We calculated the binding energy of two holes with antiparallel spin in the t-J model using a variational wave function based on the string or spin-bag picture. The symmetry of the bound state is ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$. Although the size of matrices to be diagonalized is only 3×3 we could reproduce the results of various extensive numerical calculations with reasonable accuracy. We show that a sizeable contribution of the binding energy is due to the quantum fluctuations in the ground state of the Heisenberg antiferromagnet. In contrast to exact diagonalization results on small clusters in the thermodynamical limit the binding energy decreases rapidly with increasing t/J. A detailed discussion of the various finite-size effects in a small cluster is also included.

Fluctuation contributions to the Hall and longitudinal conductivities in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ epitaxial films have been investigated. Two remarkable features were observed: (1) the fluctuation contribution to the Hall conductivity, ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}^{\mathrm{fl}}$, changes sign at temperatures ${\mathit{T}}^{\mathrm{*}}$(H)>${\mathit{T}}_{\mathit{c}}$(H=0) and (2) the ratio ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}^{\mathrm{fl}}$/${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}^{\mathrm{fl}}$ where ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}^{\mathrm{fl}}$ is the fluctuation longitudinal conductivity, shows a sharp minimum near ${\mathit{T}}_{\mathit{c}}$(H). These features may reflect an unusual behavior of the imaginary part of the relaxation time of the order parameter in the vicinity of the transition temperature.

We consider the properties of the holes on an antiferromagnetic background in the two-dimensional t-J model. The long-range dynamics of the system is defined by the interaction of a hole with spin-wave excitations. In the present work the renormalized coupling constant of this interaction f(t) is calculated. For small t, f(t)≊3.4t. For large t the coupling constant is t independent, f(t)≊2J.

We have applied a generalized random-phase-approximation analysis to a two-band Hubbard model for the cuprate superconductors which treats magnetic and orbital (quadrupolar) fluctuations on an equal footing and which allows for significant itinerant character of the copper d electrons. The two bands represent the lowest copper orbitals. We qualitatively reproduce the known results of antiferromagnetic order at half filling with an adjoining region of d-wave-symmetry superconductivity in the single-band limit. When the value of the band splitting is comparable to the hopping integral of the ${\mathit{x}}^2$-${\mathit{y}}^2$ orbitals, we find a qualitatively new region of superconductivity at increased hole doping which is clearly associated with orbital (quadrupolar) fluctuations and a significant ${\mathit{x}}^2$-${\mathit{y}}^2$→3${\mathit{z}}^2$-${\mathit{r}}^2$ charge transfer but no concomitant charge or magnetic order. The pairs are very spread out in momentum and energy space. At the optimal temperature for the new instability, the Fermi surface has two sheets, and d-wave and s-wave pair states are nearly degenerate. We discuss the possible phenomenological relevance of these results to photoemission and other data for the cuprates.

The validity of the Migdal theorem for the two-dimensional electronic system interacting with the antiferromagnetic excitations with a relaxational dynamics has been investigated. We explicitly show that the first-order vertex correction for this interaction is small for the domains of small and high frequencies.

We consider experimentally and theoretically the effect of the thickness on the critical current density ${\mathit{J}}_{\mathit{c}}$ of superconducting films. In order to eliminate possible contributions from intrinsic pinning, our measurements of ${\mathit{J}}_{\mathit{c}}$(cphi) as a function of the amplitude and orientation of the magnetic field H with respect to the film plane were performed on isotropic Nb-Ti films having thicknesses d ranging from λ/4 to 4λ, where λ is the London penetration depth, and H⊥J. The angular dependent ${\mathit{J}}_{\mathit{c}}$(cphi) has a sharp peak for H parallel to the film surface, similar to that observed for high-${\mathit{T}}_{\mathit{c}}$ films. The amplitude of the peak increases as d decreases and reaches 20–30 % of the depairing current density (${\mathit{J}}_{\mathit{d}}$) for the λ/2 film. The ratio of ${\mathit{J}}_{\mathit{c}}$ values for parallel (${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$) and perpendicular (${\mathit{J}}_{\mathit{c}\mathrm{\perp }}$) film orientation increases as d decreases, so that ${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$≪${\mathit{J}}_{\mathit{c}\mathrm{\perp }}$ for the 4λ film and ${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$≫${\mathit{J}}_{\mathit{c}\mathrm{\perp }}$ for the λ/4 film, the crossover occurring at d≊2λ. A proposed interpretation of these results is based on our calculations of the vortex behavior in thin (d≪λ) films, which give analytical formulas for the field distribution around a fluxon, the lower critical field, ${\mathit{H}}_{\mathit{c}1}$, the surface barrier, and the vortex-vortex interaction potential.

The film geometry gives rise to a significantly enhanced surface barrier and ${\mathit{H}}_{\mathit{c}1}$, a marked decrease of the range of the intervortex repulsion (to d instead of λ), and noncentral, position-dependent forces between vortices. These results are employed to evaluate the bulk and surface contributions to ${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$(d), both being shown to increase as d decreases. The bulk component of ${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$ exhibits a 1/${\mathit{d}}^2$ dependence at d>${\mathit{d}}_{\mathit{c}}$ due to the decrease of the tilt elastic modulus ${\mathit{c}}_{44}$(d) of the vortex structure, a crossover from the collective to a single-vortex regime of pinning occurring below a critical thickness at d<${\mathit{d}}_{\mathit{c}}$. The surface magnetic pinning gives the main contribution to ${\mathit{J}}_{\mathit{c}}$ for our λ/2 and λ/4 films, leading to ${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$, which increases as 1/d and becomes of order ${\mathit{J}}_{\mathit{d}}$ at H≊${\mathit{H}}_{\mathit{c}1}$. These calculations show that the ratio ${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$(d)/${\mathit{J}}_{\mathit{c}\mathrm{\perp }}$(d) increases as d decreases, with the ${\mathit{J}}_{\mathit{c}\mathrm{\parallel }}$(d)/${\mathit{J}}_{\mathit{c}\mathrm{\perp }}$(d) value being much less than unity at d≫λ and much larger than unity at d≪λ. The results obtained indicate that the effect of the film geometry can be very important when interpreting the angular dependences of critical currents of thin films.

Previously we synthesized infinite-layer cuprates, ${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Li}}_{\mathit{x}}$${\mathrm{CuO}}_2$ with 0.2≤x≤0.45 and showed that Li ions entered the Ca site. These were the first hole-doped (or p-type) cuprates, to our knowledge, that contained square-coplanar fourfold-coordinated Cu ions (without Cu ions having apex oxygen ions). Here, we studied the transport properties of these cuprates and found that it was difficult to metallize them by means of conventional hole-doping techniques. In conjunction with the present experimental results, we discussed the electronic structure of high-${\mathit{T}}_{\mathit{c}}$ superconducting cuprates.

A variational approach is used to discuss bistable behavior in composite media where one component is a nonlinear dielectric while the other has a field independent complex dielectric constant with a negative real part. Under certain conditions, the physical parameters may be adjusted so that bistability appears even though the nonlinear behavior is everywhere weak, thus allowing it to be treated as a small perturbation to the leading linear behavior.

The magnetization of a melt-textured Y-Ba-Cu-O superconducting sample has been measured in magnetic fields up to 5.5 T using a SQUID magnetometer. Partial flux jumps were observed below the temperature of 7.6 K. With the applied field parallel to the sample’s c axis, the upper bound of the instability field was found to be the maximum applied field, while with the applied field perpendicular to the c axis, the sample’s dimensions determined the upper bound. Magnetization loops with flux jumps were calculated employing a critical-state model which incorporates the flux-jump instability criterion and considers the incompleteness of jumps. The different shapes of the magnetization loops are determined by four model parameters of which the instability field of the first virgin jump has the strongest effect on the loop shape. To predict the observed loop asymmetry and the appearance of solitary jumps, the simple Bean critical-state model was found to be insufficient. Instead, a critical-state model where the critical current density decreases as a function of the magnetic field is needed. It is shown that the use of a simple Kim-type critical current density is adequate to explain in detail all our experimental flux-jump data.

Gaplike structures superimposed on different background behaviors are observed in the tunneling characteristics of Bi-Sr-Ca-Cu-O-based planar junctions. In the case of constant background, the conductance curves are quantitatively modeled by assuming a modified BCS density of states for the high-${\mathit{T}}_{\mathit{c}}$ material from which Δ=20±2 meV is inferred. In the case of linear backgrounds, we have studied the influence that increasing slopes have on the Bi-Sr-Ca-Cu-O superconducting structures. For extremely anomalous backgrounds, we have analyzed the effect that a zero-bias conductance peak, depending on its voltage amplitude, has on the superconducting structures of both the high-${\mathit{T}}_{\mathit{c}}$ material and the conventional counterelectrode.

High-quality as-grown ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{y}}$ single crystals with superconducting transition temperatures ${\mathit{T}}_{\mathit{c}}$ of 70–83 K have been annealed in air, flowing oxygen, and nitrogen at 400–750 °C. ac susceptibility measurements show that at 450–550 °C ${\mathit{T}}_{\mathit{c}}$ is atmosphere and time independently enhanced to 85–86 K and a very narrow diamagnetic transition Δ${\mathit{T}}_{\mathit{c}}$ (10–90 % of the complete transition) of 0.5–1 K is obtained, and at 550–750 °C when treated in nitrogen or oxygen ${\mathit{T}}_{\mathit{c}}$ increases or decreases and Δ${\mathit{T}}_{\mathit{c}}$ broadens with annealing temperature compared with crystals annealed at 450–550 °C. The results are difficult to explain simply by the consideration of oxygen diffusion. Combined with the phase decomposition induced in the annealed crystals, it is suggested that the structural modification may play an important role in the variation of superconductivity of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{y}}$ superconductors.

For various samples of Bi-Sr-Ca-Cu-O (2:2:2:3 phase, 2:2:1:2 phase, and 2:2:2:3-2:2:1:2 mixed phases) and Tl-Ba-Ca-Cu-O (2:2:2:3 phase) with different ${\mathit{T}}_{\mathit{c}}$, the internal friction (${\mathit{Q}}^{\mathrm{-}1}$) in the kHz range reveals a plateau (${\mathit{Q}}_{\mathit{p}}^{\mathrm{-}1}$) above ${\mathit{T}}_{\mathit{c}}$ and drops drastically below ${\mathit{T}}_{\mathit{c}}$ with the turning point at ${\mathit{T}}_{\mathit{c}}$. This kind of anomaly has not been observed for nonsuperconducting samples. The results of ultrasonic attenuation (α) in Tl-Ba-Ca-Cu-O (2:2:2:3) are similar to that of the internal friction mentioned above. Moreover, it is discovered that the ${\mathit{Q}}_{\mathit{p}}^{\mathrm{-}1}$ is nearly proportional to Hall carrier density (${\mathit{n}}_{\mathit{H}}$) for ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$O and ${\mathrm{Gd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$O with various Pr content. These results indicate that the drastic drop of ${\mathit{Q}}^{\mathrm{-}1}$ and α below ${\mathit{T}}_{\mathit{c}}$ is caused by superconducting condensation. The energy dissipation (${\mathit{Q}}_{\mathit{p}}^{\mathrm{-}1}$ and ${\mathit{a}}_{\mathit{p}}$) related to carriers can be explained reasonably by using a coupling model of carriers with local dynamic distortion. Furthermore, by taking into account the smearing of the superconducting gap structure caused by the recombination of quasiparticles and by modifying the BCS relative jump rate as S(E,E’,Γ)=Re{1-${\mathrm{\Delta }}^2$/[(E-iΓ)(E’-iΓ)]}, the calculated results of internal friction and ultrasonic attenuation below ${\mathit{T}}_{\mathit{c}}$ agree fairly well with the experimental data. The superconducting gap Δ and the damping rate Γ for both Bi-Sr-Ca-Cu-O and Tl-Ba-Ca-Cu-O have also been obtained and are in accordance with those obtained by tunneling-spectrum, NMR methods, etc.

We have investigated the coupling between ${\mathrm{CuO}}_2$ layers in high-${\mathit{T}}_{\mathit{c}}$ superconductors by direct measurements of all dc and ac Josephson effects with current flow in the c-axis direction. The measurements have been performed on small single crystals of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$, (${\mathrm{Pb}}_{\mathit{y}}$${\mathrm{Bi}}_{1\mathrm{-}\mathit{y}}$${)}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$, ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$, and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ and on a-axis-oriented ${\mathrm{YBa}}_2$${\mathrm{Cu}}_2$${\mathrm{O}}_7$ thin films. The results clearly show that all materials behave like stacks of superconductor-insulator-superconductor Josephson junctions. The current-voltage characteristics exhibit large hystereses and multiple branches, which can be explained by a series connection of highly capacitive junctions. From the modulation of the critical current in a magnetic field parallel to the layers, we infer a junction thickness of approximately 15 Å. In our microwave emission experiments we were able to prove explicitly that every pair of ${\mathrm{CuO}}_2$ double or triple layers forms a working Josephson contact. An exception is ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, where only flux-flow behavior has been observed.

The coherence-length anisotropy ratio γ of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_{3\mathrm{-}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ superconducting single crystals (x≤0.22) has been measured by the equilibrium-torque magnetometry method. The experiments were performed at temperatures several K below the onset ${\mathit{T}}_{\mathit{c}}$ of superconductivity in magnetic fields of 1–2 T. γ=9.3±0.3 for two pure ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals, which is 20% larger than that of previously published results. The γ value of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_{3\mathrm{-}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ increases with increasing Fe concentration to γ=29±1.5 for x=0.22. The direct torque from the localized magnetic moments of Fe was not observed within the experimental sensitivity. The fundamental reason for the anisotropy increase is not clear.

EPR spectra of (i) CuO annealed in air at different temperatures up to 900 °C and (ii) CuO reacted with BaO in the ratio 3:2 at different temperatures up to 900 °C were studied. In (i), evidence for the formation of monomers, dimers, and tetramers of copper ions was found. In (ii), in addition to those spectra obtained in (i), aggregates of four copper ions coupled through cyclic exchange with resultant electronic spin S=2 and affected by the immediate barium neighbors were obtained. It is found that these copper aggregates giving the EPR signals are magnetically isolated from the main CuO cluster.

In this Monte Carlo simulation, we calculate the incoherent intermediate scattering function ${\mathrm{\phi }}_{\mathit{q}}^{\mathit{s}}$(t) for a three-dimensional dense polymer melt after having made long relaxation runs in order to eliminate the history of the cooling procedure sufficiently. This function shows the signature of a two-step process in the temperature interval T∈[0.16,0.21] (the temperature is measured in units of an energy parameter introduced in the Hamiltonian of the model) whose time evolution was quantitatively analyzed in the framework of the idealized mode-coupling theory (MCT) within the β-relaxation regime. As a result of this analysis the temperature interval splits into high- and low-temperature parts. In the high-temperature part (T≥0.19), the idealized theory accounts very well for the decay of ${\mathrm{\phi }}_{\mathit{q}}^{\mathit{s}}$(t) over about three decades in time, whereas ${\mathrm{\phi }}_{\mathit{q}}^{\mathit{s}}$(t) relaxes much faster than the idealized MCT anticipates in the low-temperature region (T<0.19). Since this discrepancy between the idealized MCT and the simulation data can qualitatively be rationalized by taking hopping processes into account, we try to estimate the critical temperature ${\mathit{T}}_{\mathit{c}}$ from the fits with the idealized MCT, yielding ${\mathit{T}}_{\mathit{c}}$≊0.150.

A highly correlated p-d model of cuprate oxide superconductors is analyzed by use of composite operators on ${\mathrm{CuO}}_2$ clusters. A minimal set of composite operators to describe the electronic state is identified from the criterion that the order of the approximation is determined by coupling constants multiplied by the weight of their respective operators. It is shown that the intensity transfer among bands with hole doping is well described within the mean-field approximation. Effects of the nearest-neighbor spin correlation are investigated and it is shown that the band dispersions are strongly affected. By the local antiferromagnetic correlation, the band dispersion of the upper Hubbard band is flattened in the whole Brillouin zone, while that of the p dominant band near the Fermi level is flattened only around a certain region centered at the zone boundary. In the moderately doped region, the Fermi surface is consistent with a large Fermi surface.

We consider an electron-phonon Hamiltonian in which the electron-phonon interaction occurs through a modification of both the electron on-site energy and the intersite hopping amplitude, i.e., a combination of Holstein and Su-Schrieffer-Heeger (SSH)-like models. It is suggested that this model may apply to certain vibrational degrees of freedom in high-${\mathit{T}}_{\mathit{c}}$ oxides. This Hamiltonian is electron-hole asymmetric and reduces in the infinite-frequency limit to a model for hole superconductivity recently discussed. We solve the Eliashberg equations for the model and examine the effect of electron-hole symmetry breaking on superconductivity when the effective electron-electron interaction is retarded. It is found that superconductivity is enhanced by the electron-hole symmetry-breaking interaction even in the presence of strong retardation. Such an interaction is found to be more effective than an electron-hole symmetric interaction of equivalent magnitude in giving rise to superconductivity over a wide range of parameters for both high and low phonon frequencies. The carrier concentration dependence of the transition temperature in the electron-hole asymmetric model is found to become weaker as the phonon frequency decreases. Possible implications of our results for the understanding of superconductivity in real materials are discussed.

The O Kα x-ray fluorescence of ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ (x=0.02, 0.04, 0.07, 0.1, 0.15) has been recorded using tunable and high-resolution monochromatized synchrotron-radiation excitation. A strong variation in the shape of the O Kα emission spectra depending on incidence photon energy is observed. This variation results from different in-plane and apical oxygen contributions to the emission line. The x-ray emission bands which reflect the partial density of 2p states pertaining to the two inequivalent oxygen sites are distinguished. The experimental results show that holes induced by the Sr doping are mainly located on in-plane oxygen atoms and suggest the existence, at least at x≥0.07, of doped holes which have Cu 3${\mathit{d}}_{\mathit{x}\mathit{z},}$${\mathit{yz}}_{\mathrm{-}}$O 2${\mathit{p}}_{\mathit{z}}$π character.

The transport critical currents of (110)-, (113)-, and a-axis-oriented ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films were measured as a function of the magnetic-field direction at different temperatures (4.2–77 K) and magnetic fields (≤1.5 T). Major peaks due to the intrinsic pinning were observed when the magnetic field was parallel to the Cu-O planes while secondary peaks due to surface pinning were only seen at high temperatures. The temperature dependence of ${\mathit{J}}_{\mathit{c}}$ shows different behavior in these thin films. Possible reasons for this are discussed.