In this paper, a generalization of standard spin-fluctuation theory is considered by replacing the simple Hubbard interaction by the screened Hartree-Fock interaction for f electrons. This model is then used in both an LS and a JJ coupling scheme to construct the particle-particle scattering vertex. In an on-site approximation, this vertex is shown to lead to an instability for a superconducting pair state which obeys Hunds rules, with L=5, S=1, and J=4, whereas for near-neighbor pairing, the most attractive instability is for J=0. The degeneracy of these multiplets is broken by anisotropy of the quasiparticle wave functions. Detailed calculations are presented for the case of ${\mathrm{UPt}}_3$.

In a vertical stack of Josephson junctions, vortices in adjacent junctions are coupled by screening currents if the electrodes are thinner than the London penetration depth. We investigate typical junction parameters of both niobium multilayers and intrinsic Josephson junctions in high-${\mathit{T}}_{\mathit{c}}$ single crystals. Using coupled one-dimensional sine-Gordon equations, stable coherent motion of Josephson vortices in an external magnetic field is predicted. This motion is triggered by two-dimensional resonances of the stack. For the resonance frequencies and amplitudes analytical expressions are derived.

This paper describes an integral-equation approach to solving for the flux-front profile in the critical-state model. Both nonuniform external fields and demagnetizing geometries can be accommodated as long as cylindrical symmetry is preserved. The solution for a sphere in a uniform external field is presented and compared with those of other calculation techniques.

Systematic substitutional studies in the ${\mathrm{Bi}}_{2.1}$${\mathrm{Sr}}_{1.93}$${\mathrm{Ca}}_{0.97\mathrm{-}\mathit{x}}$${\mathit{R}}_{\mathit{x}}$${\mathrm{Cu}}_2$${\mathrm{O}}_{8+\mathit{y}}$ (R=Pr,Gd,Er; 0≤x≤0.3 in steps of 0.05 and 0.4≤x≤0.97 in steps of 0.1) system were carried out in order to determine the effect of the magnetic moment and ionic radius of the rare-earth ion on the ${\mathit{T}}_{\mathit{c}}$ suppression rate. X-ray-diffraction studies indicate that the solid solubility of Gd and Er exists up to x=0.97 whereas that of Pr is limited to x=0.6 under the preparative conditions employed. Resistivity and ac susceptibility studies have shown that superconductivity persists up to x=0.4 and a metal-semiconductor transition occurs for x>0.4. The most interesting observation is that the rate of ${\mathit{T}}_{\mathit{c}}$ suppression for the superconducting phases is found to be identical for all rare earths. We have explained that hole filling rather than Abrikosov-Gor’kov pair breaking is responsible for the decrease in ${\mathit{T}}_{\mathit{c}}$. The insulating phases with 0.5≤x≤0.97 exhibit the phenomenon of Mott’s variable-range-hopping mechanism (VRH). The physical parameters related to VRH such as localization length (${\mathrm{\alpha }}^{\mathrm{-}1}$), hopping range (R), and activation energy (W) for conduction, have been evaluated and discussed in detail.

A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact quantum Monte Carlo results. The second-order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self-energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried out through fourth order for the Hubbard model. The self-energy is quite accurately reproduced by the theory, but the vertex functions are not. Anomalous behavior occurs near half-filling because the iterated perturbation theory is not a conserving approximation.

We compute the one-loop effective action of a magnetic monopole in three-dimensional electrodynamics of massless bosons and fermions and find that it contains an infrared logarithm. So, when the number of massless matter species is sufficiently large, monopoles are suppressed and in the weak-coupling limit charged particles are unconfined. This result provides some support to the idea of new gauge interactions in planar electronic systems. It also provides a mechanism by which interlayer tunneling of excitations with one unit of the ordinary electric charge can be suppressed while that of a doubly charged object is allowed.

We employ a quantitative microscopic theory of nonuniform quantum liquids to explore the excitations in thin films of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed onto a substrate. These liquid films studied undergo a series of structural phase transitions coinciding with the completion of individual atomic layers. A generalized Feynman ansatz is used for the wave function of the excited states; multiphonon effects are included by generalizing the Feynman theory to allow for time-dependent pair correlations. We study the dispersion relation, excitation mechanisms, transition densities, and particle currents, as a function of the surface coverage, including coverages near the phase transitions. Because of the film’s layered growth, the sound velocity exhibits a series of minima and maxima. A pronounced long-wavelength softening of the lowest-energy mode is observed near the transitions. In the monolayer, the nature of the excitations undergoes a noticeable change at the coverage where the velocity of sound starts to decrease. This is a crossover from ‘‘essentially two-dimensional’’ to ‘‘essentially three-dimensional’’ behavior. At long wavelengths, below and above the crossover coverage, the lowest-energy excitation is a longitudinal phonon (propagating within the monolayer) and a surface excitation, respectively. At shorter wavelengths, a layer-phonon propagating within the liquid layers, level crosses with a surface excitation to become the lowest-energy mode. For double- and higher-layer films the excitations are complicated by multiple (layer phonon with layer phonon and layer phonon with surface excitation) level crossings. At higher coverages, a mode is identifiable that will evolve into the bulk phonon-maxon roton. Our results agree qualitatively with the available spectra obtained by neutron scattering experiments.

We report Monte Carlo (MC) method to simulate a lattice superconductor in the shape of a slab with two plane interfaces, which are parallel to each other and separating the superconductor from the vacuum. This method is based on the lattice London model introduced by Carneiro, adapted here to the slab geometry. The energy of a vortex configuration is obtained from the exact solution of this model for uniaxial anisotropy when the interfaces are either perpendicular or parallel to the axis of anisotropy. Besides the usual bulk vortex-vortex interactions, the energy has surface contributions that are similar to those derived in continuum London theory for the same geometry. The MC procedure uses vortex loops as the basic building block to generate vortex configurations, except at the interfaces where open vortex lines are used. The latter are responsible for the penetration of vortex lines in the slab’s interior when an external field is applied parallel to the interfaces. Results of simulations for an isotropic supeconducting slab are reported. It is found that the vortex lines that penetrate the slab, driven by the external field, form a vortex-line lattice at low temperatures. Melting and freezing of this lattice is studied in some detail. The magnetization is studied as a function of the applied field and temperature. Evidence is found that it changes by a small amount across the melting and freezing transitions.

The coupling between the intramolecular vibrational modes and the doped conduction electrons in ${\mathit{M}}_3$${\mathrm{C}}_{60}$ is studied by a calculation of the electronic contributions to the phonon self-energies. The calculations are carried out for an orientationally ordered reference solid with symmetry Fm3¯m and for a model with quenched orientational disorder on the fullerene sites. In both cases, the dispersion and symmetry of the renormalized modes is governed by the electronic contributions. The current-current correlation functions and frequency-dependent conductivity through the midinfrared are calculated for both models. In the disordered structures, the renormalized modes derived from even-parity intramolecular phonons are resonant with the dipole excited single-particle spectrum, and modulate the predicted midinfrared conductivity. The spectra for this coupled system are calculated for several recently proposed microscopic models for the electron-phonon coupling, and a comparison is made with recent experimental data which demonstrate this effect.

A theoretical calculation has been performed for the variable-range-hopping (VRH) conduction mechanism in the presence of temperature and electric field for quasi-two-dimensional (QTD) and quasi-one-dimensional (QOD) systems. In the present calculation, it is assumed that the localized states are randomly distributed both in energy and space coordinates. The states both below and above the Fermi level are included in the calculation of the hopping range and conductivity. The present approach differs significantly from the percolation method and others in the calculation of the mobility and the conductivity. The expressions for the hopping range, the mobility, and the conductivity are obtained for the constant and the energy-dependent density of states. The expression of the conductivity for the constant density of states can be reduced to that of Mott in certain approximations. The effect of electron-electron interaction in the calculation of the conductivity and hopping range has been included through the density of states. After some approximations, the present expression of the conductivity can be reduced to that of Efros and Shklovskii. The logarithm of the conductivity follows the (1-${\mathrm{\beta }}^2$${)}^{3/8}$ and √1-${\mathrm{\beta }}^2$ electric-field dependence for QTD and QOD systems, respectively, in the presence of the electron-electron interaction and a weak electric field. Here β is directly proportional to an electric field. The present calculations are applied to explain the recent conductivity experiments on ${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$ (PBCO) films. A possible crossover from Mott-type VRH to Efros-and-Shklovskii-type VRH has been observed in PBCO.

Voltage-current characteristics E(j) were obtained from relaxation and magnetization measurements in melt-textured and single-crystalline ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. Both samples show a change of the E(j) behavior, which is in accordance with a vortex-glass–vortex-liquid transition. In the (B,T) range below this transition, logE(logj) curves pass from a negative to a positive curvature with increasing current. Collective-creep or vortex-glass theory are in agreement with the experimental observation below the corresponding inflection point, whereas above, the exponential E(j) dependence of the Anderson model is the better approximation. The exponent μ from the collective creep model was used for the analysis of the E(j) dependence in both regimes. Because μ varies with the current, mean values were taken within a constant current window for consistency. With increasing magnetic fields, μ passes a maximum, approaches zero, and becomes -1. The transformation from collective creep into the Anderson creep occurs at the end of the plateau of S at which μ changes from positive to negative. Finally, it is argued that the maximum of the current at intermediate magnetic fields (the fishtail effect) is not based on relaxation.

We have studied the effect of an applied magnetic field ${\mathit{H}}_{\mathrm{ext}}$ on the critical current ${\mathit{I}}_{\mathit{c}}$ of a lateral superconducting-insulating-superconducting (S-I-S) Josephson junction between two layered superconductors. In this configuration the layering direction of the superconducting electrodes is parallel to the plane of the junction. We find that the behavior of ${\mathit{I}}_{\mathit{c}}$(${\mathit{H}}_{\mathrm{ext}}$) is determined by the parameter δ=${\mathit{j}}_{\mathit{c}}$${\mathit{d}}_0$/${\lambda }_{\mathrm{\perp }}$${\mathit{j}}_{\mathrm{\perp }}$, where ${\lambda }_{\mathrm{\perp }}$ and ${\mathit{j}}_{\mathrm{\perp }}$ are, respectively, the penetration depth and the interlayer critical current characterizing the bulk superconductors. Also ${\mathit{j}}_{\mathit{c}}$ is the critical current density between layers on opposite sides of the junction, while ${\mathit{d}}_0$ is the layer thickness. For δ≪1 the length scale for field penetration along the direction of the junction is given by ${\lambda }_{\mathrm{\perp }}$, leading to the usual Fraunhofer dependence for ${\mathit{I}}_{\mathit{c}}$(${\mathit{H}}_{\mathrm{ext}}$). The scenario is vastly different for δ≥1. In this case the intraelectrode layer couplings are relatively weak and Josephson vortex penetration is found to occur between the layers. The physics of this situation is determined by the standard map. We find that in the absence of an external field Josephson vortices penetrate the structure and form an ordered array. This leads to a value of ${\mathit{I}}_{\mathit{c}}$(0) proportional to the number of layers N. This situation is however upset by a small external field. In this case the vortex distribution acquires an interesting chaotic character which leads to a sizable decrease of the critical current to a value ${\mathit{I}}_{\mathit{c}}$(${\mathit{H}}_{\mathrm{ext}}$)∝ √N .

The complex microstructure of directionally solidified ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}}$${\mathrm{Y}}_2$${\mathrm{BaCuO}}_5$ composites having up to 30 vol % 2:1:1 precipitates with sizes down to 0.1 μm and critical currents above ${10}^5$ A/${\mathrm{cm}}^2$ at 77 K and zero magnetic field has been investigated through detailed transmission electron microscopy observations. It is shown that samples with a high ${\mathrm{Y}}_2$${\mathrm{BaCuO}}_5$ concentration display polygonization as a mechanism to relieve stress while only small microcracks occur which are very efficiently stopped by small ${\mathrm{Y}}_2$${\mathrm{BaCuO}}_5$ precipitates. This crystal polygonization leads to the formation of either sharp or diffuse interfaces within the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ matrix. In the first case low angle grain boundaries occur which have a minor perturbation of the critical currents, while strongly disordered smooth interfaces are observed in other cases which because of their irregular distribution can only have a minor relevance on the flux-pinning mechanism of these superconductors. Stacking faults are found to be a common defect in the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ matrix but they are very inhomogeneously distributed thus preventing to establish a clear correlation between their density and critical currents.

The formation mechanism of these stacking faults is discussed on the basis of their observed distribution. Sharp ${\mathrm{Y}}_2$${\mathrm{BaCuO}}_5$/${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ interfaces have been observed at the atomic level, even if a high density of stacking faults and dislocations occur at certain orientations of the interfaces. Owing to the homogeneous distribution of these sharp interfaces we conclude that they constitute the dominant pinning mechanism at low magnetic fields in the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}}$${\mathrm{Y}}_2$${\mathrm{BaCuO}}_5$ composites.

We examine the stability of spin-polarized cluster states (ferrons) which appear by hole doping of the antiferromagnetically ordered ${\mathrm{CuO}}_2$ planes in the high-${\mathit{T}}_{\mathit{c}}$ cuprates. The influence of additional holes is calculated within a self-consistent mean-field-type approximation. The variation procedure for the spin polarization is extended over up to five ${\mathrm{CuO}}_2$ plaquettes. Different correlation terms (${\mathit{U}}_{\mathit{p}\mathit{d}}$,${\mathit{U}}_{\mathit{p}}$) affecting the cluster stability are discussed. For all cases the cluster binding energy and the polarization of the Cu spins are calculated. In addition the interaction between different clusters is discussed.

The contribution of spin-lattice coupling to the phonon self-energy is calculated in a dilute two-dimensional antiferromagnet. The calculations are based on a bond percolation model of the ${\mathrm{CuO}}_2$ plane of high-${\mathit{T}}_{\mathit{c}}$ copper oxides recently proposed by some of the authors. Numerical results are presented for the dampings of phonon excitations relating to three different situations. They are two magnons (Case A), one magnon and one fracton (Case B), and two fractons (Case C) involved in the phonon self-energy process. At low temperatures, the damping rate is much smaller than the frequency of excitations, leading to well-defined phonons for all the cases. The overall features of the ${\mathrm{\Gamma }}_{\mathit{q}}$∼q curves possess similar characteristics: ${\mathrm{\Gamma }}_{\mathit{q}}$ increases linearly with q in the small-q region, reaching a maximum at an intermediate q, and after that scales nearly as ${\mathit{q}}^{\mathrm{-}2}$ until q approaches the edge of the Brillouin zone. The temperature-dependent phonon linewidths arising from spin-lattice coupling are also presented. We point out the sensitivity of the interaction involving fractons on bond concentration of the network. Relevance of the calculated results to experimental data are discussed.

The plasma with c-axis polarization in cuprate superconductors has a very low frequency. Experiments show that in some of the cuprate superconductors the plasma frequency is lower than the superconducting energy gap and the plasma damping is extremely weak in the superconducting state. Various electromagnetic phenomena caused by the excitation of the low-frequency plasma are studied theoretically. The reflectivity and transmissivity of the electromagnetic wave for a film of the cuprate superconductor depend strongly on the frequency and polarization of the wave and the film thickness, since the wave strongly interacts with the transverse component of the plasma. When vortices are introduced by an external magnetic field, the vortex motion and the gapless excitation in the vortex cores make the transmissivity and reflectivity strongly field dependent. The effect of the low-frequency plasma is incorporated in the ac Josephson effect. When a voltage of (h/2e)×(plasma frequency) is applied to the Josephson junction of the cuprate superconductor, the plasma is excited by the ac Josephson effect and then the excited plasma will decay by emitting electromagnetic waves. The plasma excitation also affects the current-voltage characteristics of the junction.

A variety of experimental techniques are employed to probe the electronic state of Tb in the supeconductor ${\mathrm{Y}}_{0.9}$${\mathrm{Tb}}_{0.1}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. An analysis of neutron-diffraction data reveals that Tb is incorporated into the sample, replacing Y. There are no anomalies observed in the lattice constants or the planar oxygen thermal parameters determined from the neutron data, but the low concentration of Tb prohibits the determination of Tb oxidation state from these data alone. A comparison of experimentally determined magnetic susceptibilities with those calculated from single-ion, crystal-field models assuming either ${\mathrm{Tb}}^{3+}$ or ${\mathrm{Tb}}^{4+}$ shows a close agreement between the ${\mathrm{Tb}}^{3+}$ model and experiment. The presence of ${\mathrm{Tb}}^{3+}$ is confirmed by x-ray absorption near-edge spectroscopy. ${\mathit{L}}_3$-edge data are used to argue that the Tb ions are not significantly hybridized in ${\mathrm{Y}}_{0.9}$${\mathrm{Tb}}_{0.1}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$.

The time-dependent magnetic relaxation was measured in a full-field-penetrated ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ detwinned crystal for long times up to 5×${10}^5$ sec. The relaxation data exhibit a power-law time dependence of magnetization over a wide range of temperature and magnetic field with the field oriented both parallel and perpendicular to the c axis of the crystal. The results are consistent with a flux-creep model assuming logarithmic current dependence of the flux-creep activation energy.

The growth-temperature dependence of the crystal structure and superconductivity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films has been investigated quantitatively for a series of sputter-deposited films prepared at substrate temperatures ranging from 593 to 726 °C. X-ray diffraction revealed that the reflection intensities of the films, especially I(004), I(005), and I(006), change systematically with substrate temperature. Structure analyses suggested that there is a considerable degree of disorder between Y and Ba atoms in the structure of the thin films deposited at lower substrate temperatures. This degree of disorder decreases rapidly from 14 to 3 % (percentage of the Y site substituted by Ba atoms) with increase in the substrate temperatures up to 630 °C, and then decreases slowly to zero percent and remains zero even at higher substrate temperatures. Electrical-resistivity measurements showed that the superconducting transition temperatures of the thin films increase with increasing substrate temperature, in good agreement with the recovery of the disordered structure. The results indicate that there is an intrinsic relationship between the cation disorder and ${\mathit{T}}_{\mathit{c}}$, which are both strongly dependent on the growth temperature.

This paper establishes and tests procedures which can determine the electron energy gap of the high-temperature superconductors using the t-J model with spinon and holon quasiparticles obeying fractional statistics. A simpler problem with similar physics, the spin susceptibility spectrum of the spin-1/2 fractional-statistics gas, is studied. Interactions with the density oscillations of the system substantially decrease the spin gap to a value of (0.2±0.2)ħ${\mathrm{\omega }}_{\mathit{c}}$, much less than the mean-field value of ħ${\mathrm{\omega }}_{\mathit{c}}$. The lower-few Landau levels remain visible, though broadened and shifted, in the spin susceptibility. As a check of the methods, the single-particle Green’s function of the noninteracting Bose gas viewed in the fermionic representation, as computed by the same approximation scheme, agrees well with the exact results. The same mechanism would reduce the gap of the t-J model without eliminating it.