We investigate the magnetic properties of the Cu-O planes in stoichiometric ${\mathrm{Sr}}_{\mathit{n}\mathrm{-}1}$${\mathrm{Cu}}_{\mathit{n}+1\mathrm{}}$${\mathrm{O}}_{2\mathit{n}}$ (n=3,5,7, . . .) which consist of CuO double chains periodically intergrown within the ${\mathrm{CuO}}_2$ planes. The double chains break up the two-dimensional antiferromagnetic planes into Heisenberg spin ladders with ${\mathit{n}}_{\mathit{r}}$=1/2(n-1) rungs and ${\mathit{n}}_{\mathit{l}}$=1/2(n+1) legs and described by the usual antiferromagnetic coupling J inside each ladder and a weak and frustrated interladder coupling J’. The resulting lattice is a new two-dimensional trellis lattice. We first examine the spin excitation spectra of isolated quasi-one-dimensional Heisenberg ladders which exhibit a gapless spectrum when ${\mathit{n}}_{\mathit{r}}$ is even and ${\mathit{n}}_{\mathit{l}}$ is odd (corresponding to n=5,9, . . .) and a gapped spectrum when ${\mathit{n}}_{\mathit{r}}$ is odd and ${\mathit{n}}_{\mathit{l}}$ is even (corresponding to n=3,7, . . .). We use the bond operator representation of quantum S=1/2 spins in a mean-field treatment with self-energy corrections and obtain a spin gap of ≊1/2J for the simplest single-rung ladder (n=3), in agreement with numerical estimates. We also present results of the dynamical structure factor S(q,ω). The spin gap decreases considerably on increasing the width of the ladders. For a double ladder with four legs and three rungs (n=7) we obtain a spin gap of only 0.1J. However, a frustrated coupling, such as that of a trellis lattice, introduced between the double ladders leads to an enhancement of the gap. Thus stoichiometric ${\mathrm{Sr}}_{\mathit{n}\mathrm{-}1}$${\mathrm{Cu}}_{\mathit{n}+1\mathrm{}}$${\mathrm{O}}_{2\mathit{n}}$ compounds with n=3,7,11, . . ., will be frustrated quantum antiferromagnets with a quantum-disordered or spin-liquid ground state.

Quasielastic neutron scattering is performed on a single crystal of the two-dimensional antiferromagnet ${\mathrm{Rb}}_2$${\mathrm{Cu}}_{0.12}$${\mathrm{Co}}_{0.88}$${\mathrm{F}}_4$, whose magnetic structure is frustrated by the admixture of ferromagnetic bonds. From the critical scattering, the in-plane inverse correlation length is found to decrease linearly with the temperature, with a critical exponent ν=1.02±0.04. At the onset of the sublattice magnetization, which occurs at ${\mathit{T}}_{\mathit{N}}$=88.1±0.1 K, however, the in-plane correlations have not yet become long ranged. At ${\mathit{T}}_{\mathit{N}}$, the planar domain size has grown to only 14 lattice spacings. Below ${\mathit{T}}_{\mathit{N}}$, the planar domains size increases further, to attain length scales beyond resolution at about 75 K. Conversely, the domains break up into smaller ones in this temperature range upon warming up. For the critical exponent of the susceptibility we find γ=1.5±0.2 after correction for the finite correlation remaining at ${\mathit{T}}_{\mathit{N}}$. The sublattice magnetization obeys the critical exponent β=0.16±0.04. The critical exponents found compare with the Ising values ν=1, γ=7/4, and β=1/8. Another manifestation of the frustration is the failure to reach true equilibrium below ${\mathit{T}}_{\mathit{N}}$. This is reflected in a dependence of the c-axis correlations on the cooling rate, and in a small increment of the intralayer and in-layer correlation lengths over long times.

By means of a quadratic diffusion Monte Carlo method we have performed a comparative analysis between the Aziz potential and a revised version of it. The results demonstrate that the revised version produces a better description of the equation of state for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. In spite of the improvement in the description of derivative magnitudes of the energy, as the pressure or the compressibility, the energy per particle which comes from this revised potential is lower than the experimental one. The inclusion of three-body interactions, which give a repulsive contribution to the potential energy, makes it feasible that the calculated energy comes close to the experimental result.

The Hall effect of the quasi-one-dimensional compound ${\mathrm{Tl}}_2$${\mathrm{Mo}}_6$${\mathrm{Se}}_6$ undergoes a progressive transition between an electronlike metallic regime at 300 K and a holelike semimetallic regime just above the superconducting transition (${\mathit{T}}_{\mathit{c}}$≊6.5 K). We show that, above ≊80 K, the paradoxical transport properties can be explained by an unusual anisotropic electron scattering related to the low dimensionality of the system and to its instability. A spin-density-wave (SDW) or charge-density-wave (CDW) state certainly builds up below ∼80 K—leading also to a change of regime in the thermopower but not in the conductivity—which is accompanied, at lower temperatures, by a magnetic-field dependence of the Hall coefficient and by a significant transverse magnetoresistance. The superconducting (SC) state therefore arises after the electron spectrum has been partly dielectrized by the CDW (or SDW) condensation, and it involves a very small density of states. A large paraconductivity which we attribute to superconducting fluctuations is detected just above ${\mathit{T}}_{\mathit{c}}$ and the transverse upper critical field ${\mathit{H}}_{\mathit{c}2}^{\mathrm{\perp }}$ does not saturate down to 50 mK, which confirms that we are dealing with a very unusual superconducting state, intricately connected with the other competing instabilities.

Effects of strong electron correlation on the electron-lattice interaction are studied by means of the exact diagonalization method for a finite-size cluster system. A simple two-component tight-binding Hamiltonian with the intrasite and intersite Coulomb repulsions is adopted. Upon changing the correlation energy (U) and the energy-level separation (Δ), the system is found to undergo a transition between the ionic insulating phase and the Mott insulating phase. Near the phase boundary the system becomes unstable under a small perturbation and a dramatic enhancement of the electron-lattice interaction is observed. Spin and charge properties are also strongly affected by the lattice distortion in a crossover region. The implication of the calculated results to the origins of the displacive-type ferroelectricity and the superconductivity in transition-metal oxides is discussed.

We discuss the possibility that heavy-fermion superconductors involve odd-frequency triplet pairing. A key technical innovation here is a Majorana representation for the local moments which avoids the use of a Gutzwiller projection. We employ the Kondo lattice model and develop a mean-field theory for odd-frequency pairing that entails pairing between local moments and conduction electrons, as described by a spinor order parameter. We confirm that the Meissner stiffness is positive and the state is stable. A residual band of gapless quasiparticles whose spin and charge coherence factors vanish linearly in energy, decouples from the condensate. The unusual energy dependence of these coherence factors leads to a ${\mathit{T}}^3$ NMR relaxation rate at a conduction electron site that coexists with a linear specific heat. Two verifiable predictions of the theory are (i) that a Korringa relaxation will fail to develop in heavy-fermion superconductors, even in the limit of strong pair breaking and severe gaplessness and (ii) that the hitherto unmeasured NMR relaxation rate at the actinide or rare-earth site will become exponentially activated in the superconducting phase.

Superconductivity beyond the Gorkov decoupling is examined with an emphasis on the thermodynamic properties. In the Gorkov decoupling, the interaction term is factorized into the pairing correlation. Therefore, in contrast to the strong pair-pair correlation in coordinate space, the correlation between the Cooper pairs in momentum space is neglected. In this paper, in addition to the conventional pairing interaction, we consider a more general type of attractive interaction that cannot be factorized into the product of the pairing correlation. Accordingly, it becomes necessary to include the neglected correlation. We assume a variational functional where the general type of interaction is taken into account, and determine the state self-consistently at finite temperature. The following results are obtained: (1) The state obtained is more stable at low temperature, compared with the BCS state with the same parameters. (2) As the temperature is increased, our state approaches the BCS state. (3) At the same temperature as in the BCS theory, our system undergoes a phase transition from the superconducting phase to the normal phase.

We determine the phase diagram of a quasi-one-dimensional superconductor (weakly coupled chains system with an open Fermi surface) in a magentic field. A field H(0,H,0) along the y direction (perpendicular the direction x of highest conductivity) tends to confine the electronic motion in the z direction. At low temperature, this effect cannot be neglected and the Ginzburg-Landau theory breaks down. We find that the usual Ginzburg-Landau regime is followed, when the field is increased, by a cascade of superconducting phases separated by first-order transitions, which ends with a strong reentrance of the superconducting phase where the chains interact by Josephson coupling. This high-field superconductivity can survive even in the presence of Pauli pair breaking because the quasi-one-dimensional Fermi surface allows one to construct a Larkin-Ovchinnikov-Fulde-Ferrell state that can exist far above the Pauli-limited field. Moreover, elastic scattering does not destroy the superconducting phases in clean materials with sufficiently large anistropy. We show that the superconducting state evolves from an Abrikosov vortex lattice in weak field towards a Josephson vortex lattice in the reentrant phase. Between these two limits, the order parameter and the current distribution show a laminar-type symmetry. The relevance of our results is discussed for quasi-one-dimensional organic superconductors and quasi-two-dimensional superconductors.

Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled clean system becomes superfluid via a finite-temperature Kosterlitz-Thouless transition. The relationship between low-temperature superfluid density and particle density is symmetric and appears parabolic about the half filling point. Disorder appears to break the superfluid phase up into two distinct localized states, depending on the particle density. We find that these results strongly correlate with the results of several experiments on high-${\mathit{T}}_{\mathit{c}}$ superconductors.

The disordered Bose-Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wave function in the presence of disorder is found by solving a nonlinear Schrödinger equation. Using the Bogoliubov approximation to find the excitations above this condensate, we calculate the condensate fraction, superfluid density, and density of states for a two-dimensional disordered system. These results are compared with experiments done with ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed in porous media.

The sheet current, electric field, and penetrating magnetic field in response to an applied perpendicular ac magnetic field are calculated for a thin type-II superconducting strip characterized completely by its sheet resistivity, which may be either nonlinear and frequency independent or linear, complex, and frequency dependent. The general formulation is given for the linear or nonlinear response of a strip and a circular disk in perpendicular time-varying magnetic field. An elegant and rapid numerical method is presented which solves this, in general, nonlinear one-dimensional integrodifferential equation with high precision on a personal computer and which accounts for the facts that the integral kernel has a logarithmic singularity and the sheet current for nearly ideal shielding (occurring at short times or high frequencies or for strong pinning of flux lines) has a one-over-square-root singularity near the specimen edges. As examples the linear Ohmic response of the strip to a sudden change of the applied field and to an ac field are given; Ohmic response is realized during flux flow or thermally activated flux flow. The complex magnetic susceptibility and the ac losses of the Ohmic strip are computed and approximated by simple expressions. This work completes the calculation of dissipation peaks in vibrating superconductors caused by various diffusion modes of the flux lines.

We solve a correlated single-impurity Hamiltonian, developed from a model for the copper oxides. It consists of the Anderson or Wolff Hamiltonian supplemented by finite-range interactions. These couple the impurity to additional screening channels of conduction electrons in a way that allows low-energy fluctuations of both spin and charge. We use Wilson’s numerical renormalization-group technique supplemented by analytic results to show that as the screening interactions increase, the effective repulsion at the impurity site changes to attraction. In the particle-hole symmetric model studied here, the low-energy properties then change from a spin Kondo effect to a charge Kondo effect in which the impurity fluctuates between zero occupation and double occupation. As the screening interactions are further increased, this Kondo-effect–Fermi-liquid ground state gives way to a critical line of non-Fermi-liquid states, through a Kosterlitz-Thouless-type transition.

We present a theoretical expression for the spin-echo decay rate 1/${\mathit{T}}_{2\mathit{G}}$ in the quantum-critical regime of square-lattice quantum antiferromagnets. Our results are in good agreement with recent experimental data by Imai et al. [Phys. Rev. Lett. 71, 1254 (1993)] for ${\mathrm{La}}_2$${\mathrm{CuO}}_4$.

We report on magnetic and structural neutron-diffraction studies of single-crystal ${\mathrm{La}}_2$${\mathrm{CuO}}_{4+\mathit{x}}$ versus temperature. The low-temperature diffraction data are consistent with the coexistence of two structurally related phases: nearly stoichiometric, antiferromagnetic (AF) domains, with average domain diameter ∼500 Å in the ${\mathrm{CuO}}_2$ plane, and oxygen-rich, metallic, and superconducting domains. The ordered magnetic moment in the AF domains does not saturate at 10 K, and is on average, μ=(0.3±0.05)${\mathrm{\mu }}_{\mathit{B}}$/Cu atom. The phase-separation transition to these two phases occurs at ${\mathit{T}}_{\mathrm{PS}}$=260±5 K, which is about 15 K higher than the Néel temperature, ${\mathit{T}}_{\mathit{N}}$=245±3 K. The value of ${\mathit{T}}_{\mathrm{PS}}$ is identical within the errors with that (259±2 K) found previously from specific-heat measurements on the same crystal. The structural properties of the single crystal are discussed and compared to those of polycrystalline oxygen-rich ${\mathrm{La}}_2$${\mathrm{CuO}}_{4+\mathit{x}}$.

Recently, several experimental groups have found superconducting behavior of one-unit-cell (i.e., one ${\mathrm{CuO}}_2$ bilayer) thick ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ films. Using the functional-integral method, we calculate the critical temperature ${\mathit{T}}_{\mathit{c}}$ for a system of two ${\mathrm{CuO}}_2$ planes coupled via a tunneling matrix element that results in Josephson-type coupling. The Coulomb interaction between the two planes is considered via inclusion of quantum phase fluctuations. We take into account the fluctuations of the modulus of the superconducting order parameter in the planes and the fluctuations of the phase difference of the order parameter between the planes. While for samples of infinite size ${\mathit{T}}_{\mathit{c}}$ is strictly zero, samples of finite size L yield an effective two-dimensional to zero-dimensional transition at a finite temperature ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$, characterized by a jump in the specific heat. We obtain ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$ as a function of L, Josephson coupling parameter, and Coulomb interaction strength and predict the temperature dependence of the specific heat near ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$. Our results are consistent with the ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$ values observed on the single ${\mathrm{CuO}}_2$ bilayer.

The ab-plane thermal conductivity κ(T) of insulating ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{YCu}}_2$${\mathrm{O}}_8$ and superconducting ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ is measured from T=10 to 300 K on single-crystal samples. Metallic ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ has a significantly higher κ than ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{YCu}}_2$${\mathrm{O}}_8$; the difference Δκ agrees well in magnitude with a Wiedemann-Franz estimate of the electronic contribution to κ in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$. The shape of κ(T) in insulating ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{YCu}}_2$${\mathrm{O}}_8$ differs from normal insulators described by the Peierls-Boltzmann theory. Assuming that atomic vibrations are the main heat carrier, and noting that κ is more similar to that of silica glass than to a normal insulating crystal like CuO, we suggest that the ‘‘phonon’’ mean free path is sufficiently short that the Peierls-Boltzmann theory is not applicable. This is consistent with evidence from neutron scattering that phonons are poorly defined. Our data support the idea that the peak in κ(T) observed below ${\mathit{T}}_{\mathit{c}}$ in superconducting samples originates from electronic rather than vibrational heat currents.

The dynamical behavior of magnetic flux in superconducting Tl-Ba-Ca-Cu-O films has been studied using the Nernst effect. Large temperature gradients of ∼${10}^5$ K/cm and, correspondingly, large thermal forces on flux lines were obtained by pulsed laser heating of films. Due to the large thermal driving forces it was possible to observe, at temperatures well below ${\mathit{T}}_{\mathit{c}}$, the transition from thermally assisted flux flow to flux creep and viscous flux flow.

The low-temperature transition from superconductor to metal of overdoped ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ has been monitored by measurements of resistivity versus temperature as a function of pressure over the compositional range 0.15≤x≤0.30. Polycrystalline samples were annealed under oxygen for periods up to 1 month to obtain homogeneous, stoichiometric samples. The pressure dependence of the critical temperature is ${\mathit{dT}}_{\mathit{c}}$/dP>0 in the orthorhombic phase found for x≤0.22; it vanishes in the tetragonal phase occurring with x>0.22. Pressure favors the tetragonal phase, lowering the orthorhombic-tetragonal transition temperature ${\mathit{T}}_{\mathit{t}}$ and shifting the transitional composition ${\mathit{x}}_{\mathit{t}}$ to ${\mathit{x}}_{\mathit{t}}$<0.20 above 10 kbar. This shift is shown to be due to an unusually large compressibility of the Cu-O bonds in the ${\mathrm{CuO}}_2$ sheets. The persistence of ${\mathit{T}}_{\mathit{c}}$ into the tetragonal phase with x>${\mathit{x}}_{\mathit{t}}$ is not due to orthorhombic-phase fluctuations, as has been speculated. Whereas the superconductive transition temperature ${\mathit{T}}_{\mathit{c}}$ decreases with increasing x, an elastic transition at ${\mathit{T}}_{\mathit{d}}$≊37 K persists over the entire compositional range, including the metallic phase at x=0.30. Careful measurements of resistance and Seebeck coefficient across ${\mathit{T}}_{\mathit{d}}$ reveal a ${\mathit{T}}_{\mathit{d}}$≥${\mathit{T}}_{\mathit{c}}$; but superconductive-pair fluctuations may occur below a ${\mathit{T}}_{\mathit{f}}$>${\mathit{T}}_{\mathit{d}}$ where ${\mathit{T}}_{\mathit{c}}$≊${\mathit{T}}_{\mathit{d}}$, which is consistent with a transition from two- to three-dimensional metallic conduction. The data also suggest that the superconductor-metal transition is not smooth.

The transparency of a film/substrate interface for thermal phonons was investigated for ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ thin films deposited on MgO, ${\mathrm{Al}}_2$${\mathrm{O}}_3$, ${\mathrm{LaAlO}}_3$, ${\mathrm{NdGaO}}_3$, and ${\mathrm{ZrO}}_2$ substrates. Both voltage response to pulsed-visible and to continuously modulated far-infrared radiation show two regimes of heat escape from the film to the substrate. That one dominated by the thermal boundary resistance at the film/substrate interface provides an initial exponential decay of the response. The other one prevailing at longer times or smaller modulation frequencies causes much slower decay and is governed by phonon diffusion in the substrate. The transparency of the boundary for phonons incident from the film on the substrate and also from the substrate on the film was determined separately from the characteristic time of the exponential decay and from the time at which one regime was changed to the other. Taking into account the specific heat of optical phonons and the temperature dependence of the group velocity of acoustic phonons, we show that the body of experimental data agrees with acoustic mismatch theory rather than with the model that assumes strong diffusive scattering of phonons at the interface.

The in-plane magnetoresistance of a high-quality single crystal of ${\mathrm{La}}_{1.925}$${\mathrm{Sr}}_{0.075}$${\mathrm{CuO}}_{4+\mathrm{\delta }}$ has been measured in both the high-symmetry transverse geometry and in the longitudinal geometry. In both orientations, the magnetoresistance is positive and shows conventional weak-field behavior. The measured longitudinal magnetoresistance, however, is found to be almost an order of magnitude smaller than the measured transverse magnetoresistance. A semiphenomenological theory based on anisotropic scattering from hypothesized hole-pocket Fermi surfaces is introduced, which can account for the latter positive effect, as well as for known Hall-effect measurements. We predict that, in the limit corresponding to perfectly coherent in-plane hole motion along (π,π), there should be no saturation effect in the high-symmetry transverse magnetoresistance.