The superconducting transition temperature and the upper critical magnetic field of amorphous ${\mathrm{Zr}}_{67}$${\mathrm{Co}}_{33\mathrm{-}\mathit{x}}$${\mathrm{P}}_{\mathit{x}}$, x=0,5,11, are studied. Comparison of critical-field parameters for several different amorphous alloys show that an anomalously enhanced critical field cannot be simply correlated to other material properties. Results from different methods to increase disorder in three-dimensions are compared. The normalized ${\mathit{T}}_{\mathit{c}}$ of ${\mathrm{Zr}}_{67}$${\mathrm{Co}}_{33\mathrm{-}\mathit{x}}$${\mathrm{P}}_{\mathit{x}}$ samples, and published results for H-doped samples and neutron-irradiated samples all show a similar dependence of the resistivity increase. This relation extends to below 20% of the initial ${\mathit{T}}_{\mathit{c}}$ and it can be obtained from the Fukuyama-Ebisawa-Maekawa theory with a single adjustable parameter. The widths of the superconducting transitions in the magnetic field decrease strongly with decreasing temperature for Zr-Co-P but remain finite at the lowest measuring temperatures. The critical magnetic field increases with increased disorder, which agrees with recent observations from neutron irradiation and cannot be explained by current theories for disorder effects.

Interstitials and vacancies in the Abrikosov phase of clean type-II superconductors are line imperfections, which cannot extend across macroscopic equilibrated samples at low temperatures. We argue that the entropy associated with line wandering nevertheless can cause these defects to proliferate at a sharp transition which will exist if this occurs below the temperature at which the crystal actually melts. Vortices are both entangled and crystalline in the resulting ‘‘supersolid’’ phase, which in a dual ‘‘boson’’-analog system is closely related to a two-dimensional quantum crystal of ${\mathrm{He}}^4$ with interstitials or vacancies in its ground state. The supersolid must occur for B≫${\mathit{B}}_{\times }$, where ${\mathit{B}}_{\times }$ is the decoupling field above which vortices begin to behave two dimensionally. Numerical calculations show that interstitials, rather than vacancies, are the preferred defect for B≫${\mathrm{\phi }}_0$${\lambda }_{\mathrm{\perp }}^2$, and allow us to estimate whether proliferation also occurs for B≲${\mathit{B}}_{\times }$. The implications of the supersolid phase for transport measurements, dislocation configurations, and neutron diffraction are discussed.

A full three-band model for the ${\mathrm{CuO}}_2$ plane with inclusion of all essential interactions—Cu-O and O-O hopping, repulsion at the copper and oxygen and between them—is considered. A general procedure of the low-energy reduction of the primary Hamiltonian to the Hamiltonian of the generalized t-t’-J model is developed. An important role of the direct O-O hopping is discussed. Parameters of the effective low-energy model (the hopping integral, the band position, and the superexchange constant J) are calculated. An analysis of the obtained data shows that the experimental value of J fixes the charge-transfer energy Δ=(${\mathrm{\epsilon }}_{\mathit{p}}$-${\mathrm{\epsilon }}_{\mathit{d}}$) in a narrow region of energies.

The dynamics of the fluxon in a long circular Josephson junction is studied. A bias charge across the junction is shown to act like a gauge potential on the fluxon. The system is then quantized, and the energy levels of the fluxon are found to resemble those of a small capacity-dominated Josephson junction. The quantized fluxon is shown to exhibit a persistent motion in analogy with the persistent current of electrons in a metal ring threaded by a magnetic flux. This motion manifests itself in a voltage across the junction. At finite temperatures the voltage is reduced by the thermal distribution of the fluxon’s energy. The dependence of the voltage on the ratio of the junction’s circumference to the Josephson penetration depth is examined.

To treat the phonon-induced electron pairing in a way which allows for vortex corrections and retardation effects, we develop a method using a canonical transformation involving a variational function. This method is expected to be useful for developing a unified theory for phonon-induced electron pairing ranging between adiabatic and nonadiabatic behavior, or, respectively, between Copper-pair condensation in momentum space and bipolaron condensation in real space. To demonstrate the power of our variational treatment we determine for a model pairing potential, involving a temperature-dependent energy cutoff c(T) as a variational parameter, the thermodynamical properties of the conventional intermediate- and strong-coupling superconductors. Thus, we obtain results which compare well with those obtained by solving the Eliashberg equations.

Outstanding difficulties in a deformable type-II superconductor model for the fluxon inertial mass per unit length ${\mathrm{\mu }}_{\mathit{d}}$ are resolved. An identity for the inertial mass, valid for an arbitrary quasiparticle fraction when the ionic displacement field is irrotational, plays a critical role in the analysis. This approach avoids previously employed approximations, leading to qualitatively different results, including a fluxon mass which properly vanishes at the transition temperature and which has a greatly reduced magnitude. A framework for the solution of the elasticity equation for an isotropic superconductor is presented and the close relation between ${\mathrm{\mu }}_{\mathit{d}}$ and the ionic strain field is shown.

We present in this paper the first quantitative calculation of critical temperature ${\mathit{T}}_{\mathit{c}}$ and gap parameter β(≡2Δ/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$) of superconductors with fractal structure in the light of electron-fracton coupling. The Kresin’s formula which is valid for any arbitrary value of λ is used. The calculations are based on the McMillan function ${\mathrm{\alpha }}^2$F(ω) of electron-fracton interaction recently developed by the authors. Variations of ${\mathit{T}}_{\mathit{c}}$ and β with the fractal dimension D are plotted. The results exhibit the possibility of obtaining high critical temperature in superconductors where electrons and fractons are strongly coupled. Application of the calculations to amorphous superconductors is discussed.

Helium films of thickness less than the critical coverage for superfluid onset at T=0 K were studied using a high-resolution calorimetry technique. The films were adsorbed on three disordering substrates: a planar geometry as offered by Mylar tape, a cylindrical geometry as provided by Anopore membranes, and a randomly connected porous geometry as obtained from Millipore fibrous filter paper. The substrates were characterized by nitrogen adsorption isotherms and scanning electron microscopy. A heat-capacity ‘‘bump’’ centered at a temperature that decreases with increasing thickness is found in all cases. The presence of the bump is interpreted as a universal feature for localized helium films adsorbed in substrates introducing disorder. The parameters characterizing such a bump are nonuniversal. The heat-capacity results are analyzed using models for adsorption on heterogeneous substrates.

The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical XY model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of the magnetic field is characterized by the frustration f. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent z, the correlation length exponent ν, and the universal conductivity ${\mathrm{\sigma }}^{\mathrm{*}}$. For the disorder-free model with f=1/2, we obtain z≊1, 1/ν≊1.5, and ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.52±0.03, where ${\mathrm{\sigma }}_{\mathit{Q}}$ is the quantum conductance. We also study the case with f=1/3, in which we find ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.83±0.06. The value of ${\mathrm{\sigma }}^{\mathrm{*}}$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find z=1.07±0.03, ν≊1, and ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.27±0.04 for the case f=0, and z=1.14±0.03, ν≊1, and ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.49±0.04 for the case f=1/2.

The critical-state behavior of an infinitely long type-II superconducting thin-film strip is theoretically analyzed for an arbitrary sequence of applied transport currents and perpendicular magnetic fields. Included are solutions for applied field only, transport current only, transport current applied to a sample initially in the remanent critical state, ac applied field, ac transport current, and simultaneously applied field and transport current. The results are compared side by side with corresponding solutions for the more famililar slab geometry; there are striking differences in behavior.

Tunneling break junctions of single crystals of Bi-Sr-Ca-Cu-O show a reproducible superconducting-gap structure that can be fully described with a broadened BCS density of states. The obtained ratio between the energy gap Δ and the critical temperature ${\mathit{T}}_{\mathit{c}}$ amounts to 2Δ/${\mathit{T}}_{\mathit{c}}$=6.2. In a magnetic field up to 20 T, the conductance curve shows additional broadening but the energy gap remains constant. From a comparison of the magnetoresistance and tunneling data for different orientations of the magnetic field, it follows that the break junctions probe the superconducting properties in the ab plane. Both the magnetic field and temperature dependence of the tunneling characteristics are in agreement with the known dependences for the classical superconductors.

A model for spin-charge-separated superconductivity in two dimensions is introduced where the phases of the spinon and holon order parameters couple guage invariantly to a statistical gauge field representing chiral spin fluctuations. The model is analyzed in the continuum limit and in the low-temperature limit. In both cases we find that physical electronic phase correlations show a superconducting-normal phase transition of the Berezinskii-Kosterlitz-Thouless type, while statistical gauge-field excitations are found to be strictly gapless. It is argued that the former transition is in the same universality class as that of the XY model. We thus predict a universal jump in the superfluid density at this transition. The normal-to-superconductor phase boundary for this model is also obtained as a function of carrier density, where we find that its shape compares favorably with that of the experimentally observed phase diagram for the oxide superconductors.

We report room-temperature optical reflectivity and transmission measurements on a variety of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ and ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{2\mathit{n}+4\mathrm{}}$ thin films in the 500–25 000 ${\mathrm{cm}}^{\mathrm{-}1}$ frequency range. Reflectivity data when not biased by the substrate are used to compute the optical conductivity. A comparison of our results with published reflectivity data on single-domain ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ crystals suggests an overwhelming contribution of the ${\mathrm{CuO}}_2$ planes (with respect to the chains) to the optical conductivity. The data can be analyzed in terms of a Drude low-frequency contribution and a so-called midinfrared band. However, the anomalous infrared response appears to be uniquely described by a generalized Drude response: for all the samples investigated, the relaxation rate (which increases linearly with frequency) and the effective mass are found to be the same as a function of frequency.

In this paper the variations of the normal-state characteristic associated with the metal-insulator transition for ${\mathrm{Bi}}_2$${\mathrm{Sr}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ba}}_{\mathit{x}}$${\mathrm{CuO}}_{\mathit{y}}$ were investigated by means of x-ray photoemission spectroscopy, Raman scattering, as well as the measurement of thermoelectric power. The experimental data reveal that in the Ba-doped ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CuO}}_{\mathit{y}}$ system the Coulomb correlation of Cu 3d electrons tends to strengthen with the partial substitution of Ba for Sr. The metal-insulator transition in this system is very likely to originate from the change of Cu 3d electrons from partially delocalized to localized states. In addition, the experiment also shows that in the Ba-doped 2:2:0:1 phase the change in the incommensurate modulation structure results in intensifying the structural distortion of the 2:2:0:1 phase. The variation of the Cu 3d electrons with Ba substitution possibly comes from such a structural distortion. This suggests that for high-${\mathit{T}}_{\mathit{c}}$ cuprates the superconductivity is closely related to the crystal microstructure.

A description of the anisotropy of elastic and nonlinear acoustic properties of dense (95% of theoretical), highly textured, sinter-forged, ceramic ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathit{y}}$ (Bi-2:2:1:2) high-${\mathit{T}}_{\mathit{c}}$ superconductors is provided from measurements of the velocities of longitudinal and shear ultrasonic waves as functions of temperature and hydrostatic pressure. A high proportion of the grains are aligned preferentially with the c axis along the forging direction in this material, while it is essentially isotropic in the plane normal to the forging axis. A complete set of the elastic stiffness tensor components has been determined as a function of temperature from 10 to 290 K, treating this material as if it had cylindrical symmetry. The results are used to compute the orientation dependences of the Young’s modulus and Poisson’s ratio which are compared with those estimated for single crystal Bi-2:2:1:2. The main finding is a marked anisotropy of the elastic stiffness moduli and their dependences on pressure. The elastic and nonlinear acoustic properties of the textured and single-crystal Bi-2:2:1:2 comply with the behavior expected for a layerlike material with rather weak interlayer binding forces: ${\mathit{C}}_{11}$>${\mathit{C}}_{33}$, the linear compressibility and thermal expansion along to the c axis, i.e., normal to the layers, being substantially larger than in the ab plane. The hydrostatic pressure derivative (∂${\mathit{C}}_{33}$/∂P${)}_{\mathit{P}=0\mathrm{}}$(=21.3) of the elastic stiffness tensor component, which corresponds to a longitudinal wave propagated along the c axis, is larger than that (∂${\mathit{C}}_{11}$/∂P${)}_{\mathit{P}=0\mathrm{}}$(=15.1), for such a wave propagated in the ab plane. The anisotropies of the linear compression and the acoustic mode Grüneisen parameters are also typical of a layerlike material.

We calculate the effects of the energy density of states due to superconductive fluctuation on the nuclear relaxation rate in the dirty high-temperature superconductors. We show that the correction to the Korringa law has an order of (${\mathit{E}}_{\mathit{F}}$τ${)}^{\mathrm{-}3/2}$ for a three-dimensional (3D) superconductor and for a realistic parameter is very small. In the case of a 2D superconductor the correction to the Korringa law has the order of (${\mathit{E}}_{\mathit{F}}$τ${)}^{\mathrm{-}1}$ and may become important for ${\mathit{E}}_{\mathit{F}}$τ∼1.

The location of the positive muon, used as a tool for probing the magnetic properties of high-${\mathit{T}}_{\mathit{c}}$ systems, is investigated for ${\mathrm{La}}_2$${\mathrm{CuO}}_4$. Our calculations, using the unrestricted Hartree-Fock cluster procedure, indicate that the muon is located in the a-c plane, at a distance of 1.08 Å from the apical oxygen, with the ${\mathrm{\mu }}^{+}$-O(a) direction making an angle of 25° with the O(a)-Cu direction. The magnitude and direction of the hyperfine field at the equilibrium position are determined. Our results, which are in reasonable agreement with μSR data in powdered samples and single crystals, show the importance of including the local contact and dipolar contributions to the hyperfine field associated with the unpaired spin distribution in the neighborhood of the muon. Possible additional factors that could lead to a bridging of the remaining quantitative differences with experimental hyperfine data will be discussed.

The superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ and the Hall coefficient have been measured on ${\mathrm{IBi}}_{2.2}$${\mathrm{Sr}}_{1.8}$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathit{y}}$ single crystals under hydrostatic pressure. The ${\mathit{T}}_{\mathit{c}}$ linearly decreases at the rate ${\mathit{dT}}_{\mathit{c}}$/dP∼-3.5 K/GPa, indicating the facts that the charge transfer occurs between intercalated iodine atoms and ${\mathrm{CuO}}_2$ layers, and the hole concentration situates in the overdoped region. The facts have been further identified by our Hall-coefficient measurements at ambient pressure, showing an increase of the hole concentration after intercalation. The number of holes transferred from intercalated iodine atoms was calculated to be 0.3 per iodine atom. The pressure derivative of the Hall coefficient is -0.39×${10}^{\mathrm{-}3}$ ${\mathrm{cm}}^3$ ${\mathrm{C}}^{\mathrm{-}1}$ ${\mathrm{GPa}}^{\mathrm{-}1}$, which is approximately twice as large as the value on the pristine crystal, indicating the valence change of the intercalated iodine under pressure.

A generalized tight-binding method to calculate quasiparticle band structure and density of states in strongly correlated systems is presented. The band structures of undoped and weakly hole-doped ${\mathrm{CuO}}_2$ layer are calculated. The insulator gap has a charge transfer nature with a minor contribution from a Cu-O Coulomb interaction. Doping results in the appearance of an in-gap state with a simultaneous decrease of the density of states at the band edges in agreement with small cluster results and experimental data.

We report electrical conductivity and magnetization measurements on single crystals of the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ with partial substitution of Fe, Ni, and Zn for Cu. Even concentrations of the doping element below 1 at. % cause a strong increase of the electrical resistivity, a definite increase of the London penetration depth, and a decrease of the correlation length. Concomitantly the critical current is lowered and the irreversibility line shifts towards lower field values with increasing concentration of the dopants. For the initial slope ${\mathit{dT}}_{\mathit{c}}$/dx we derive a value of -5 K/at. % independent of the substitutional element.