Nonequilibrium theory of dirty,current-carrying superconductors: phase-slip oscillators in narrow filaments near T c

General equations for the dynamic behavior of dirty superconductors in the Ginzburg-Landau regime T _c-T T _care derived from microscopic theory. In the immediate vicinity of T _ca local equilibrium approximation leads to a simple generalized time-dependent Ginzburg-Landau equation. The oscillatory phase-slip solutions presented previously are discussed in greater detail.Supported by the Science Research Council (England) under grant GR/A65218, and by the Deutsche Forschungsgemeinschaft.     

The influence of light- and heavy-ion irradiation on the structure,resistivity, and superconducting transition temperature of V3Si. A comparative study

Channeling and x-ray diffraction measurements on Kr- and He-irradiated V₃Si single crystals and films reveal different damage levels for fluences in cases where the superconducting transition temperature T _chas been reduced by the same amount. This indicates that only special defect structures are responsible for the T _c-reduction mechanism. In the fluence region where T _cis decreasing, T _ccorrelates with residual resistivity _o, independent of the kind of irradiation. However, at particle fluences where T _csaturation occurs, different saturation values of _o are observed. The exponential decrease and the saturation of T _cwith fluence are explained by a similar behavior of g9_o versus fluence in the damage production and saturation processes. The increase of the lattice parameter is not uniquely dependent on the decrease of T _c, but also on the amount of damage present.     

Fluctuations of the Order Parameter''s Phase in Layered Superconductors

The influence of the quantum fluctuations of the order parameter's phase on the critical temperature T _c is studied for a Josephson coupled layered superconductor. Two characteristic critical temperatures exist for a system, namely the superconducting critical temperature T ⁽²⁾ _c for a single layer estimated by the mean-field theory and the transition temperature for the outset or the superconducting phase coherence T* _c . The true critical temperature T _c is shown to vary inside the intervals T* _c T _c T ⁽²⁾ _c . For a strong quantum phase fluctuation limit, the superconducting layers become decoupled.     

Transistor Doping-Predictions for Superconductivity in the Charge Order Model

Transistor doping of potential superconductors promises to illuminate inherent levels and limits for the materials in question. Here some of these limits are quantitatively predicted on a charge order or radical model for a variety of experiments. This model is based on a universal T _c scaling with anionic radical concentration. It is applicable to systems with covalently bonded, high electronegativity components. For the cuprates its general features are a linear increase of T _c with holes, which are normalized per total hole carrying species (e.g., O^– radical density). This dependence proceeds up to optima, corresponding to a uniform alternate hole charge order limit and T _c decreases thereafter with various slopes. The optima are quantitatively calibrated through the deleterious influence of the Blocking layer as measured by its O content. Amongst the predictions is a general limit of T _c ^max 167 K for oxide superconductors, obtainable in infinite layer type compounds (CaCuO₂). Other predictions are optimal T _c 83 K for La₂CuO₄ and maximum values potentially near 500 K for borides or carbides.     

Thermal conductivity of a Kondo superconductor in the gapless state

The thermal conductivity coefficient for a Kondo superconductor in the gapless state is obtained within the framework of the Matsuura, Ichinose, and Nagaoka theory. By expanding the heat current correlation function appearing in the Kubo formula for the thermal conductivity in powers of the order parameter, analytical expressions for the thermal conductivity to second power in the order parameter are obtained. The thermal conductivities for bothT _KT _c 0 andT _KT _c 0 superconductors are obtained.     

Scaling Equation of State for a Nonequilibrium Solution Under Gravity Close to Phase Interface

Experimental investigations of equilibration kinetics for a methanol-hexane binary solution under gravity have been carried out at temperatures T below the critical consolute temperature, T<T _c , by using a refractometry technique. As a result of the experiment, both equilibrium n _z (z,t _e ) and nonequilibrium n _z (z,t) height dependences of the refractive index gradient n _z at different times t after the beginning of thermal equilibration have been obtained. Analysis of the data shows that the relaxation properties of the system at different fixed heights are determined not by a single relaxation time (z), but by a spectrum of relaxation times _i (z _j ,t). On the basis of the experimental data, the height dependence of the relaxation times has been analyzed for the studied solution in the course of its transition to equilibrium. The average relaxation time has been shown to decrease when nearing the phase interface (z=0). The relaxation time (z,t) at a certain height z has been shown to also decrease when the system approaches an equilibrium state. A dynamic nonequilibrium equation of state has been proposed on the basis of the fluctuation theory of phase transitions for a substance under gravity close to the phase interface of a binary solution. It is based on the assumption that for small solution concentrations, (c–c _c )/c _c <<1, every nonequilibrium height distribution n _z (z,t) corresponds to an equilibrium distribution n _z (z,T) at a certain temperature T=T–T _c . Here, c _c is the critical concentration of the solution.     

Musical, Bond Ordered Superconductors—Does a Common Phenomenological Model Hold for All High Tc Materials [Cuprates, C60, MgB2, C–S Composites etc.]?

The presence of high T _c (e.g., 117 K) in doped C₆₀ poses the question for the ultimate condition of superconductivity in this and related systems, which are devoid of complex ingredients such as magnetic transition metals. To answer this question, essential aspects of cuprate phenomenology are generalized. A quantitative and universal T _c formalism is developed from empirical rules for the cuprates. Accordingly, T _c increases linearly on doping up to a sharp peak, corresponding to an optimal charge order filling, and decreases thereafter. The hole filling degree of an optimal bond order depends on lattice pressure. Shape of the T _c-hole dependence and magnitude of T _c on the bond order model are born out by transistor doping of CaCuO₂, which is here used as a calibration. Inferences are drawn concerning the optimal bond order. Accordingly, linear local pair kernels are based on a newly postulated trijugate bond system that is mobile, while electronically frozen orders are based on tetrajugate bonding. In the superconductor, linear pair patterns are correlated into a two-dimensional bond order pattern by energies such as elasticities. This concept is here extended to materials based on other electronegative materials. Accordingly, arguments are presented that a common basis for their superconductivity lies in a novel chemical bonding state (e.g., trijugate) in a doped covalent lattice. The hallmarks of the bond order model are also born out by the curve shape of transistor doping of C₆₀. A disproportionation of pairs per molecule is proposed for optimal doping. Complex redox equilibria within laminated layers in the structure can lead to self-doping and can relieve lattice pressure in complex cuprates, MgB₂, C₆₀, or C–S composites.     

Optimization of superconducting critical temperatures by control of cation and anion stoichiometry in Bi2Sr2CaCu2Oδ-based solid solutions

T _c data are reported for powders of cation-stoichiometric Bi₂Sr₂CaCu₂O and for nonstoichiometric samples based on the three mechanisms BiSr, SrCa and Sr vacancy. For each, the T _c values depend critically on the final oxygen contents, which were varied by heating samples in either O₂ or N₂ at different temperatures. Stoichiometric Bi₂Sr₂CaCu₂O has the highest T _c, 92 K, obtained after heating in O₂ at 820 °C. Heating in O₂ at lower temperatures gives rise to overdoping and T _c decreases to 60 K. The other cation compositions show a smaller maximum T _c but also less reduction in T _c on overdoping. Under-doped samples, with reduced T _c values were obtained on heating in N₂. These data, together with selected literature results, lead to a unified picture of the variation of T _c with cation composition and oxygen content.     

Isotactic polypropylene/polyisobutylene blends: morphology-structure-mechanical properties relationships

Morphological observations by optical and scanning electron microscopy, wide (WAXS) and small (SAXS) angle X-ray scattering, differential scanning calorimetry (DSC) and mechanical tests have been performed on sheet specimens of isotactic polypropylene (iPP)/polyisobutylene (PIB) blends obtained under different crystallization conditions. Two kinds of morphologies have been observed, particularly at high crystallization temperatureT _c, on thin sections of the same sheets: a spherulitic one in the centre and a row-like structure on the edges. The size of the spherulites, as well as the thickness of the row-like regions, decreases with diminishingT _c, and seemsto be independent of the amount of rubber. The adhesion among the spherulites and between the spherulites and the row-like regions seems to become poorer with higherT _c. The rubber particles seem to be evenly dispersed into the iPP matrix for samples quenched at low temperatures, whereas for samples isothermally crystallized (at highT _c) their concentration seems to be slightly higher at the border of the spherulites than in the centre. The overall crystallinity measured by DSC and by WAXS is an increasing function ofT _c and decreases with increasing amount of PIB. The index of iPP phase, quite low indeed (max 3%), drops with loweringT _c and with enhancing PIB percentage. The long spacingL for a given quenching temperatureT _q is independent of PIB content, whereas for isothermally crystallized samples at low undercooling varies differently according toT _c. The lamellar thicknessL _c is always a decreasing function of rubber content. Stress-strain analysis shows a more and more brittle behaviour both with increasingT _c (beyondT _c=122° C all the specimens are very brittle irrespective of PIB amount) and PIB amount in accordance with the morphological observations. Some tentative hypotheses have been made to explain the observed behaviour.     

c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

Questioning the Assumptions of the Parabolic Model for Superconductive Cuprates

The assumptions of the parabolic model are questioned. These assumptions pertain to an expectation of universal T _c optima for cuprates at an experimental hole concentration of p = 0.16n, where n is the number of CuO₂ planes. This model was developed based on the T _c maximum for La_{2 – x} Sr _x CuO₄ at x = 0.16. However, a variety of cases are presented for higher optimal hole concentrations, including La₂CuO_4.16, where it is twice as high. Also, the success of a charge order model in universally predicting optimal T _c at formal stoichiometric holes, h = 0.5n, suggests a need for expansion of the parabolic model. By quantitatively taking into account the deleterious effect of the blocking layer, optimal T _c can be absolutely calibrated at a uniform optimal charge order with alternate holes.     

Pair breaking, “intrinsic”Tc, and the upper limit ofTc in the cuprates

The presence of magnetic impurities leads to a drastic decrease inT _c in the overdoped region, gaplessness, and the usual temperature dependence ofH _c2. The magnetic moments are localized on the apical oxygen site, and this allows us to explain the increase inT _c with the increase in the number of Cu-O planes in the unit cell. Applied pressure can raiseT _c above the usual value at optimum doping, toward the intrinsicT _c. The cuprates as a class of compounds have an upper limit ofT _c in the rangeT _c,upp=160–170 K.     

Enhancement of superconductivity in Pb-Bi-Sn and Pb-Bi-In alloy filaments produced by glass-coated melt spinning

The enhancement ofT _c in Pb-Bi-Sn and Pb-Bi-In system alloy filaments produced by glass-coated melt spinning was investigated as a means of producing a new type of superconducting filament with highT _c. Long filaments of Pb-Bi-Sn alloy withT _c higher than 10 K and Pb-Bi-In alloy withT _c higher than 9 K were obtained from the molten state at a temperature of 1500 K with a winding speed of 2.63 m sec^–1. For example, a Pb₄₅Bi₃₅Sn₂₀ filament withT _c of 10.1 K was 15 m in diameter and polycrystalline with a grain size of 100 nm. The structure of the filament was a mixture of , tin and bismuth phases and a metastable phase of mixed structure of bismuth and supersaturated solid solution of tin in -phase was detected. TheT _c of the filament decreased on heat treatment. A metastable phase of mixed structure of bismuth and -phase was also detected for a Pb₄₅Bi₄₅In₁₀ filament withT _c of 9.3 K. As the metastable phase for the Pb-Bi-In filament was more unstable than that for the Pb-Bi-Sn filament, theT _c of the filament was drastically decreased by heat treatment. The metastable phase was considered to play an important role in the enhancement ofT _c for Pb-Bi-Sn and Pb-Bi-In alloy filaments.     

Pressure Effect in High-Temperature Superconductors and Fullerides

The explanation for the pressure effect in high-temperature superconductors and fullerides is offered. Besides the dependence of the pressure derivative of the critical temperature T _c on doping, the direct dependence of T _c on pressure and the universal dependence of the relative change of T _c ^max–T _c with pressure are obtained for high-temperature superconductors. The unity of the model of the pressure effect in high-temperature superconductors and fullerides is justified. The dependence of T _c on the lattice constant and the connection between the pressure effect and the chemical pressure effect in fullerides are discussed.     

Nonequilibrium Thermodynamics of Mesoscopic Systems

The Markovian dynamics of a Brownian particle is derived in the case that the local temperature is a stochastic variable. The isolated mesoscopic particle plus environment system is analyzed in the microcanonical ensemble by means of nonlinear-process projection methods. The ensuing generalized Kramers FokkerPlanck equation involves a thermodynamic potential of mean force that is different from the canonical free energy, and the conditional entropy (or availability) emerges as the relevant steady-state potential. By coupling the system to a heat bath, we provide a microscopic foundation for the phenomenological theory of nonisothermal activation in mesoscopic systems. In the second part of this article, we then prove the existence of an availability potential governing the nonisothermal features of a Josephson junction in a SQUID, by studying the Josephson internal energy (and entropy) for T T _c in a model of two BCS superconductors coupled by a tunneling Hamiltonian. The predicted periodic dependence of the junction's T _c as a function of the flux in the SQUID has meanwhile been confirmed experimentally.     

Equation of State for Complex Liquid Mixtures from Surface Tension

The present work shows a successful extension of previous studies to molecular liquids for which the second virial coefficients are not known. Recent advances in the statistical mechanical theory of equilibrium fluids can be used to obtain an equation of state (EOS) for compressed normal liquids and molten alkali metals. Three temperature-dependent quantities are needed to use the EOS: the second virial coefficient, B(T), an effective van der Waals covolume, b(T), and a scaling factor, (T). The second virial coefficients are calculated from a correlation that uses the surface tension, _tr, and the liquid density at the triple point. Calculation of (T) and b(T) follows by scaling. Thus, thermodynamic consistency is achieved by use of two scaling parameters (_tr, _tr). The correlations embrace the temperature range T _tr<T<T _c and can be used in a predictive mode. The remaining constant parameter is best found empirically from _tr data for pure dense liquids. The equation of state is tested on 42 liquid mixtures The results indicate that the liquid density at any pressure and temperature can be predicted within about 5%, over the range from T _tr to T _c.     

How “Musical” Are High-Tc Superconductors and What Can Empirical Rules Tell About Their Origin?

It is shown that parameters such as optimal T _c for cuprate superconductors or details of their doping curves can be organized on phenomenological rules. Accordingly, T _c in a range between a kink and the optimum scale linearly with the number of effective holes h _e, according to T _e = h _e T _c ^e, with T _c ^e = 600 K. Effective holes are composed of the difference between holes in the Cu—O bonds in the CuO₂ planes, h _p, and holes in the Cu—O bonds with the c axis or apical O, h _e, according to h _e = h _p– h_c = fh _p. The deleterious effect of the apical O manifests itself in three levels, depending on the basic modes of its coordination of the CuO₂ planes in zero, one, or two sheets (according to factor f = 1, 2/3, ¹/₂). The values of h _p at T _c optimum tend to rational fractions, ranging from 1/6 to 1/3, and are determined by lattice pressure. This musical or harmonic T _c matrix, originating from two structurally determined factors, groups optimal T _c into families. Knight shift data, establishing h _p, bear out the general assumptions. Some flexibility in the range within families is observed. This flexibility indicates the operation of more complex influences from structural detail, such as the varying distance of Cu to the apical O. The existence of ranges within optimal T _c families indicate a somewhat tunable rather than a strict musical T _c-level scheme with measured intervals. The details of the doping curves are similarly organized. These phenomenological rules suggest the operation of bond ordering effects. Arguments for the actual nature of the bond orderings are presented in terms of local pairs of doped bonds in trijugate positions. These quantitative concepts can be expanded to other characteristic features in the doping curves of cuprates and other high-T _c materials such as C or B containing systems, providing a universal frame for explaining high-T _c superconductivity in bond ordering terms.     

Thermal shock of quartz lascas

As a pre-treatment to grinding, quartz lascas (crushed pieces) were thermally shocked into room-temperature water by quenching from temperatures between 50 and 800 °C. Comminuted particles exhibited two distinctive geometries, granular forT _q(quench) <T _c (573 °C) and needle-like whenT _q>T _c. The needle-like shapes become thinner and longer with increasing temperature aboveT _c. The differences in shape are believed to result from the differences in the crack generation patterns which are governed by the thermoelastic properties in the -phase and -phase of the quartz during the thermal shock process. Crack densities induced by the thermal shock were measured as a function ofT _q. For the temperature range of 200 °C<T _q<T _c andT _c<T _q<800 °C, the resulting crack densities were determined to be governed by the rate of crack nucleation, which is characterized by an Arrhenius-type equation. The activation energies associated with the crack nucleation rates for the two regions were determined to be 14 and 39 kJ mol^–1, respectively.     

Investigation of the hexagonal NbGe2 phase

NbGe₂ thin films and hot pressed powder samples were made over a wide range of preparation conditions. Resistive and inductiveT _c values, residual resistance ratios, specific resistances, and grain sizes were determined as a function of the substrate temperature during evaporation. C40-NbGe₂ thin films have a maximum resistiveT _c of 2.18 K and an inductiveT _c of 2.10 K. The maximum residual resistance ratio was 17.7, the lowest specific resistance at room temperature was 57 µ-cm. During formation at higher temperatures or under pressure NbGe₂ has an affinity for carbon and nitrogen, leading to the formation of niobium carbonitrides with aT _c up to 16.2 K. PublishedT _c values up to 16 K for NbGe₂ are probably due to a contamination with niobium carbonitride.     

Synthesis Conditions and Superconductivity in 123-Type Superconductors

We have synthesized REBa₂Cu₃O_7–, where RE = Y, Sm, Gd, and SM(123):Ag under the identical conditions and characterized R – T and SEM–EDAX measurements by XRD. It is observed for sample SmBa₂Cu₃O_7– with = 0.3 that substitution of 10% Ag in place of Cu reduces T _c by 13 K along with the enhancement of normal-state resistivity by almost 200 times. When the T _c of the samples were optimized, it was found that the normal-state resistivity decreases by the substitution of Ag along with a decrease in T _c.