Microwave Measurements of Overdoped Y0.9Ca0.1Ba2Cu3O7−δ Thin Films

In the present report we show, for the first time, that a complex order parameter is not just a surface effect, but a bulk property in overdoped Y_0.9Ca_0.1Ba₂Cu₃O_7– thin films. The penetration depth change versus temperature is very well fitted to a complex order parameter of the form d_x ^{2-y 2} + id _xy , where = 14.5 meV and = 2meV. This result contrasts our previous results for optimally doped YBCO thin films where a power law for the penetration depth, versus temperature was reported, corresponding to a d_x ^{2-y 2}-wave order parameter. The penetration depth behavior is accompanied by a rapid reduction of the scattering rate at low temperatures, in contrast with a flattening of this quantity for the optimally doped YBCO films.     

Effects of phonons and antiferromagnetic spin fluctuations on the pairing and density of states in high-T c superconductors

We solve the Eliashberg equations for a two-dimensional, tight-binding band and anisotropic interaction due to exchange of phonons and antiferromagnetic spin fluctuations. For small band fillings, a mixture of simple and extendeds-wave pairing is stable, while for band fillings closer to half-filling thed-wave pairing state becomes stable. The density of statesN() becomes highly asymmetric in for smaller band fillings, which is an effect of particle-hole asymmetry. For thed-wave stateN() is linear in for small and exhibits a logarithmic singularity at the gap amplitude. For the mixeds-wave stateN() shows the BCS singularity at the gap edge. Antiferromagnetic spin fluctuations give rise to a pseudogap inN() for the normal state.     

Oscillation in a nonequilibrium superconductor

Using the ^*-model and the Rothwarf-Taylor equations, this paper predicts that a superconductor will oscillate between two nonequilibrium superconducting states with different energy gaps when quasiparticles are injected at the edge of the energy gap through the tunneling effect. The main sources of origin of this oscillation are the quasiparticle injection at the gap edge and the existance of recombination phonons with energy = 2(n). Under certain nonequilibrium conditions, the recombination phonon system does not take part in Cooper pair-breaking processes and can further stimulate the quasiparticles to recombine into pairs. The uncertainty N_p of the number N _pof Cooper pairs has the same order of magnitude as N _pitself in such an oscillating superconductor, so that the phase of the wave function has a definite value. If superconducting weak coupling is formed between such two oscillating superconductors, this system should be described in the -representation.     

Superconducting Gap in the Multi-band System MgB2

Based on the angle-resolved photoemission spectra of single crystals, it is demonstrated that a couple of bands cross the Fermi energy in MgB₂, which is in good agreement with band theory. The superconducting gap in this multiband system is carefully examined by Raman scattering spectroscopy with various polarizations. It has been revealed that the large gap (24k _B T _c) that is typical for a clean limit s-wave superconductor is restricted to the -bands, while the gap on the -bands is much smaller (21.1k _B T _c) and strongly affected by the impurity scattering, which gives a dirty limit behavior. This unusual two-gap behavior might be caused by the lack of interband scattering due to special separation of the - and -bands, as predicted by Mazin et al.     

Variation of the Kondo temperature with the nature and concentration of the solute metal

From the available data on the physical properties of dilute magnetic alloys, Daybell and Steyert obtain V-shaped semilog plots ofT _K vs. N (whereT _K is the Kondo temperature andN is the serial number of the magnetic solute in the 3d series). This requires a large variation in the rather small exchange interaction parameterJ, while the Kondos–d exchange model is based on a smallJE _F (whereE _F is the Fermi energy). Taking the ordinary scattering into account,T _K =T _F exp((1– cos ²)/(JD cos²)), whereJ<0, 1, is the phase shift for ordinary scattering, andD is the density of states of one spin direction per atom. It has been shown by us recently, from the concentration dependences of the Kondo slopes and the extremum values of the thermoelectric power of dilute magnetic alloys, that 0<d shells, and 3/4<< for those having less-than-half filled 3d shells. We show, on this basis, that the range of variation ofJ is now reduced to more acceptable values, as the solute metal traverses the 3d series. Again, based on our inference that increases with the increase of the solute concentrationc, we show that an increase of the more-than-half filled solute concentration decreasesT _K , while the increase of the less-than-half filled solute concentration increasesT _K . The fact that the increase of cobalt content in copper or gold favors magnetism while the increase of vanadium content in gold favors nonmagnetism is understandable on this basis.     

STM Spectroscopy on Anisotropic Superconductors

The superconducting phase of organic superconductors -(BEDT-TTF)₂Cu(NCS)₂ and (MDT-TTF)₂AuI₂ was investigated by the electron tunneling spectroscopy using low temperature STM. The tunneling differential conductance at the lateral surface of -(BEDT-TTF)₂Cu(NCS)₂ varies its shape depending on the tip direction. The in-plane anisotropy of the conductance is well explained by the d-wave symmetry with line nodes along the direction 45° from the c-axis. For (MDT-TTF)₂AuI₂, the tunneling conductance at T = 1.4 K shows the superconducting energy gap structure clearly. The finite conductance inside the gap edge suggests the gap anisotropy. The tunneling spectrum is explained by the d-wave pairing. The obtained gap ₀ = 2 meV (2₀/kT _c = 12) is larger than that of the weak coupling limit. The pseudogap structure is observed near T _c .     

A superconducting vibrating reed applied to flux-line pinning. I. Theory

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic fieldB _a. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending distorts the external field. This generates a magnetic restoring force (line tension) B _a ² which is independent of the reed thicknessd, whereas the mechanical restoring force (stiffness) is d ³. Therefore, the resonance frequency /2 of a thin superconducting reed increases drastically when a fieldB _a is applied, or for a givenB _a, when the reed is cooled below its critical temperatureT _c. With decreasing pinning strength (characterized by Labusch's parameter ) the resonance frequency decreases, ²²– _pin ² where _pin ^{2 –1}, and an attenuation _v ^–2 occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping _h ^–3 occurs due to the hysteretic losses caused by elastic instabilities during flux motion.On leave from Centro Atómico, Bariloche, Argentina.     

Superconducting state in M3C60: Strong vs. weak coupling

The superconducting state in the doped fullerenes is due to strong coupling (e.g.,2.1 for Rb₃C₆₀) to low-frequency intramolecular modes _L 250 cm^–1 (^21/2). The analysis is based on an equation describingT _c for any strength of the coupling and on recent isotope effect and NMR data.     

The significance of many-body interactions in physical adsorption

The significance of many-body interactions in the physical adsorption of rare gas atoms on solid surfaces has been investigated. A simple model of the system was considered in which the atoms of the solid and the adsorbed atom were represented by interacting isotropic point dipoles. The fullN-body interaction energy between the adsorbed atom and the solid was calculated exactly to lowest order in the expansion parameter [₀(₀/)²]/4d ³ (, and ₀, ₀ are the solid atom's and adsorbed atom's characteristic frequency and polarizability,d is the distance from the surface of the adsorbed atom, and is the number of atoms per unit volume in the solid). The interaction was then evaluated for the adsorption of various rare gas atoms on rare gas solids. It was found that the fullN-body interaction deviated at most by only2 1/2% from the interaction obtained by considering only two-body interactions. In addition, it was found that a finite expansion in two-, three-, ... body expressions may lead to erroneous results for the interaction energy since extensive cancellations occur between successive terms of the series.     

A note on the resistance to brittle fracture in various ceramic materials

The square of the ratio of the abraded bending strength, _d, to the unabraded bending strength, , is proposed as a measure of the resistance to crack propagation in ceramic materials. Data for various porcelains, glass-ceramics, and glasses showed that _d is essentially constant and that (_d/)² decreased rapidly with increase of the unabraded strength.     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

Longitudinal critical current in type II superconductors. I. Helical vortex instability in the bulk

The vortex lattice in type II superconductors is unstable against the growth of helical perturbations if the current along the vortices exceeds a critical value. The longitudinal critical current, the pitch, and the spatially varying amplitude of the elliptically polarized helices are calculated from the London theory at the onset of instability in planar current distributions far from the surface. For weak pinning (_L² c ₆₆) the wavelength and width of the mode extend over the entire specimen, and the critical current is 2H(c ₆₆/c ₁₁)^1/4. For moderate pinning (c _{66 L}² c ₁₁) the wavelength and width are close to Campbell's pinning length (c ₁₁/_L)^1/2, and the critical current times its mean density is 2H ²(_L/c ₁₁)^1/2. For strong pinning (_L² c ₁₁) helical instability occurs at pin-free vortex sections, the helix wavelength is 2.2d, and the critical current density is 0.47Hd/² (H, d, c ₁₁ and c ₆₆), and _L are the magnetic field, spacing, elastic moduli, and pinning parameter of the vortex lattice, and is the magnetic penetration depth).     

Analysis of nonequilibrium double tunnel junctions

The double tunnel junction M₁-S₂-M₃ consists of generator and detector tunnel junctions with a common electrode S₂. The quantity R ₂(E), the time rate of change of the quasiparticle distribution function (produced by the generator current), is calculated for each branch of the excitation spectrum in S₂. The rates of change of the quasiparticle number density \.n ₂, the particle branch imbalance \.Q ₂, and the distribution function branch imbalance \.Q ₂ ^*are also calculated. The detector excess current-voltage characteristic I _dvs. V _d is calculated for arbitrary excess distributions f _< (E) and f _>(E) in S₂. Computed characteristics are obtained assuming square distributions of appropriate amplitudes for f _<and f _>; these characteristics show a zero-voltage current I _d(0) and asymmetric structure at eV_d = ±(₂ + ₂) and eV_d = ±(eV_g – ₁ ± ₃). The square distributions are only approximate; the actual distributions would produce additional structure at eV_d = ±(eV_g + ₁ ± ₃). The results are discussed for M₁ and M₃ either normal or superconducting.This work was supported in part by the National Science Foundation through grant DMR 74-23661.     

Measurements of Critical Current of Superfluid 4He through An Array of Submicron Apertures very near Tλ

Far from the lambda transition the critical flow of superfluid ⁴ He through a small orifice is determined by thermal nucleation of quantized vortices. Between 300 mK and 2 K linearly decreasing critical flow velocity has been observed earlier. As the temperature approaches T the size of the vortex core increases and becomes comparable to that of the orifice. We report here measurements of the critical mass current in this temperature range. An array of 24 3×0.17 m holes in parallel with a macroscopic parallel path and flexible-diaphragm Helmholtz resonator have been used. The temperature range explored was from 80 mK to 20 K below T. Preliminary analysis of the data shows that for a reduced temperature t=(T–T)/T1·10 ^–4 the critical current scales approximately as t ^1.25 . Closer to T the critical phase difference across the array becomes comparable to 2 and the results have to be analyzed in terms of Josephson effect. The superfluid density has been measured at the same time as the critical current.     

Excitation spectrum and the density of states for a superconducting bilayer composite

The single-particle excitation spectrum and the density of states (DOS) for a superconducting bilayer composite are calculated by solving the Bogoliubov equations. The bilayer consists of two different superconducting films in contact. The superconducting order parameters of the films ₁ and ₂ are assumed constant. For various film thicknesses the dependence of the DOS on the ratio ₁/₂ is shown. This dependence is most prominent for states with excitation energy less than ₂.     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

On Electronic and Transport “Anomalies” in Layered Oxides

We briefly discuss some electronic and transport anomalies observed in superconducting perovskites. In particular we consider: (i) the complex electronic (and crystallographic) phase diagram, (ii) the symmetry of the gap with a special emphasis on the evidence for s-wave component in various experiments, and (iii) non-Fermi-liquid transport in superconducting Sr₂RuO_4– perovskite (T _c<1 K) that, like LSCO cuprate, exhibits linear resistivity up to 1050 K.     

Spin Gap and Hole Pairing of Sr14−x A x Cu24O41(A = Ca and La) Single Crystals Studied by the Electrical Resistivity and Thermal Conductivity

We have measured the electrical resistivity and the thermal conductivity of Sr _14–x A _x Cu ₂₄ O ₄₁(A = Ca and La) single crystals. The Arrhenius plot of ln vs T ^–1 gives two kinds of activation energy with a boundary temperature T . The activation energy at T < T is in approximate agreement with the spin gap in the ladder estimated from the NMR measurements, suggesting that holes in the ladder are paired and localized at T < T. The observed has been analyzed to be composed of _ph , _spin and _hole due to phonons, spins and holes, respectively. The _ph exhibits a small peak at 30 K in every direction of every single-crystal. The contribution of _spin is observed along the c-axis except for x(Ca) 6, and the spin gap, which corresponds to the spin excitation from spin-singlet to spin-triplet, has been estimated to be 420 K. For x(Ca) 6, the spin gap, which corresponds to the destruction of spin-singlet pairs i. e. the dissociation of hole pairs, has been estimated from along the c-axis at T > T to decrease with increasing x(Ca).     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Dependence of the Gap Ratio on the Fermi Level Shift in a Van Hove Superconductor

The dependence of the zero temperature gap to the critical temperature for s- and d-wave superconductors on the Fermi level shift () from the Van Hove singularity is studied within the BCS theory. Exact numerical calculations for the s and d gap ratios are carried out and approximate analytic expressions for the ratio are given. We find that the maximum gap ratio occurs at = 0 and it decreases slowly with increasing , and that this behavior is symmetric with respect to .