The transport properties of a small superconductor–normal-metal–superconducting tunnel junction can be controlled by a gate electrode coupled capacitively to the central island. We evaluate the critical Josephson current ${\mathit{I}}_{\mathit{c}}$ through such a system as a function of the gate voltage ${\mathit{V}}_{\mathit{g}}$ taking into account parity effects in the superconductors. The dependence ${\mathit{I}}_{\mathit{c}}$(${\mathit{V}}_{\mathit{g}}$) shows resonant singularities and has a qualitatively different character for Δ<${\mathit{E}}_{\mathit{C}}$ and Δ>${\mathit{E}}_{\mathit{C}}$, Δ being the superconducting gap and ${\mathit{E}}_{\mathit{C}}$=${\mathit{e}}^2$/2C being the charging energy. Due to the sweeping of the gate voltage, the system can be driven to states which are metastable with respect to a change of the number of electrons on the central island. Since the lifetime of the metastable states can be macroscopically large, one can observe a remarkable bistability of the Josephson current. A weak magnetic field suppresses the interference of the electrons propagating through the central electrode, and, consequently, the magnitude of the critical current.

We investigate the dielectric response of a planar Bose plasma in the presence of a constant external magnetic field. The conductivity tensor is derived in the self-consistent random-phase approximation. The tensor components are evaluated at zero temperature, leading to explicit dispersion relations for the electrodynamic modes of the plasma. For plasma layers, longitudinal and transverse modes are in general coupled. These coupled modes are investigated in detail.

We investigate the dielectric response of a planar Fermi plasma in the presence of a constant external magnetic field. The conductivity tensor is derived in the random-phase approximation taking into account the effects of the spin of the electron. This proper inclusion of spin makes a significant difference to the results compared with all previous studies, which ignored the intrinsic spin of the electron. In studying the dispersion relations for the electrodynamic modes of the plasma in an external magnetic field, it is necessary to observe that the longitudinal and transverse modes are coupled. These coupled modes are investigated in some detail.

A simple crossing-symmetric approximation for the fully reducible vertex is compared with Monte Carlo simulations of the two-dimensional Hubbard model. Up to quarter-filling, in the intermediate coupling regime, accuracies better than 10% are obtained for several static correlation functions, including spin and charge, as well as the pairing channels most widely studied in the context of high-${\mathit{T}}_{\mathit{c}}$ superconductivity. The accuracy is generally better for the pairing channels. The results shed light on the applicability of the renormalized generalized-random-phase-approximation scheme, its relation to Fermi-liquid theory, and on the regime where nontrivial effects may appear in pairing channels. The approximation under study consists in assuming that for parallel spins the fully reducible particle-particle vertex vanishes, while for antiparallel spins it is equal to the T matrix. The fully reducible particle-hole vertex is then obtained from the latter vertex by using crossing symmetry. This simple approximation is not conserving but it preserves global symmetries. It suggests that Monte Carlo results for the two-dimensional Hubbard model in small systems at low density and intermediate coupling can be interpreted using a weakly correlated Fermi-liquid picture.

We have calculated S(q) and the single particle distribution function 〈${\mathit{n}}_{\mathbf{q}}$〉 for N holes in the t-J model on a nonsquare √8 × √32 16-site lattice with periodic boundary conditions. We justify the use of this lattice by appealing to results obtained from the conventional 4×4 16-site cluster, and an undoped 32-site system, each having the full square symmetry of the bulk. This new cluster has a high density of k points along the diagonal of reciprocal space, viz. along k=k(1,1). The results clearly demonstrate that when the single-hole problem has a ground state with a system momentum of k=(π/2,π/2), the resulting ground state for N holes involves a shift of the peak of the system’s structure factor away from the antiferromagnetic state q=(π,π). This shift effectively increases continuously with N. When the single hole problem has a ground state with a momentum that is not equal to k=(π/2,π/2), something that may easily be accomplished through the use of the t-t’-J model with t’/t small and positive, then the above-mentioned incommensurability for N holes is not found—the maximum of S(q) remains at q=(π,π) for all N.

The existence of the incommensurate ground states are presented in conjunction with the electron and hole momentum distribution functions. Our results may be interpreted as evidence for rigid-band filling of the dipolar spin distortion states of Shraiman and Siggia—by studying the hole-hole correlation function we demonstrate that the holes on our cluster tend to stay as far apart as is possible, and thus rigid-band filling is not unexpected. Thus, these results demonstrate that in some instances important results for moderately doped ${\mathrm{CuO}}_2$ planes can be predicted from a knowledge of the properties of weakly doped planes. However, the electron Fermi surface that we obtain also satisfies Luttinger’s theorem, and has dimples at the wave vectors of the single hole ground state, k=(±π/2,±π/2). Finally, we comment on the relation of all of these results to the incommensurability found in S(q).

We derive an exact solution for the total kinetic energy of noninteracting spinless electrons at half-filling in two-dimensional bipartite lattices. We employ a conceptually different approach that maps this problem exactly into a Feynman-Vdovichenko lattice walker. The problem is then reduced to the analytic study of the sum of magnetic phase factors on closed paths. We compare our results with the ones obtained through numerical calculations.

We carry out Monte Carlo simulations of the uniformly frustrated three-dimensional XY model as a model for vortex-line fluctuations in high-temperature superconductors in an applied magnetic field. We show, comparing systems of different size, that there are two distinct phase transitions. At a lower ${\mathit{T}}_{\mathit{c}\mathrm{\perp }}$, the vortex lattice melts, and coherence is lost in planes perpendicular to the magnetic field. At a higher ${\mathit{T}}_{\mathit{c}\mathit{z}}$, a vortex tangle percolates throughout the system, and coherence is lost parallel to the magnetic field. Cooling below ${\mathit{T}}_{\mathit{c}\mathit{z}}$, high-energy barriers for vortex-line cutting lead to an entangled glassy state.

We argue that extended saddle points observed at the Fermi level for optimally doped superconductors are essentially the bifurcated saddle points predicted by density-functional [local density approximation (LDA)] calculations. Such saddle points are caused by the dimple of the ${\mathrm{CuO}}_2$ planes and are enhanced by plane-plane hopping. Dimpling may provide a mechanism for pinning the Fermi level to the saddle points. Simple tight-binding Hamiltonians and an analytical expressions for the constant-energy contours are derived from the LDA bands of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7.}$ In addition to the ${\mathrm{O}}_2$ x O3 y, and Cu ${\mathit{x}}^2$-${\mathit{y}}^2$ orbitals, we find that O2 z and O3 z are crucial and Cu s, are crucial. The O z orbitals allow the pdσ antibond to tilt with the dimple.

The ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ nuclear transverse relaxation rate in the normal state of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.33}$ (${\mathit{T}}_{\mathit{c}}$=62 K) is reported here. The Gaussian relaxation rate 1/${\mathit{T}}_{2\mathit{G}}$ at the planar Cu sites increases with decreasing temperature from 300 down to 100 K, below which it becomes independent of temperature. This behavior is quite different from the nuclear spin-lattice relaxation rate 1/(${\mathit{T}}_1$T), which shows a peak near 150 K, and indicates that antiferromagnetic spin correlations in the ${\mathrm{CuO}}_2$ planes continue to grow in the temperature range where the low-frequency spin fluctuations are depressed by a spin gap.

We have studied the structural and superconducting properties of ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ by neutron and x-ray powder diffraction, thermogravimetry, ac susceptibility, and dc magnetization. The kinetics of the synthesis reaction were studied in order to determine the optimum conditions for preparing single-phase samples. The room-temperature and low-temperature structural properties, as determined by neutron powder diffraction, are discussed in detail. By comparing the results of the neutron-diffraction and magnetic measurements, we conclude that superconductivity exists in both the orthorhombic and tetragonal phases. The thermodynamic conditions for the stability of the ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ phase are also investigated.

Using fast-Fourier-transform techniques, we calculated several properties of a two-dimensional D-wave superconductor directly from the phenomenological form of the magnetic susceptibility suggested by Millis, Monien, and Pines. A BCS-type formalism is employed, but no assumptions are made about the exact form of the gap anisotropy. The results for the gap exhibit D-wave symmetry and go beyond the usual cosine minus cosine model. The results obtained are compared with those obtained from the simpler and much used separable model.

We have studied the transport and structural properties of ${\mathrm{Pr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ca}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films grown by pulsed-laser deposition, focusing on Ca substitution levels x≥0.3 for which the bulk material is metastable. Films with 0.4≤x≤0.5 exhibit a superconducting transition due to divalent cation doping on the rare-earth site. ${\mathrm{Pr}}_{0.5}$${\mathrm{Ca}}_{0.5}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ epitaxial thin films exhibit a superconducting onset temperature as high as 47 K with ${\mathit{T}}_{\mathit{c}}$(R=0)=35 K. X-ray-diffraction and electrical-transport data suggest that Ca doping levels greater than x=0.5 are possible, although disorder is introduced as the divalent to trivalent cation ratio becomes large. This work demonstrates that 1:2:3-phase superconductivity can be achieved by substituting Ca for Pr, without the presence in the alloy of Y or any other rare-earth element, R, for which R${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ is superconducting. This result supports the view that hole localization, due to hybridization of the Pr 4f electronic levels with the O 2p orbitals, contributes substantially to the suppression of superconductivity by Pr in ${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, and demonstrates that this suppression can be partially compensated by appropriate hole doping with Ca.

We have measured the thermal conductivity κ and the thermal diffusivity a of a dense bulk ceramic polycrystalline sample of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ (1:2:4) in the temperature range 30–300 K. We find κ≊10 W ${\mathrm{m}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$ at 100 K, significantly higher than in ceramic ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (1:2:3) and approaching the in-plane value for single-crystal 1:2:3, and decreasing to 7.6 W ${\mathrm{m}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$ at 300 K. The data for this sample can be described by standard theories for phonon thermal conductivity of crystalline materials with boundary, phonon, and electron scattering. The higher κ in 1:2:4 as compared to 1:2:3 is, in this model, due to the smaller point defect scattering in the former. The fitted parameters for the three scattering mechanisms all agree with independent estimates based on simple models; inserting data for electric resistivity, grain size, carrier density, and lattice properties we can predict κ and its T dependence to within about 20%. We also discuss models for the phonon and electron thermal conductivities in some detail, including some second-order effects such as inelastic electron scattering and a T-dependent carrier density.

Microwave transmission and reflection measurements are performed simultaneously on thin films (∼1800 Å) of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ having their c axis perpendicular to the ${\mathrm{LaAlO}}_3$ substrate. We determine power transmission and reflection fractions, scrT(T,H) and scrR(T,H), as functions of temperature and static magnetic field (0<H<5.4 T), the latter being applied perpendicular to the film. A guided-wave model, which we develop for our experimental situation, is the basis of a computational algorithm that extracts quantitative values of the complex penetration depth λ̃, or alternatively the complex surface impedance ${\mathit{Z}}_{\mathit{s}}$, from scrT and scrR data. This inversion algorithm is successful when applied to test data generated from a phenomenological theory describing the electrodynamic response of a type-II superconductor. The procedure is applied to scrT(T,H) and scrR(T,H) measurements to infer the temperature- and field-dependent complex penetration depth λ̃(T,H) that completely characterizes the superconductive film’s electromagnetic response.

Measurements of the temperature dependence of the electrical resistivity and the Hall effect in epitaxial films of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ are reported. The resistivity is close to linear in T and the cotangent of the Hall angle proportional to ${\mathit{T}}^2$ at temperatures sufficiently above ${\mathit{T}}_{\mathit{c}}$. Deviations from this behavior near ${\mathit{T}}_{\mathit{c}}$ are attributed to thermodynamic fluctuations and are analyzed in terms of theories for direct (Aslamazov-Larkin) and indirect (Maki-Thompson) fluctuation contributions in a layered superconductor. We obtain an unequivocal fit to both paraconductivity and excess-Hall-effect data with a consistent set of three parameters, i.e., the c-axis coherence length ${\xi }_{\mathit{c}}$(0)=1.5 Å, the phase-relaxation time ${\mathrm{\tau }}_{\mathrm{\phi }}$=8.6×${10}^{\mathrm{-}14}$ s at 100 K, and the electron-hole asymmetry parameter β=-0.17. We observe a sign change of the excess Hall effect close to ${\mathit{T}}_{\mathit{c}}$, when the Aslamazov-Larkin process becomes dominant.

Reversible and irreversible magnetizations (M) have been measured on a polycrystalline sample of ${\mathrm{HgBa}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{6+\mathrm{\delta }}$ (Hg 1:2:1:2) before and after oxygenation. For the preoxygenated sample, the superconducting transition temperature (${\mathit{T}}_{\mathit{c}}$) is ∼114 K with a transition width of ∼2 K. The irreversibility line (${\mathit{H}}_{\mathrm{irr}}$) is approximated by a power law ${\mathit{H}}_{\mathrm{irr}}$∼(1-${\mathit{T}}_{\mathrm{irr}}$/${\mathit{T}}_{\mathit{c}}$${)}^{\mathit{n}}$ with n∼5/2 between 0.1 and 5.5 T. For the oxygenated sample, ${\mathit{T}}_{\mathit{c}}$ is ∼120 K with a width ∼4 K and the n for ${\mathit{H}}_{\mathrm{irr}}$ is almost the same. The values of n, which are ∼3/2 for Y 1:2:3:, ∼5/2 for Hg 1:2:1:2, and ∼11/2 for the Bi and Tl families, seem to correlate well with the distance between adjacent ${\mathrm{CuO}}_2$ blocks. A scaling law M∝[1-(T/${\mathit{T}}^{\mathrm{*}}$${)}^2$]F(H), is observed for reversible M up to a few degrees below ${\mathit{T}}_{\mathit{c}}$ with a ${\mathit{T}}^{\mathrm{*}}$∼112 K before oxygenation. This suggests that Hg 1:2:1:2 is a quasi-two-dimensional system, where the effects of thermal fluctuations have been previously demonstrated.

The application of superconducting ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ wires or tapes to electronic devices requires the optimization of the transport properties in Ohmic contacts between the superconductor and the normal metal in the circuit. This paper presents results of tunneling theory in superconductor–normal-metal–superconductor (SNS) junctions, in both pure and dirty limits. We derive expressions for the critical-current density as a function of the normal-metal resistivity in the dirty limit or of the ratio of Fermi velocities and effective masses in the clean limit. In the latter case the critical current increases when the ratio γ of the Fermi velocity in the superconductor to that of the weak link becomes much less than 1 and it also has a local maximum if γ is close to 1. This local maximum is more pronounced if the ratio of effective masses is large. For temperatures well below the critical temperature of the superconductors the model with abrupt pair potential on the SN interfaces is considered and its applicability near the critical temperature is examined.

The spin-excitation spectrum as observed in neutron-diffraction and NMR experiments in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ is theoretically examined in the weak-coupling limit of a two-dimensional Hubbard lattice model in which the next-nearest-neighbor hopping term t’ is considered in order to fit the shape of the Fermi surface observed in angle-resolved-photoemission experiments. The presence of a Van Hove singularity in the density of states at ω=4t’, no longer centered at the center of the band if t’≠0, leads to correct predictions for the variation of the Knight shift with doping when compared to experiments. As long as pairing effects are not included, the frequency dependence of χ’’(Q,ω) at T=0 has no gap for the current regime of interest (4t’<μ<0), but instead presents a typical double-cusp structure that we discuss. In the presence of d-wave pairing, it is shown how the spectrum of excitations gains four additional superconducting ellipses around the nodes of excitations. Consequently at T=0, χ’’(Q,ω) exhibits a resonance superimposed on a gap structure which bears striking resemblance with the neutron results reported by Rossat-Mignod et al. [Physica B 169, 58 (1991)] in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.92}$. The resonance is analyzed as a Kohn anomaly of the second kind in the Cooper channel. The value of the threshold ${\mathit{E}}_{\mathit{G}}$ evolves between two different regimes as the chemical potential goes from 0 to 4t’, associated with two different scales for the temperature at which the spin gap fills up. Finally, the Knight shift is calculated showing a Yosida-like law with a linear T dependence at very low temperatures as expected for axial superconductivity in two dimensions.

Attempts to describe the normal-state electronic behavior of the copper oxide superconductors have been unable to reconcile the following observations: (i) a well-defined Fermi surface with a locus predicted by band theory, but having charge carriers of a sign predicted for a Mott-Hubbard splitting of the band; (ii) a change in sign of the carriers to that predicted by band theory, but without a significant change in the locus of the Fermi surface, on overdoping beyond the narrow superconductive compositional range; (iii) a remarkable stability of the narrow range of superconductive charge-carrier concentrations in the ${\mathrm{CuO}}_2$ sheets even in the presence of charge transfer from nonsuperconductive intergrowth layers; (iv) a dramatic sensitivity of the Néel temperature of the parent compound to oxidation of the ${\mathrm{CuO}}_2$ sheets, but the persistence of antiferromagnetic spin fluctuations into the superconductive compositions; and (v) unusual transport properties that cannot be treated within the Migdal approximation and are insensitive to high magnetic fields. To address this impasse, we propose a phenomenological polaron model based on the observation that the system must accommodate to the coexistence of ‘‘ionic’’ and ‘‘covalent’’ Cu-O bonding having different equilibrium Cu-O bond lengths.

We designate this entity a correlation polaron. Covalent Cu-O bonding with molecular-orbital formation occurs within the polaron, which moves in a background of ionic Cu-O bonding. Vibronic coupling at the ‘‘avoided crossover’’ from ionic to covalent bonding allows diffusional motion of uncoupled polarons without any motional enthalpy in the mobility. At temperatures T>${\mathit{T}}_{\mathit{l}}$≳300 K the polarons are uncoupled and move randomly; in the narrow superconductive compositional range they condense below ${\mathit{T}}_{\mathit{l}}$ to form a distinguishable thermodynamic phase consisting of extended vibronic states. In this ‘‘polaron liquid,’’ a distinction between bonding and antibonding states within the polarons opens a gap at the half-band position, not the Fermi energy, and some spectral weight associated with the ionic Cu-O bonding still remains at the energies of the upper and lower Hubbard bands of the parent compound.

We have carried out strong-coupling calculations using the Eliashberg formalism for ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$. We consider the influence of potential impurity scattering on ${\mathit{T}}_{\mathit{c}}$. We find that, as the strength of the impurity potential increases, the unitary limit is reached comparatively quickly. In this (unitary) limit, the influence of isotropic impurity scattering on ${\mathit{T}}_{\mathit{c}}$ is relatively weak. We show, with the aid of a simple model to describe the disruption of the local magnetic order brought about by the substitution of Zn, that the latter has a strong influence on ${\mathit{T}}_{\mathit{c}}$. We consider the competition between antiferromagnetic and superconducting instabilities and find that, for our model parameters, the instability to a superconducting state always comes first. Next, we examine the sensitivity of our results for ${\mathit{T}}_{\mathit{c}}$ to the details of the spin-fluctuation spectrum and hole concentration. When that spectrum is modified so that it is consistent with both NMR ${\mathit{T}}_1$ and ${\mathit{T}}_2$ measurements, a superconducting transition temperature of 90 K is obtained with a dimensionless coupling contant, λ<1/2. Strong-coupling calculations of the normal state, using these latter parameters and including vertex corrections, yield an in-plane resistivity which varies linearly with temperature, with a magnitude at 100 K of 20 μΩ cm, and, with minor changes in parameters, a frequency dependence of the optical conductivity in quantitative agreement with experiment for energies <50 meV. With an interlayer hopping ${\mathit{t}}_{\mathrm{\perp }}$ of 8 meV, the c-axis resistivity is found to be linear in temperature with a magnitude at 150 K of 2.5 mΩ cm.