The (2+1)-dimensional quantum dimer model on a square lattice, proposed by Rokhsar and Kivelson as a theory of layered superconductivity, is shown to be equivalent to a many-body theory of free, transversely oscillating strings obeying Fermi statistics. A Jordan-Wigner construction for string field operators is presented. Topological defects are shown to be linearly confined in pairs by dynamical strings. Exact upper and lower bounds are placed on the ground-state energy and the string tension. It is argued that the system is in a spin-fluid phase and that there is no gap in the excitation spectrum.

${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ (PBCO) is unique in the R${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ (R=rare earth) series because it is not superconducting. In fact, for ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, ${\mathit{T}}_{\mathit{c}}$ drops monotonically with Pr concentration, with ${\mathit{T}}_{\mathit{c}}$ going to zero at ∼55% Pr. There have been many studies of this material with the hope that an explanation for the lack of superconductivity in PBCO might help explain why ${\mathrm{YBa}}_2$${\mathrm{CU}}_3$${\mathrm{O}}_7$ (YBCO) is superconducting. Explanations center around hole localization, requiring an extra hole on the Y (Pr) site or a localized hole in the O 2p shell, at the expense of a mobile hole in the Cu-O planes. To help provide clues that could point to a particular model, and to search for anomalies in the local structure, we present K-edge x-ray-absorption fine structure (XAFS) data for various concentrations of Pr in ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$. The character of the Pr K-edge XAFS data indicates that most of the Pr substitutes onto the Y site and is well ordered with respect to the unit cell. These data also show that the amplitude of the first Pr-O peak is greatly reduced when compared to the first Y-O peak in pure YBCO, and decreases with increasing Pr concentration.

In contrast, the Y K-edge data for these alloys show little if any change in the oxygen environment, while the Cu K-edge data show a 10% reduction in the first Cu-O peak. Fits to the Pr data suggest that some oxygen atoms about the Pr become disordered and/or distorted; most of the Pr-O nearest-neighbor distances are 2.45 Å, but about 15–40 % of them are in a possibly broadened peak at 2.${27}_{\mathrm{-}0.12}^{+0.03\mathrm{}}$ Å. The Cu K-edge XAFS data show a slight broadening but no loss of oxygens, which is consistent with a radial distortion of the Pr-O bond. The existence and the size of these two bond lengths is consistent with a mixture of ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Pr}}^{4+}$ bonds, and to a formal valence of +3.${33}_{\mathrm{-}0.18}^{+0.07\mathrm{}}$ for the Pr ion.

In this paper, magneto-optical observations and analyses of skeleton structures of flux distributions in type-II superconductors are presented. It will be shown that these structures are formed by lines where the critical current is bending. Such lines are a characteristic feature of a vortical vector field if the absolute value of the vector is constant as for the current distribution in a type-II superconductor in the full critical state. Thin samples offer enhanced sensitivity to observe these current discontinuity lines magneto-optically due to two facts: The Meissner phase contracts to these lines and remains there up to fields, which are higher than the full penetration field ${\mathit{H}}^{\mathrm{*}}$. At much higher magnetic fields, when the Meissner phase has vanished, the logarithmic infinity of the magnetic flux density at these lines leads to sufficiently high contrast. The positions of the discontinuity lines are not affected directly by particular defects, but are determined by the shape of the sample. Because the vortices are not able to cross these lines, the current discontinuity lines determine the flux distribution in the superconductor like a magnetic skeleton. An analysis of the observed structures yields characteristic parameters of the sample as anisotropy, inhomogeneity, or irradiation-induced enhancement of the critical current density. Additionally, the presence of defects allows the observation of the direction of flux motion and, thus, to visualize directly the current distribution. A strong concentration of flux motion near defects without any pecularities of the current and magnetic flux distribution can be predicted using the consideration presented in this paper.

The coupled-cluster method has recently proved to be efficient in calculating the ground state of strongly interacting spins or fermions on lattices. We apply it to the ground state of one hole in the half-filled Hubbard model on a two-dimensional square lattice. In a wide range for the interaction 10≲U/t≲80, the ground-state energy of a hole is fitted by a simple function ε/t≊-3.40+8.9(t/U${)}^{0.70}$, in good agreement with the results obtained through exact diagonalizations on small clusters. The effective mass of a hole ${\mathit{m}}^{\mathrm{*}}$=8t/W (W represents the bandwidth) is proportional to U/T (${\mathit{m}}^{\mathrm{*}}$≊0.845U/t) for 5≲U/t≲20 and saturates to a constant value ${\mathit{m}}^{\mathrm{*}}$≊84 for large U/t.

The Hall effect and resistivity have been measured in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{2\mathit{n}+4\mathrm{}}$ (n=2 and 3) thin films as a function of magnetic field and temperature. In the normal state, the ratio of the normal resistivity to the Hall resistivity (the cotangent of the Hall angle) is found to vary as ${\mathit{T}}^2$. Three models are able to account qualitatively for such behavior: a bipolaron model, BCS with a Van Hove singularity, and resonating valence bond. Analyses of the resistivity and the Hall effect in the superconducting fluctuations region above ${\mathit{T}}_{\mathit{c}}$ clearly demonstrate the two-dimensional character of the 2:2:1:2 compound. The sign reversal of the Hall constant in the vortex state is related to vortex motion. An explanation is presented based on the motion of an antivortex, or a defect of the local vortex lattice, in moving vortex bundles. The calculated activation energy of approximately 730 K agrees well with the measured value of 750 K, and the model gives the correct sign for the Nernst effect.

The nuclear and magnetic structures of (${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ca}}_{\mathit{x}}$)${\mathrm{Ba}}_2$${\mathrm{Fe}}_3$${\mathrm{O}}_{8+\mathrm{\delta }}$ with x=0.05, 0.10, and 0.20 have been investigated by neutron-powder diffraction at room temperature. The compound crystallizes with the symmetry of space group P4/mmm and has a structure similar to that of the superconductor ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ (1:2:3). There are two types of Fe atoms in the unit cell, one having fivefold pyramidal coordination and the other octahedral coordination. The Ca and Y atoms are randomly distributed over the 1/2,1/2,1/2 position, which are exclusively occupied by Y in the 1:2:3 superconductor. Since the oxygen sites on the basal plane of the structure are fully occupied to achieve octahedral coordination for the iron atoms on this plane, the oxygen content is eight atoms per formula unit, the barium atoms are twelvefold coordinated, and the coordination polyhedron is a cuboctahedron. Extra oxygen atoms corresponding to δ=0.08 and 0.05 are located in the Y/Ca layer. The presence of these atoms produces disorder in the structure resulting in a shift of the oxygen atoms located near the plane of the pyramidal iron atoms. The charge compensation required by the substitution of ${\mathrm{Y}}^{3+}$ by ${\mathrm{Ca}}^{2+}$ is achieved in these materials by elimination of the extra oxygen, rather than oxidation of the iron atoms. The magnetic structure is based on a unit cell related to that of the nuclear structure by the transformation of axes (1,-1,0/1,1,0/0,0,2).

The magnetic origin of some of the observed diffraction peaks was established by polarized neutron diffraction measurements. As in ${\mathrm{YBa}}_2$${\mathrm{Fe}}_3$${\mathrm{O}}_8$, the iron moments are coupled antiferromagnetically within each (${\mathrm{FeO}}_2$) layer as well as along the c axis of the structure, and they lie in the planes perpendicular to c. The magnetic moments of the two iron atoms are practically identical and have values at room temperature of 〈μ〉=3.50(3)${\mathrm{\mu }}_{\mathit{B}}$, 3.52(2)${\mathrm{\mu }}_{\mathit{B}}$, and 3.62(2)${\mathrm{\mu }}_{\mathit{B}}$ for the three compositions x=0.05, 0.10, and 0.20, respectively.

The effect of interaction between different Cu atoms is studied by calculations on clusters with more Cu atoms for various kinds of spectroscopy, using a multiband Hubbard Hamiltonian. It is found that the inclusion of more Cu sites often leads to final states lower in energy than those that would have been found if the calculations were restricted to the Anderson-impurity limit. These effects are studied for both undoped and doped systems. These interactions are not only important for systems involving a core hole but can also be induced by the ${\mathit{U}}_{\mathit{d}\mathit{d}}$ Coulomb interaction. Furthermore, we show that the wide shape of the main line of the Cu 2p XPS spectrum is not incompatible with a narrow 2p XES spectrum within a one-step model.

The basic growth mode of a thin epitaxial cuprate film (<200 Å) on a given substrate depends sensitively on the balance between various thermodynamic and kinetic factors related to the high-${\mathit{T}}_{\mathit{c}}$ phase formation and the surface microstructure at the growth front of the deposited film. Under the standard optimized growth conditions for high-quality epitaxial films, the deposition of a ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ film on an atomically smooth (110) ${\mathrm{SrTiO}}_3$ substrate, for example, is characterized by a strong damping in the reflection high-energy electron diffraction (RHEED) oscillation suggesting a predominant island growth mode. We have demonstrated that with an atomic oxygen and the technique of RHEED-controlled growth interruption it is possible to minimize surface roughness and to fabricate unit-cell smooth ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films over a large area (∼0.5 cm×1 cm). The results of this study suggest that two-dimensional layer growth can be induced by the combined use of atomic oxygen and growth conditions, such as low deposition rate, low oxygen partial pressure (<2 mTorr), that produce low supersaturation at the growth front.

We propose an experimental approach to study the dynamical properties of vortices in high-temperature as well as in conventional type-II superconductors. The experimental technique is based on direct measurements of the power dissipated by vortices moving in the bulk of a superconductor. This magnetocaloric approach provides an alternative, and in a number of cases a unique, information source to a wide range of fundamental problems including vortex pinning, critical currents, surface barrier, vortex movement by quantum tunneling, magnetic instabilities, etc. Some typical results are presented for Y-Ba-Cu-O, Bi-Sr-Ca-Cu-O, and NbTi samples.

Films of R${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ (R=Y, Ho, and Eu) have been obtained with c-axis orientation perpendicular to the film plane, by two dc sputtering methods, on different kinds of substrates. Also, pure a-axis-oriented films of ${\mathrm{EuBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ have been grown by dc magnetron sputtering. The films have been characterized by x-ray diffraction, resistivity, and critical current. The Hall effect has been measured in the normal and in the mixed state using a magnetic field up to 9 T. The films show a strong anisotropy in the normal state, with n-type and p-type behaviors in a-axis and c-axis films, respectively. All the films show sign reversal of the Hall resistivity in the mixed state. The maximum positive value (a-axis films) and the minimum negative value (c-axis films) of the Hall-effect resistivity are sample dependent. The analysis of this result shows that the enhancement of the effect occurs when the samples are in the transition region between the dirty and clean regimes. Films with very different values of the mean free path l and coherence length ${\xi }_0$ show a vanishing small effect in comparison with films that present l≃${\xi }_0$.

We report an extensive study on the temperature (T) dependence of the upper critical field ${\mathit{H}}_{\mathit{c}2}$ on ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$ single crystals. The ${\mathit{H}}_{\mathit{c}2}$(T) curve shows a reproducible upward curvature at ∼22 K. This can be due to the presence of two superconducting phases, one with ${\mathit{T}}_{\mathit{c}}$∼30 K and low ${\mathit{H}}_{\mathit{c}2}$ ([${\mathit{dH}}_{\mathit{c}2}$/dT${]}_{\mathit{T}\mathit{c}}$∼0.5 T/K) and another one with ${\mathit{T}}_{\mathit{c}}$∼ 25 K and higher ${\mathit{H}}_{\mathit{c}2}$ ([${\mathit{dH}}_{\mathit{c}2}$/dT${]}_{\mathit{T}\mathit{c}}$∼1.1 T/K). However, we find that ${\mathit{H}}_{\mathit{c}2}$ may rise up to 32 T at 1.8 K. It turns out that the reduced critical field ${\mathit{h}}_{\mathit{c}2}$=${\mathit{H}}_{\mathit{c}2}$/[${\mathit{T}}_{\mathit{c}}$(${\mathit{dH}}_{\mathit{c}2}$/dT${)}_{\mathit{T}\mathit{c}}$] is ≥1 at low temperatures for both the 30- and 25-K phases, i.e., much higher than what is expected for a conventional superconductor. We compare the low-temperature ${\mathit{h}}_{\mathit{c}2}$ data with calculations recently performed by Marsiglio and Carbotte in the framework of an extended Werthamer-Helfand-Hohenberg theory.

Voltage-current curves obtained from transport measurements on c-axis-oriented thin films of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ allow us to determine the temperature, field, and field-orientation dependence of the pinning potential on the basis of the simple Kim-Anderson model for the thermal activation of flux lines. A strong increase of the pinning potential is found at low temperatures, followed by a field-dependent maximum between 60 and 70 K and a decrease towards the transition temperature ${\mathit{T}}_{\mathit{c}}$. The results are compared to literature data of the pinning potential ${\mathit{U}}_0$(T) obtained from relaxation measurements and discussed in terms of thermal activation theory and related models for the current dependence of ${\mathit{U}}_0$. The analysis of the E-J curves, results on the angular dependence of ${\mathit{J}}_{\mathit{c}}^{\mathit{a}\mathit{b}}$, calculations of the pinning potential based on the core contribution, and due consideration of the different nature of the flux lines at low and high temperatures lead to a consistent picture, in which all results are explained in a qualitative way, without the need of invoking recent models on complex pinning interactions and on new phases of the flux-line lattice. It is shown that the pinning potential at low temperatures is of the order of the core contribution of a small number of pancake vortices and therefore intrinsically limited to small values, while at higher temperatures the correlation length along the field direction increases, which naturally leads to higher potentials.

We calculate in a k-averaging approximation, the vertex corrections for pairing at a Van Hove singularity mediated by an Einstein phonon. The vertex correction leads to a modest reduction in ${\mathit{T}}_{\mathit{c}}$, which can still reach the experimental values for realistic phonon couplings, and to a significant deepening of the dip in the isotope shift at the ${\mathit{T}}_{\mathit{c}}$ maximum. Interference between first- and second-order vertex graphs diminishes the effect of the Coulomb interaction on ${\mathit{T}}_{\mathit{c}}$. The isotope-shift dip is shallower for repulsive Coulomb interaction, and deeper in the case of an attractive interaction introduced to model an excitonic contribution to pairing.

The measurements of linewidth of the transitions between 4f levels of Tm split by the crystal field in Y-Ba-Cu-O compounds are analyzed using the spin-wave approximation and the phenomenological approach of Millis, Monien, and Pines. It was shown that in the insulating state the main contribution to the linewidth arises from one-magnon processes and a gap in the spectrum of magnetic excitation is rather small (Δ<100 K). In superconducting compounds the main contribution to the linewidth arises from zone-center magnetic fluctuations and the temperature dependence of the linewidth is determined by static spin susceptibility.

We simplify the Pennington-Slichter expression for the transverse NMR relaxation rate (${\mathit{T}}_{2\mathit{G}}^{\mathrm{-}1}$) in the cuprate superconductors, and use our result to calculate spin-fluctuation parameters in the normal state and ${\mathit{T}}_{2\mathit{G}}$ for the superconducting state of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$.

X-ray and ultraviolet photoelectron spectroscopic (XPS and UPS) data were obtained for ${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{NbO}}_3$ (x=0.8,0.85,0.9). The valency of the Nb ion was found to be between pentavalent and tetravalent. No shifts of the XPS core-level spectra, such as O 1s, Sr 3p, and Sr 3d, were observed in this system even when x was varied. For all samples, sharp Fermi edges were observed with He I (21.2 eV) photon excitation. The results indicate that this valence band was mainly caused by the hybridization between the O 2p and Nb 4d orbitals, as had been proposed for the tungsten bronze by Goodenough. Eu substituted samples, (Sr,Eu${)}_{0.9}$${\mathrm{NbO}}_3$, were also studied. An additional sharp peak, due to Eu 4f state, was clearly observed in the valence-band region close to the Fermi level.

The normal state of the high-${\mathit{T}}_{\mathit{c}}$ superconductors near optimal doping is characterized by the presence of strong inelastic scattering, leading to anomalous properties, most prominently a linear-in-temperature resistivity over a very large temperature range. We study the effect of this scattering on the correction to the conductivity due to thermal fluctuations of the order parameter and on the Ginzburg-Landau parameters above ${\mathit{T}}_{\mathit{c}}$. The fluctuation conductivity is affected (reduced) by the inelastic scattering, as compared to the case with a constant pairbreaking scattering rate (magnetic impurities). This leads to a substantial enhancement of an effect that was recently proposed by Ioffe et al. to account for the observed upturn of the c-axis resistivity above ${\mathit{T}}_{\mathit{c}}$.

The behavior of the penetration depth λ at low temperatures is an important probe of the symmetry of the order parameter in superconductors. For this reason, the penetration depth in the high-${\mathit{T}}_{\mathit{c}}$ oxide has been the focus of much recent experimental and theoretical attention. In this paper we provide detailed results for the behavior of λ at T=0, as a function of impurity scattering, for an unconventional order parameter.

Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-${\mathit{T}}_{\mathit{c}}$ cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.

Monte Carlo simulations of percolation on a square lattice with anisotropic inhomogeneous probability distribution are reported. Finite-size scaling is used for data analysis. As inhomogeneity increases, the critical probability decreases; whereas the correlation-length exponent remains, within computation errors, the same as in classical two-dimensional percolation.