low characteristic impedance of thick film microstrip are observed for pastes with high palladium concentration.