We propose a modified Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities from the Landau-Ginzburg order parameter of the superfluid, so that two kinds of gauge symmetries appear, making the continuity equation and conservation of the total vorticity manifest. The topological term gives rise to the Berry phase term in the vortex mechanical actions.

The problem of a vortex situated near the edge of a thin superconducting film is solved. The flux associated with the vortex is shown to be less than the flux quantum in a broad domain adjacent to the film edge. The suppression of the vortex flux is strong in narrow thin-film bridges and scales with the ratio of the strip width to the film penetration depth.

In situ IR reflectivity was used to study the doping of thin ${\mathrm{C}}_{60}$ films with K and Rb by a load and equilibrate procedure. Nearly pure phases of ${\mathit{A}}_{\mathit{x}}$${\mathrm{C}}_{60}$ for x=1, 3, 4, and 6 were obtained in this way and the IR spectra were characterized. A quantitative analysis of the reflectivity spectra using a multilayer response function revealed the line positions, linewidths and the oscillator strengths for the ${\mathit{F}}_{1\mathit{u}}$ modes. The second-lowest mode and the highest mode showed good agreement with the charged phonon model with respect to line shift and absorption intensity and were thus assigned as charged phonon modes. The coupling constants for these modes to the virtual ${\mathit{t}}_{1\mathit{u}}$→${\mathit{t}}_{1\mathit{g}}$ transition were found to be of the order 0.01. This value is smaller but not negligible compared to the coupling of the gerade modes with ${\mathit{A}}_{\mathit{g}}$ and ${\mathit{H}}_{\mathit{g}}$ symmetry. Thus, the coupling from the virtual ${\mathit{t}}_{1\mathit{u}}$→${\mathit{t}}_{1\mathit{g}}$ transition may contribute as well to the pairing process in the superconducting phase.

The transport properties of ${\mathrm{K}}_{\mathit{x}}$${\mathrm{C}}_{70}$ thin films doped to their maximum conductivity are reported. At this doping level, ${\mathrm{K}}_{\mathit{x}}$${\mathrm{C}}_{70}$ (nominally ${\mathrm{K}}_4$${\mathrm{C}}_{70}$), with room-temperature-conductivity (σ) values ranging between ∼10–600 S/cm, is characteristic of a disordered metal near the Anderson localization regime, whose σ values are larger than the minimum metallic conductivity. The conduction bandwidth is estimated as 0.2–0.6 eV and the charge transport is modeled by the fluctuation-induced-tunneling model. The temperature dependence of the thermopower (S) and Hall coefficient (${\mathit{R}}_{\mathit{H}}$) are similar to that for superconducting ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ and graphite intercalation compounds. Thermopower anomalies in S(T) are observed in the same temperature range 80<T<100 K as the sign change of ${\mathit{R}}_{\mathit{H}}$(T), reflecting a possible change in structure or scattering process in this T range. The temperature and magnetic field dependence of the magnetoresistance of ${\mathrm{K}}_{\mathit{x}}$${\mathrm{C}}_{70}$, also similar to that of ${\mathrm{K}}_3$${\mathrm{C}}_{60}$, is compared with weak-localization theory, electron-electron-interaction theory and a two-band-metal model. Based on these models, we extract information about the intrinsic conductivity of the metallic regions. No superconducting transition in ${\mathrm{K}}_{\mathit{x}}$${\mathrm{C}}_{70}$ is observed above 1.35 K.

The critical behavior of a model with N-vector complex order parameters and three quartic coupling constants that describes phase transitions in unconventional superconductors, helical magnets, stacked triangular antiferromagnets, superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and zero-temperature transitions in fully frustrated Josephson-junction arrays is studied within the field-theoretical renormalization-group (RG) approach in three dimensions. To obtain qualitatively and quantitatively correct results perturbative expansions for β functions and critical exponents are caluculated up to three-loop order and resummed by means of the generalized Padé-Borel procedure. Fixed-point coordinates, critical-exponent values, RG flows, etc., are found for the physically interesting cases of N=2 and 3. Critical (marginal) values of N at which the topology of the flow diagram changes are determined as well. It is argued, on the basis of several independent criteria, that the accuracy of the numerical results obtained is about 0.01, an order of magnitude better than that given by resummed two-loop RG expansions. In most case the systems mentioned are shown to undergo fluctuation-driven first-order phase transitions. Continuous transitions are allowed in hexagonal d-wave superconductors, in planar helical magnets (into sinusoidal linearly polarized phase), and in triangular antiferromagnets (into simple unfrustrated order states) with critical exponents γ=1.336, ν=0.677, α=-0.030, β=0.347, and η=0.026, which are hardly believed to be experimentally distinguishable from those of the three-dimensional XY model. The chiral fixed point of RG equations is found to exist and possess some domain of attraction provided N≥4. Thus, magnets with Heisenberg (N=3) and XY-like (N=2) spins should not demonstrate chiral critical behavior with unusual values of critical exponents; they can approach the chiral state only via first-order phase transitions.

The crossover between ideal Josephson behavior and uniform superconducting flow is studied by solving exactly the Ginzburg-Landau equation for a one-dimensional superconductor in the presence of an effective δ-function potential of arbitrary strength. As the effective scattering is turned off, the pairs of Josephson solutions with equal current evolve into a uniform and a solitonic solution with nonzero phase offset. It is also argued that a microscopic description of the crossover must satisfy the self-consistency condition, which is shown to guarantee current conservation. The adiabatic response to an external bias is briefly described. The ac Josephson effect is shown to break down when the external voltage is applied at points which are sufficiently far from the junction.

We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction U reaches a critical value ${\mathit{U}}_{\mathit{c}}$. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one-dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.

We report careful measurements of the transition temperature ${\mathit{T}}_{\mathit{c}}$ of (${\mathrm{Ca}}_{\mathit{x}}$${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$) (${\mathrm{Ba}}_{1.75\mathrm{-}\mathit{x}}$${\mathrm{La}}_{0.25+\mathit{x}}$)${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{y}}$ as a function of oxygen content y, mainly for compositions x=0.1 and 0.4. This 1:2:3 superconductor family, that exists in the composition range 0≤x≤∼0.5, is tetragonal and has a maximal ${\mathit{T}}_{\mathit{c}}$ of ∼82 K. Through mutual charge-compensating cosubstitutions, it preserves a constant charge on the noncopper cations (Q=7.25), independent of x. We observed a monotonic decrease in ${\mathit{T}}_{\mathit{c}}$ as y varies from the initial value ∼7.15 to the insulator state roughly at y≃6.9. At the metal-insulator (MI) transition, the value of ${\mathit{y}}_{\mathrm{MI}}$ decreases with increasing x. Most unusual is the substantial increase in ${\mathit{T}}_{\mathit{c}}$ by 21 to 24 K when x changes from 0.1 to 0.4, under conditions where the charge density remains constant. It is accompanied by a twofold decrease in resistivity ρ. We attribute this to the change in band structure with composition x, which occurs due to increase in Ca content and to oxygen redistribution near La that substitutes for Ba. This induces a net electron transfer from the planes to the disordered chains. This assumption is supported by the decrease in ${\mathit{y}}_{\mathrm{MI}}$ and in lattice parameters with increasing x. It implies that changes in mobile hole density, which are responsible for the increase in ${\mathit{T}}_{\mathit{c}}$ and decrease in ρ, take place despite the total charge density being constant.

A simple model is presented to describe the nonmetallic behavior observed over wide doping ranges of perovskite-type ${\mathrm{BaBi}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pb}}_{\mathit{x}}$${\mathrm{O}}_3$ and ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$ alloys. The model is based on the idea that the oxygen octahedra endure static distortion waves of a ‘‘breathing’’ type, with wave vectors Q(x) nesting to the respective alloy Fermi surfaces as obtained from the energy bands of a virtual-crystal band model. For ${\mathrm{BaBi}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pb}}_{\mathit{x}}$${\mathrm{O}}_3$, Bi-Pb ordering waves are added by placing the Bi atoms onto those octahedral sites that exhibit the largest breathing distortions. Using a simple tight-binding Hamiltonian based on realistic energy-band calculations, the model has been studied on large supercells, testing a multitude of lattice configurations. Experimental consequences are discussed.

We examine the effect of thermal and quantal fluctuations on small super-conducting grains using a BCS-like Hamiltonian. A comparison between the static path approximation to the Hubbard-Stratonovich representation of the partition function (${\mathit{Z}}_{\mathrm{HS}}$) and the order-parameter representation (${\mathit{Z}}_{\mathrm{OP}}$) based on the Landau theory of phase transitions shows that one should use the expectation value of the pairing potential scrG instead of the BCS energy gap Δ for the order parameter of a superconducting system. Unlike ${\mathit{Z}}_{\mathrm{HS}}$, ${\mathit{Z}}_{\mathrm{OP}}$ is not restricted to positive-definite pairing potentials and can be used for general momentum-dependent pairing potentials. We find that quantal fluctuations are negligible for the crystallites of the polycrystalline high-${\mathit{T}}_{\mathit{c}}$ materials and that the results obtained using ${\mathit{Z}}_{\mathrm{OP}}$ are a good approximation to the exact results. Both the sharpening of the peak in the specific heat and the increase in the critical temperature observed during the sintering process of polycrystalline high-${\mathit{T}}_{\mathit{c}}$ materials can be qualitatively understood by taking into account thermal fluctuations. In polycrystalline high-${\mathit{T}}_{\mathit{c}}$ materials there is an anomaly in the specific heat rising above the BCS peak which is not reproduced by including these finite-size effects.

The lengths of the O-Cu-O chains in the basal ${\mathrm{CuO}}_{\mathit{x}}$ plane are calculated by the cluster variation method for the orthorhombic phases ${\mathit{O}}_{\mathit{I}}$ and ${\mathit{O}}_{\mathit{I}\mathit{I}}$ of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$. A variation of the interaction constants is performed in order to obtain the best fit to experiments. The dependence on x of other quantities, measured in Cu NMR/NQR and Gd EPR experiments, such as the monovalent copper count or the EPR line intensities for different oxygen chain configurations, is obtained. Also, the dependence of the amount of the transferred O 2p holes on x is calculated. The plateau at x>0.5 is found to be strongly related to the formation of chains in the ${\mathit{O}}_{\mathit{I}\mathit{I}}$ phase.

We present measurements of the critical current in an epitaxial ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ film as a function of the magnetic field, the temperature, and of the angle ϑ between the field and the a,b planes. The orientational study reveals an increasing anisotropy in ${\mathit{J}}_{\mathit{c}}$ with increasing temperature. The isothermal curves ${\mathit{J}}_{\mathit{c}}$(H) taken at various angles 0°≤ϑ≤90° are found to collapse to a single curve when the magnetic field is normalized to a scaling function f(ϑ): ${\mathit{J}}_{\mathit{c}}$(H,ϑ)=${\mathit{J}}_{\mathit{c}}$[H/f(ϑ)]. The best fit for f(ϑ) is obtained using an expression originally derived for ${\mathit{H}}_{\mathit{c}2}$(T,ϑ) by Tinkham. The increase in ${\mathit{J}}_{\mathit{c}}$(0°)/${\mathit{J}}_{\mathit{c}}$(90°) with increasing temperature is reflected by the increase in the anisotropy ratio f(0°)/f(90°), consistent with the quasi-two-dimensional Tinkham expression. Consistently, the same model quantitatively describes the increasing anisotropy with increasing temperature.

We report a systematic study of the magnetoresistance of Bi-2:2:1:2 single crystals using a small transport current and in magnetic fields less than 1 T. A few kelvin below the transition temperature we find excellent agreement with the theory of superconducting order-parameter fluctuations in two-dimensional systems. The critical temperature of an isolated double ${\mathrm{CuO}}_2$ sheet is estimated at 37 K, and the field which decouples ${\mathrm{CuO}}_2$ sheets at 0.1–0.2 T. By measuring the magnetoresistance in weak applied fields it is possible to determine the presence of small amounts of the Bi-2:2:2:3 phase. The presence of this latter phase makes the analysis of the fluctuation-enhanced conductivity above ${\mathit{T}}_{\mathit{c}}$ very complicated.

We report the infrared reflectances R(ν,T) of ${\mathrm{YBa}}_2$(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films (M=Zn and Ni) for frequencies 50 ${\mathrm{cm}}^{\mathrm{-}1}$<ν<1000 ${\mathrm{cm}}^{\mathrm{-}1}$ and temperatures T=10, 100, and 300 K. The ‘‘best fit’’ conductivities, ${\mathrm{\sigma }}_1$(ν,10 K), for both Zn- and Ni-doped films show no clear evidence of superconductivity, i.e., the superconducting density of states is very gapless. This degree of gaplessness is consistent with the large penetration depths measured in the same films. It agrees with estimates based on the measured carrier scattering rate 1/τ (10 K) and theories of d-wave superconductors. The carrier scattering rate 1/τ(T) increases with dopant concentration x and with T; it does not change rapidly just below ${\mathit{T}}_{\mathit{c}}$ as in pure ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. The plasma frequency ${\mathrm{\omega }}_{\mathit{p}}$=8500±500 ${\mathrm{cm}}^{\mathrm{-}1}$, independent of dopant concentration and T, agrees with values obtained in pure ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$.

The magnetic field in the center of a superconducting ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ hollow cylinder is measured as a function of the applied field for temperatures ranging from 20 to 85 K. The aim of this paper is to explain the low-field hysteresis of the magnetization encountered in this and similar polycrystalline materials through the use of the generalized critical state model. Parameters of the model are determined by fitting the data giving an exponent close to n=2, a zero field critical current density ${\mathit{J}}_{\mathit{c}0}$ ranging from 0 to 1300 A/${\mathrm{cm}}^2$, and a characteristic field ${\mathit{H}}_0$ which varies from 0 to 125 G. A related study of the full penetration field as a function of the wall thickness is also presented. We include the effect of the demagnetizing factor in the theoretical analysis when the cylinders are short compared to their diameter and their wall thickness. This leads to a shielded volume fraction ${\mathit{f}}_{\mathit{g}}$ of the sample of around 0.55.

We observe via polarized far-infrared-reflectance measurements of single-crystal samples of ${\mathrm{Pb}}_2$${\mathrm{Sr}}_2$R${\mathrm{Cu}}_3$${\mathrm{O}}_8$, where R is a rare-earth element, significant doping and temperature-induced changes in two c-axis phonons assigned to motion within the structural block containing the double ${\mathrm{CuO}}_2$ planes. In the normal state both phonons shift to lower frequency as the level of doping increases, with a monotonic transfer of oscillator strength from the lower [bending motion along c of the planar oxygen, O(3)] to the higher [vibrations of the apical oxygen, O(1)]. This doping-induced transfer of oscillator strength to the apical oxygen, accompanied by a sudden increase in asymmetry in the normal-state line shape of metallic samples which exhibit superconductivity at low temperatures, suggests that this process may play a role in the mechanism leading to the superconducting pairing. The linewidth of these two phonons shows a maximum as a function of doping near which, upon entry into the superconducting state, there is further anomalous broadening. A third phonon, attributed to vibrations of oxygen within the O(2)-Cu(1)-O(2) ‘‘sticks’’ and thus spatially removed from the ${\mathrm{CuO}}_2$ planes, shows no unusual behavior. These observations are consistent with a strong interaction between the phonons and the carriers of the structural block containing the ${\mathrm{CuO}}_2$ planes.

We conducted a detailed study of the structure and magnetic properties of (${\mathit{R}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$)${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ sintered samples, where R=Lu, Yb, Tm, Er, Y, Ho, Dy, Gd, Eu, Sm, and Nd for x=0.5–1.0. We found that the temperature dependence of the dc susceptibility follows the Curie-Weiss law in the temperature range 20–300 K and the paramagnetism of the Pr and R sublattices exist independently of one another. The antiferromagnetic ordering temperature ${\mathit{T}}_{\mathit{N}}$ of Pr ions decreases monotonically with increasing R concentration (1-x). At a given x, ${\mathit{T}}_{\mathit{N}}$ is R-ion-size dependent. The slope in the ${\mathit{T}}_{\mathit{N}}$ vs x curve is steeper for ions with smaller ionic radii. The observed results are interpreted in terms of the hybridization between the local states of the Pr ion and the valence-band states of the ${\mathrm{CuO}}_2$ planes.

Magnetic susceptibility χ and resistivity were measured in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$. Enhancement of χ due to a ferromagnetic correlation, which is inherent in the orthorhombic phase at low Sr concentrations, disappears at around x=0.05, near the margin of the superconducting regime. In superconducting samples with 0.1≲x≲0.2, χ exhibits a broad peak at a temperature ${\mathit{T}}_{\max }$. The T-dependent part of χ, ${\mathrm{\chi }}^{\mathit{s}}$(T), follows a single curve F regardless of x when ${\mathrm{\chi }}^{\mathit{s}}$ and T are normalized with the peak value ${\mathrm{\chi }}_{\max }^{\mathit{s}}$ and ${\mathit{T}}_{\max }$, as has been reported. However, the present scaling curve F decreases much more at T≪${\mathit{T}}_{\max }$ than the reported one. The resistivity exhibits a T-linear dependence above a temperature ${\mathit{T}}^{\mathrm{*}}$ and deviates downward from the T-linear dependence below ${\mathit{T}}^{\mathrm{*}}$. For x>0.1 the temperature ${\mathit{T}}^{\mathrm{*}}$ agrees well with ${\mathit{T}}_{\max }$, indicating that the deviation from a T-linear resistivity is related to the decrease of χ below ${\mathit{T}}_{\max }$. On the other hand, for x<0.1 a large reduction of χ is seen below ∼${\mathit{T}}^{\mathrm{*}}$ in the data up to 1000 K by Yoshizaki et al., although no peak is seen in the χ-T curve. The T dependence of χ in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{Cu}}_{1\mathrm{-}\mathit{y}}$${\mathrm{Zn}}_{\mathit{y}}$${\mathrm{O}}_4$ is also reported for x=0.16 and 0.22.

The remanent magnetic flux density trapped in the cavity and in the wall of sintered tubes of Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O was measured as a function of ${\mathit{H}}_{\mathrm{cool}}$, the axial magnetic field present during field cooling and then removed, and of ${\mathit{H}}_{\mathrm{cycle}}$, the axial magnetic field impressed and removed after zero-field cooling. For both procedures the two specimens exhibit very different behavior. A simple critical-state model which takes into account the return field of the magnetized grains quantitatively reproduces all of our observations and the corresponding data reported by others.

The thermal conductivity of single-crystal ${\mathrm{KH}}_2$${\mathrm{PO}}_4$ has been measured from 10 K to room temperature in an applied electric field. The applied field causes a small increase in the thermal conductivity at temperatures close to the ferroelectric-to-paraelectric transition. The results are compared with the dielectric polarization ${\mathrm{KH}}_2$${\mathrm{PO}}_4$ in an applied electric field.