A theoretical study of the electron-correlation effects on the properties of ${\mathrm{La}}_{\mathit{x}}$${\mathrm{Sr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{TiO}}_3$ is presented. Using a single band repulsive Hubbard model employing the Gutzwiller approximation we study the effect of electron correlations on the effective-mass, band narrowing, plasma frequency, and spin susceptibility. The doping dependence of these properties are found to be qualitatively in agreement with recent experimental studies on ${\mathrm{La}}_{\mathit{x}}$${\mathrm{Sr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{TiO}}_3$. We have also proposed a possibility for inducing superconductivity using the idea of proximity effect. The induced superconducting gap in ${\mathrm{La}}_{\mathit{x}}$${\mathrm{Sr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{TiO}}_3$ is predicted to be maximum near the half-filling of the Ti 3d band.

The motion of a hole doped into the antiferromagnetic ${\mathrm{CuO}}_2$ plane is studied by means of a perturbation theory on the basis of the d-p model. The existing perturbation theories are improved by calculating the perturbation corrections up to the third order of the transfer integrals and also by taking account of various spin-exchanged states explicitly. The calculated results show that the third-order perturbation correlation cannot change the qualitative properties of the hole motion and that the spin-exchanged states play a vital role in determining the band structure of the hole motion. The obtained lowest band of the hole is split off far away from upper excited bands and corresponds to spin-singlet states which consist of antiparallel spins of neighboring Cu d and O p orbits. The bottom of the lowest band appears at the same position in the reciprocal space as that obtained on the basis of the t-J model. Nevertheless, its bandwidth is much larger than that predicted by the t-J model, revealing quite different processes of the hole motion between the d-p and t-J models. The simplification of the d-p model by assuming an infinite Coulomb interaction ${\mathit{U}}_{\mathit{d}}$ on Cu sites gives rise to a large quantitative change in the band structure for a set of realistic parameter values. This result is argued in connection with slave-boson theories of the d-p model.

Effects of nonmagnetic and magnetic impurities on d-wave and extended-s-wave superconductors in two dimensions are studied. After the effects on the density of states are investigated, the effects on the dynamical spin susceptibility are studied. In the clean limit, the magnetic response has significant wave-vector dependence if the gap has a large anisotropy. When impurities are introduced this dependence is smeared. In the extended-s-wave superconductor with a fully open gap, the response at low frequencies is strongly suppressed at low temperatures in the clean limit. Magnetic impurities can give rise to low-lying excitations in the gap and enhance the low-frequency magnetic response at low temperatures. It is found, however, that the intensity is still quite weak with a moderate concentration of the impurities. It is discussed how these results can help in the determination of the symmetry of the order parameter of the high-${\mathit{T}}_{\mathit{c}}$ superconductors.

Within a Hubbard model with on-site repulsion U and nearest-neighbor hopping t¯ in the two-dimensional copper oxide plane, we have carried out self-consistent calculations of the superconducting critical temperature ${\mathit{T}}_{\mathit{c}}$ resulting from spin and charge fluctuations. The gap is found to have ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ symmetry and ${\mathit{T}}_{\mathit{c}}$≃0.016t¯. Superconductivity exists only for a narrow range of U, very near the antiferromagnetic instability (${\mathit{U}}_{\mathit{c}}$). In this region near ${\mathit{U}}_{\mathit{c}}$, the Stoner enhancement in the incommensurate peaks of the spin susceptibility near (π,π) is of order 100–200. The absolute size of the peaks at ${\mathit{T}}_{\mathit{c}}$ is of the same order as measured, as is also the relative height of peaks to background. However, the theory predicts a suppression of these structures as T is reduced below ${\mathit{T}}_{\mathit{c}}$ which is much faster than observed.

The crystal structure, the magnetic and transport properties, and the lattice vibrations of the (Y,Ce${)}_2$${\mathrm{Sr}}_2$${\mathrm{CuFeO}}_8$ compound were studied by Rietveld refinement, Mössbauer spectroscopy, dc magnetic susceptibility, electrical-resistivity measurements, and Raman spectroscopy. The Rietveld-refinement results and Raman spectra show that the space group which describes the structure is P4mm. Mössbauer spectra can be fitted with one component with hyperfine parameters which correspond to ${\mathrm{Fe}}^{+3\mathrm{}}$ in a high-spin state coordinated by five oxygen atoms arranged in a square pyramid. Most of the observed phonon lines can be assigned to definite atomic vibrations. Magnetic measurements show an antiferromagnetic transition at 30 K. Fitting of dc-susceptibility data in the paramagnetic region gives an effective magnetic moment of (3.6±0.1)${\mathrm{\mu }}_{\mathit{B}}$ per ion. The resistivity data show insulating behavior.

We have computed zero-temperature properties of the t-J Hamiltonian using the formalism of anyon superconductivity. The results of these calculations agree quantitatively with exact-diagonalization studies. These properties include the optical conductivity, the ground-state kinetic energy, and the ground-state magnetic energy. Implicit in this calculational procedure is a Kosterlitz-Thouless transition temperature for the onset of superconductivity.

For any purely fermionic system on a lattice in arbitrary space dimension we prove that there is a different but well-defined system on the same lattice, consisting of both bona fide fermions and bosons with an interaction depending on a parameter λ, which characterizes a same-site repulsion between particles. The energy spectrum and the scattering matrix of the former are identical to those in the finite energy sector of the latter, in the limit λ→∞ (i.e., hard-core repulsion). This general theorem is applied to a resonance-boson model in a lattice fermion system, whose solution may have relevance to high-${\mathit{T}}_{\mathit{c}}$ superconductivity.

The role of the intergranular and intragranular critical current densities in silver-sheathed Pb-Bi-Sr-Ca-Cu-O tapes is investigated by means of magnetic-moment measurements in perpendicular field at different temperatures using a superconducting quantum interference device magnetometer. We find that low-field magnetic-moment loops are mainly caused by the intergranular (transport) critical current density ${\mathit{J}}_{\mathit{c}}^{\mathit{J}}$ but that in high fields the contribution from the intragranular critical current density ${\mathit{J}}_{\mathit{c}}^{\mathit{G}}$ becomes significant. The low-field data can be described well in terms of a critical-state model for a thin strip of a homogeneous type-II superconductor in a perpendicular field where ${\mathit{J}}_{\mathit{c}}^{\mathit{J}}$ flows over the entire tape. The high-field data require in addition a description in terms of a critical-state model for the grains where ${\mathit{J}}_{\mathit{c}}^{\mathit{G}}$ circulates in each grain. Strong mechanical bending of the tape causes ${\mathit{J}}_{\mathit{c}}^{\mathit{J}}$ to disappear while ${\mathit{J}}_{\mathit{c}}^{\mathit{G}}$ is unaffected. The experimental data reveal the hysteretic nature of ${\mathit{J}}_{\mathit{c}}^{\mathit{J}}$ which is caused by the trapping of flux in grains. In all the tapes measured, ${\mathit{J}}_{\mathit{c}}^{\mathit{J}}$ is found to be much smaller than ${\mathit{J}}_{\mathit{c}}^{\mathit{G}}$. Comparing the remanent ${\mathit{J}}_{\mathit{c}}^{\mathit{J}}$ with ${\mathit{J}}_{\mathit{c}}^{\mathit{G}}$ in different tapes, we find that strong pinning in grains does not imply a high remanent intergranular critical current density.

Angle-resolved photoemission measurement has been performed on a twin-free ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ single crystal to study the band-folding effect due to the BiO superstructure. It was found that the superstructure running along the b axis considerably modulates the electronic structure near the Fermi level (${\mathit{E}}_{\mathit{F}}$) in that direction, almost smearing out the dispersive feature of a band which crosses the Fermi level. In contrast with the energy region near ${\mathit{E}}_{\mathit{F}}$, the main body of the valence band (1 to 7 eV in binding energy) shows a comparable but different energy dispersion between the a- and b-axis directions. This indicates that the band-folding effect may be different between the near-${\mathit{E}}_{\mathit{F}}$ region and the whole valence band in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$.

We have used the bihybridization model to study the superconducting characteristics of ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$, including the energy gap, effective interaction, and the critical temperature ${\mathit{T}}_{\mathit{c}}$, and given a formula for ${\mathit{T}}_{\mathit{c}}$ at low impurity concentrations. The results show that the hybridization of Pr 4f states with ${\mathrm{CuO}}_2$ valence-band states may be the reason for the abnormal characteristics of ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$. The Coulomb repulsion +${\mathit{U}}_{\mathit{f}}$ between the Pr 4f states can destroy the superconductivity by hybridization of the f electrons with the conduction electrons and hence reduce ${\mathit{T}}_{\mathit{c}}$ significantly. Also, the localized character of the Pr 4f states can localize the carriers of the ${\mathrm{CuO}}_2$ band states and suppress the effect of -U centers.

Our x-ray core-level spectroscopic measurements show that the valence state of Tl in Ba containing single-Tl-O-layered compounds ${\mathrm{TlBa}}_{2\mathrm{-}\mathit{x}}$${\mathrm{La}}_{\mathit{x}}$${\mathrm{CuO}}_5$ and ${\mathrm{TlBa}}_2$${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Gd}}_{\mathit{x}}$${\mathrm{Cu}}_2$${\mathrm{O}}_7$ is +3 whereas in Sr containing single-Tl-O-layered compounds ${\mathrm{TlSr}}_{2\mathrm{-}\mathit{x}}$${\mathrm{La}}_{\mathit{x}}$${\mathrm{CuO}}_5$ and ${\mathrm{TlSr}}_2$${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Gd}}_{\mathit{x}}$${\mathrm{Cu}}_2$${\mathrm{O}}_7$ is between +3 and +1. The origin of holes in the latter is discussed in terms of charge transfer between the Tl 6s band and the Cu 3${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ band in addition to the holes generated due to excess oxygen. This is in contrast to the former wherein the origin of the holes is due to the excess of oxygen only.

The phonon self-energy at q=0 and zero temperature is calculated for a conventional electron-phonon superconductor with pair breaking, in the spin-flip model of Abrikosov and Gor’kov for paramagnetic impurities. It is found that for a phonon with a frequency of less than twice the spectral gap, i.e., 2${\mathrm{\Delta }}_0$, the phonon is softened and narrowed upon entering the superconducting state. Whereas, above 2${\mathrm{\Delta }}_0$ but below twice the energy gap for the pure material 2${\mathrm{\Delta }}_{00}$, it is softened and broadened. Above 2${\mathrm{\Delta }}_{00}$, the behavior for the clean limit is recovered and the phonon is hardened and broadened. We compare our results with experiments on ${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$.

We develop a simple theory of the electromagnetic response of a d-wave superconductor in the presence of potential scatterers of arbitrary s-wave scattering strength and inelastic scattering by antiferromagnetic spin fluctuations. In the clean London limit, the conductivity of such a system may be expressed in ‘‘Drude’’ form, in terms of a frequency-averaged relaxation time. We compare predictions of the theory with recent data on Y-Ba-Cu-O and Bi-Sr-Si-Cu-O crystals and on Y-Ba-Cu-O films. While fits to penetration-depth measurements are promising, the low-temperature behavior of the measured microwave conductivity appears to be in disagreement with our results. We discuss implications for d-wave-pairing scenarios in the cuprate superconductors.

A systematic study of the ${\mathit{T}}_{\mathit{c}}$ dependence of the disordered ${\mathit{R}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ (RPr-124) system (R=Y,Eu) on the Pr concentration x is reported here. Like (Y,Eu${)}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ (RPr-123), ${\mathit{T}}_{\mathit{c}}$ of these systems decreases monotonically with Pr concentration. ${\mathit{dT}}_{\mathit{c}}$/dx, however, is found to be smaller in RPr-124 than in RPr-123. Moreover, unlike RPr-123, ${\mathit{dT}}_{\mathit{c}}$/dx does not vary monotonically with x at least in the YPr-124 system, although the relative variation of ${\mathit{T}}_{\mathit{c}}$ with the rare-earth (Y,Eu) ionic radius is similar in both the cases. The observed results are discussed in terms of the hole-filling model and the Abrikosov-Gorkov (AG) theory. It is found that the AG theory is not adequate to explain the observed ${\mathit{T}}_{\mathit{c}}$ variation with x in the RPr-124 systems. We have attributed the failure of the AG theory in the RPr-124 systems to the linear x dependence of the carrier-impurity scattering rate. A modified AG theory considering the observed carrier-impurity scattering rate is found to provide a reasonable explanation of ${\mathit{T}}_{\mathit{c}}$ variation in the RPr-124 systems. The different ${\mathit{T}}_{\mathit{c}}$ variations in the YPr-124 and EuPr-124 systems are qualitatively understood on the basis of an indirect effect of the Pr impurity on the coupling of the Y,Eu state with the Cu 3d–O 2p state. The relatively smaller value of ${\mathit{dT}}_{\mathit{c}}$/dx in Y,Eu-124 than in Y,Eu-123 is understood on the basis of the larger separation of the ${\mathrm{CuO}}_2$-(Y,Eu/Pr)-${\mathrm{CuO}}_2$ regions in the former system.

Starting from the vortex equation of motion, we construct an effective Euclidean action and formulate the quantum statistical mechanics of the vortex system. The formalism is applied to the calculation of various thermodynamic quantities such as the specific heat and the magnetic susceptibility of the vortex lattice. Furthermore, we investigate the effect of quantum fluctuations on the vortex-lattice melting transition.

The temperature dependence below ${\mathit{T}}_{\mathit{c}}$ of the line shape of optical phonons of different symmetry as seen in Raman scattering is investigated for superconductors with anisotropic energy gaps. It is shown that the symmetry of the electron-phonon vertex produces nontrivial couplings to an anisotropic energy gap which leads to unique changes in the phonon line shape for phonons of different symmetry. The phonon line shape is calculated in detail for ${\mathit{B}}_{1\mathit{g}}$ and ${\mathit{A}}_{1\mathit{g}}$ phonons in a superconductor with ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ pairing symmetry. The role of satellites peaks generated by the electron-phonon coupling are also addressed. The theory accounts for the substantial phonon narrowing of the ${\mathit{B}}_{1\mathit{g}}$ phonon, while narrowing of the ${\mathit{A}}_{1\mathit{g}}$ phonon which is indistinguishable from the normal state is shown, in agreement with recent measurements on ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$.

Starting from the Ginzburg-Landau free energy of a type-II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest-Landau-level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasiperiodic boundary conditions. We find that the answers are very similar suggesting that the energy is localized to the crossing point. The crossing energy is found to be field and temperature dependent with a value at the experimentally measured melting line of ${\mathit{U}}_{\times }$≃7.5${\mathit{kT}}_{\mathit{m}}$≃1.16/${\mathit{c}}_{\mathit{L}}^2$, where ${\mathit{c}}_{\mathit{L}}$ is the Lindemann-melting-criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson, and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar et al.

The mixed boson-fermion model of superconductivity of Friedberg and Lee is adapted to two dimensions. Owing to the finite correlation length $l\left(T\right)\mathrm{}$, Bose-Einstein (BE) condensation can prevail only for a finite, but still macroscopic system. It is shown that for $T<\mathrm{}{T}_c\sim 40$ K, BE condensation of charged bosons that are converted from fermion (electron or hole) pairs leads not only to a perfect Meissner effect but also an energy gap in the fermion excitation spectrum. For the temperature range $T_c<T<\mathrm{}{T}_{\mathrm{May}}$, where $T_{\mathrm{May}}$ depends, in part, on the thickness of the two-dimensional layer, although the system shows no vestige of BE condensation, a near-perfect Meissner effect would yet persist until $T\simeq T_{\mathrm{May}}\sim 150$ K, based on the adaptation of the theory of May to the present model.

Precise dielectric-constant and hysteresis-loops measurements at very low heating and cooling rates (∼0.5 °C/h) near ${\mathit{T}}_{\mathit{c}}$≊22.0 °C in single crystals of triglycine selenate reveal previously unobserved discontinuities and a very small thermal hysteresis (ΔT≊0.05 °C), indicative of a first-order transition very close to a tricritical point. The set of tricritical exponents β≊1/4, δ≊5, γ≊1, borne out by present data, and α≊1/2 (from Ema’s specific-heat data) describe very well the observed behavior in the vicinity of the phase transition.

Although stable under hydrostatic pressures up to 20 GPa, ${\mathrm{C}}_{60}$ molecules transform to a transparent and insulating material if compressed nonhydrostatically at room temperature. On the other hand, quasihydrostatic loading at higher temperatures yields black, electrically conducting samples. We report here on detailed x-ray synchrotron-radiation and electron-diffraction characterization of these samples. The former transparent samples consist in polycrystalline cubic diamond embedded in a bulk ${\mathit{sp}}^3$ amorphous matrix, while the latter samples correspond to a graphitic amorphous ${\mathit{sp}}^2$ structure.