We compute the local variation of order parameter induced by an impurity for the two-dimensional order parameters of the general non-s-wave gap as well as an anisotropic s-wave gap, while taking into account the Born and unitarity limits of impurity scattering at all temperatures. The anisotropy of the perturbed gap is determined by the symmetry of the underlying order parameters. The perturbation for the anisotropic s-wave gap is much weaker than the non-s-wave gaps.

A superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ of 8.0 K is reported for the nonmagnetic (${\mathrm{Th}}^{4+}$) ${\mathrm{ThNi}}_2$${\mathrm{B}}_2$C compound with the ${\mathrm{LuNi}}_2$${\mathrm{B}}_2$C-type structure and a derived coherence length ξ(0) of 230 Å and a penetration depth λ(0) of 860 Å. No transition down to 2 K was observed for the magnetic, mixed-valence (${\mathrm{U}}^{4+}$/${\mathrm{U}}^{6+}$ or average valence of +5.2) ${\mathrm{UNi}}_2$${\mathrm{B}}_2$C compound with the same structure. Systematic variation of ${\mathit{T}}_{\mathit{c}}$ for the quaternary and pseudoquaternary compounds in the R${\mathrm{Ni}}_2$${\mathrm{B}}_2$C system (R=Sc, Y, La, Lu, Th, U, or magnetic lanthanides) is studied through the variation of ${\mathit{T}}_{\mathit{c}}$ with the R ionic radius, Ni-Ni nearest-neighbor in-plane distance, and the normal-state Pauli-like temperature-independent paramagnetic susceptibility. Maximum ${\mathit{T}}_{\mathit{c}}$ at 16.6 K for ${\mathrm{LuNi}}_2$${\mathrm{B}}_2$C with an optimum Ni-Ni distance of 2.45 Å was observed, along with a large normal-state Pauli paramagnetic susceptibility. As a comparison, the 8.0-K ${\mathrm{ThNi}}_2$${\mathrm{B}}_2$C superconductor has a longer Ni-Ni distance of 2.60 Å and a smaller normal-state susceptibility. Variations of the Ni(3d)-dominated conduction band and the density of states at the Fermi level N(${\mathit{E}}_{\mathit{F}}$) are believed to be the driving force for the ${\mathit{T}}_{\mathit{c}}$ variation of nonmagnetic compounds in the present system.

The superconducting levitation force F acting on a magnet placed above a type-II superconductor in both Meissner and mixed states is calculated as a function of temperature, based upon the London model. A simple relationship between the levitation force and the London penetration depth λ is found. In particular, in the limit of a/λ≫1, where a is the separation between the magnet and the superconductor, F varies linearly with λ, regardless of the shape of the magnet. The temperature dependences of λ and F are examined for various superconducting pairing states, including s-wave, d-wave, and s+id states. It is found that, at low temperatures, both λ and F show an exponential temperature dependence for s-wave, linear-T for d-wave, and ${\mathit{T}}^2$ dependence in a wide low-temperature range for the s+id state with a dominant d-wave component. The magnetic force microscope (MFM) is proposed to accurately measure the temperature-dependent levitation force. It is shown that the microscopic size of the MFM tip enables one to obtain the intrinsic temperature-dependent penetration depth of a single grain, in spite of the overall quality of the superconducting sample.

We have studied flux pinning by a periodic array of columnar defects in a two-dimensional geometry using large Josephson junctions with lithographically patterned defects in the junction barrier. The field-dependent critical current ${\mathit{I}}_{\mathit{c}}$(H) exhibits enhancement to values of order ${\mathit{I}}_{\mathit{c}0}$==${\mathit{I}}_{\mathit{c}}$(H=0) at commensurate fields for which the number of flux quanta in the junction is an integral multiple of the number of defects, and we model this behavior by considering the blocking of Josephson currents by the defects. Current-voltage characteristics taken near the commensurate fields reveal junction dynamics analogous to those found near zero field: at the commensurate fields, we find ‘‘commensurate field steps’’ arising from fluxon propagation previously seen only at zero field, and as the field is increased or decreased from a commensurate value, the evolution of the current-voltage characteristics closely resembles that found near zero field.

Precise nuclear magnetic susceptibility results on ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ adsorbed on Grafoil are presented for submonolayer coverages in the temperature reange 5–600 mK. At low areal densities, the film is in a two-dimensional homogeneous liquid state. Some ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms, however, are localized by the substrate heterogeneity; our quantitative measurements show that their amount increases from 2% to 4% of a monolayer thereby leading to significant corrections of the fluid-phase density. The Fermi tempreature of the liquid has been determined as a function of coverage; it decreases continuously for densities larger than 0.01 atoms/A${\mathrm{̊}}^2$. At high fluid densities, the susceptibility is enchanced by one order of magnitude with respect to the ideal-gas value. At ρ=0.0449 atoms/A${\mathrm{̊}}^2$, a two-phase coexistence region begins on a Grafoil sample; ρ=0.0434 atoms/A${\mathrm{̊}}^2$ is estimated for a perfect graphite surface. The coexistence is characterized by a linear increase (linear decrease) of the solid (liquid) fraction and a constant Fermi temperature of the liquid phase. Finally, at ρ=0.0646 atoms/A${\mathrm{̊}}^2$, the liquid phase disappears completely. Our results are compared to previous heat capacity and NMR measurements at submonolayer coverages.

The scaling of positron-implantation (stopping) profiles has been reported by Ghosh et al., who used the BNL Monte Carlo scheme to generate stopping profiles in semi-infinite elemental metals. A simple scaling relationship reduced the stopping profiles of positrons implanted at different energies (ranging from 1–10 keV) onto a single universal curve for that particular metal. We have confirmed that the scaling relationship also applies to the quite different Jensen and Walker Monte Carlo scheme, for more materials, and over an expanded energy range of 1–25 keV. The mean depths of the stopping profiles calculated by the two Monte Carlo schemes are found to be different, mainly due to differences in the inelastic mean free paths and the energy-loss functions. However, after scaling, the profiles generated by the two schemes can be superimposed onto a single curve which can be appropriately parametrized. The scaled profiles are found to be only weakly material dependent. The mean depths, backscattered fractions, and scaled stopping profiles are fitted to simple parametric functions, and the values of these parameters are obtained for several elements.

The competition in the pinning of a directed polymer by a columnar pin and a background of random point impurities is investigated systematically using the renormalization-group method. With the aid of the mapping to the noisy-Burgers equation and the use of the mode-coupling method, the directed polymer is shown to be marginally localized to an arbitrary weak columnar pin in 1+1 dimensions. This weak-localization effect is attributed to the existence of large scale, nearly degenerate optimal paths of the randomly pinned directed polymer. The critical behavior of the depinning transition above 1+1 dimensions is obtained via an ε expansion.

We have studied the mean-field quasiparticle states and quasiparticle interactions in the infinite-U Anderson lattice in the presence of crystal electric field of cubic symmetry. We assume a lattice of 4f sites, each with a total angular momentum of J=5/2 that is split into a low-lying doublet of ${\mathrm{\Gamma }}_7$ symmetry and an excited quartet of ${\mathrm{\Gamma }}_8$ symmetry. Slave bosons on the 4f sites create and destroy 4${\mathit{f}}^0$ configurations and Lagrange multipliers at each 4f site enforce the occupancy constraint due to the infinite Coulomb repulsion. The quasiparticle states are strongly peaked at the points where the Fermi surface intersects the axes of the cubic Brillouin zone, leading to what we call ‘‘hot spots.’’ We have calculated the effective magnetic moment and the Wilson ratio for these anisotropic quasiparticle states. Quasiparticle interactions are due to exchange of 4f density fluctuations. We use the analytic tetrahedron method to calculate the dressed (to order 1/N) boson Green functions. In weak coupling, the exchange of the dressed bosons gives rise to a superconducting instability of ${\mathit{T}}_{1\mathit{g}}$, xy(${\mathit{x}}^2$-${\mathit{y}}^2$), symmetry. The ${\mathit{A}}_{1\mathit{g}}$, ‘‘s-wave,’’ channel has strongly repulsive interactions and hence no pairing instability. The ${\mathit{T}}_{2\mathit{g}}$ channel exhibits weakly repulsive interactions. Average quasiparticle interactions in the ${\mathit{E}}_{\mathit{g}}$, ${\mathit{x}}^2$-${\mathit{y}}^2$, 3${\mathit{z}}^2$-${\mathit{r}}^2$, channel fluctuate strongly as a function of the number of tetrahedra used to calculate the bosonic Green functions, lending only weak evidence for an instability of ${\mathit{E}}_{\mathit{g}}$ symmetry.

Discovery of a quaternary superconducting system Y-Ni-B-C has been reported recently. Our structural studies on ${\mathrm{YNi}}_2$${\mathrm{B}}_2$C (${\mathit{T}}_{\mathit{c}}$≊15.5 K) reveal large and anisotropic thermal vibrations of C atoms in the Y-C plane of the structure. No crystallographic phase transition is observed down to 50 K. Our specific-heat data suggest that ${\mathrm{YNi}}_2$${\mathrm{B}}_2$C is a strong-coupling superconductor. Results of our resistivity, magnetic, and specific-heat data clearly suggest coexistence of superconductivity and magnetism (of Er spins) in ${\mathrm{ErNi}}_2$${\mathrm{B}}_2$C (${\mathit{T}}_{\mathit{c}}$≊10.5 K) below ≊7 K.

We calculate the spin susceptibility at and below ${\mathit{T}}_{\mathit{c}}$ for a ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$-wave superconductor with resonant impurity scattering and Coulomb correlations. Both the impurity scattering and the Coulomb correlations act to maintain peaks in the spin susceptibility, as a function of momentum, at the Brillouin zone edge. These peaks would otherwise be suppressed by the superconducting gap. At the highest impurity concentration considered here, the predicted amount of suppression of the imaginary part of the spin susceptibility in the superconducting state compared to the normal state is in qualitative agreement with results from recent magnetic neutron-scattering experiments on ${\mathrm{La}}_{1.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_4$ for momentum values at the zone edge and along the zone diagonal. The predicted peak widths in the superconducting state, however, are narrower than those in the normal state, a narrowing which has not been observed experimentally.

The Raman spectrum of the ${\mathit{B}}_{1\mathit{g}}$ phonon in the superconducting cuprate materials is investigated theoretically in detail in both the normal and superconducting phases, and is contrasted with that of the ${\mathit{A}}_{1\mathit{g}}$ phonon. A mechanism involving the charge-transfer fluctuation between the two oxygen ions in the ${\mathrm{CuO}}_2$ plane coupled to the crystal field perpendicular to the plane is discussed and the resulting electron-phonon coupling is evaluated. Depending on the symmetry of the phonon, the weight of different parts of the Fermi surface in the coupling is different. This provides the opportunity to obtain information on the superconducting gap function at certain parts of the Fermi surface. The line shape of the phonon is then analyzed in detail both in the normal and superconducting states. The Fano line shape is calculated in the normal state and the change of the linewidth with temperature below ${\mathit{T}}_{\mathit{c}}$ is investigated for a ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ pairing symmetry. Excellent agreement is obtained for the ${\mathit{B}}_{1\mathit{g}}$ phonon line shape in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$.

For untwinned single-crystal ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ in a magnetic field H, we find that the in-plane Hall conductivity ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$ just below the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ is the sum of two terms, ${\mathit{C}}_1$/H and ${\mathit{C}}_2$H, where ${\mathit{C}}_1$ and ${\mathit{C}}_2$ are field independent, in agreement with recent theoretical predictions of Dorsey et al. and Kopnin et al. ${\mathit{C}}_1$ and ${\mathit{C}}_2$ have opposite signs, as required by the observation that the Hall effect changes sign as the applied field is varied. ${\mathit{C}}_1$ is proportional to ${\mathrm{\tau }}^2$, and ${\mathit{C}}_2$ is approximately proportional to τ, where τ=(${\mathit{T}}_{\mathit{c}}$-T)/${\mathit{T}}_{\mathit{c}}$, so the crossover field ${\mathit{H}}_0$, where ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$=0, is proportional to ${\mathrm{\tau }}^{1/2}$.

The dependence of the transport critical-current density on an applied magnetic field and temperature of a high-${\mathit{J}}_{\mathit{c}}$ (Bi,Pb${)}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{x}}$ silver-sheathed tape has been measured in the range from 10 to 110 K. It is found that the transport critical current follows the relation ${\mathit{J}}_{\mathit{c}}$=${\mathit{J}}_{\mathit{c}0}$(1-aT+${\mathit{bT}}^2$). For T<40 K, b=0, while for T>40 K, b>0. ${\mathit{J}}_{\mathit{c}}$ and the applied field follow a power-law relation ${\mathit{J}}_{\mathit{c}}$∝${\mathit{B}}^{\mathrm{-}\mathrm{\alpha }}$ (α≊0.3) for T<40 K and an exponential-law relation ${\mathit{J}}_{\mathit{c}}$∝exp(-βB) for T>65 K. For 40 K<T<65 K, there is a transition field for ${\mathit{J}}_{\mathit{c}}$(B,T). This represents a transition of the above two relations for ${\mathit{J}}_{\mathit{c}}$(B). The experimental results can be explained within the framework of the flux-creep model in terms of different potential-barrier forms. The limitation of ${\mathit{J}}_{\mathit{c}}$ from 10 K to ${\mathit{T}}_{\mathit{c}0}$ seems to be attributed to the flux creep for high-${\mathit{J}}_{\mathit{c}}$ textured Bi(2223) Ag-sheathed tapes. The flux lattice seems to experience a transition that is similar to the flux-lattice melting in this material in both applied-magnetic-field orientations near 40 K.

When one measures the thermal diffusivity χ of a thin film on a substrate by the mirage method, the photothermal deflection of the probe beam is caused by the heat field contributed by both the film and the substrate which are heated by the pump beam. To include the effects due to the presence of the substrate, we present a method to measure the diffusivities of both the film and substrate in one set of mirage detection. Using the off-axis magnetron sputtering process, we fabricated ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films of suitable thickness (∼60 nm) on ${\mathrm{SrTiO}}_3$ as our sample for χ measurements along the c and b axes. Our results are consistent with published ones.

Calculations are presented of the energy barriers between topologically different configurations of two entangled vortex lines in a superconductor. The results suggest that the line-cutting barriers in high-${\mathit{T}}_{\mathit{c}}$ superconductors are somewhat larger than previous numerical estimates indicated, but not large enough to support a kinetic ‘‘polymer glass’’ interpretation of the irreversibility line in fields much greater than ${\mathit{H}}_{\mathit{c}1}$. The consequences of a crossing barrier for transport properties are discussed briefly.

Systematic measurements of the resistivity of the polycrystalline samples of the ${\mathrm{YBa}}_2$(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_4$${\mathrm{O}}_8$ system with M=Fe, Ni are reported. The resistivity behavior depends strongly on the dopant concentration. For the Fe 6-at. % sample, there is no metallic behavior in the resistivity, but for T>50 K, the resistivity decreases very slowly with temperature. The behavior of the resistivity of the Fe 10-at. % and Ni 5-at. % samples is analyzed, and it is found that the variable-range hopping process may occur in these samples below about 30 K. While the Ni 5-at. % sample is found to show signs of the nearest-neighbor hopping process of conductivity above about 150 K, the Fe 10-at. % sample does not show such behavior up to 300 K. On this basis it is found that localization may not be a possible reason of the large ${\mathit{T}}_{\mathit{c}}$ depression in the ${\mathrm{YBa}}_2$(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_4$${\mathrm{O}}_8$ system by the Fe and Ni dopants. We have examined the possibility of ${\mathit{T}}_{\mathit{c}}$ degradation due to carrier-impurity potential scattering also by using a single-crystal analog of the polycrystalline sample. This analogy is justified to within a factor of less than 1.33. On the basis of this analogy we have found that potential scattering may not be a reasonable source of ${\mathit{T}}_{\mathit{c}}$ degradation in the Ni- and Fe-doped samples of the system considered.

Neutron powder diffraction was used to study the crystallographic structure of a quenched tetragonal sample of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.25}$ during room-temperature annealing. It is found that the lattice parameters decrease with anneal time. The time dependence of the two lattice parameters is characterized by a single relaxation time ∼760 min. Similar relaxation times were recently found for the electrical resistances ${\mathit{R}}_{\mathit{a}\mathit{b}}$, ${\mathit{R}}_{\mathit{c}}$, in tetragonal single crystals of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.25}$. These results are interpreted in terms of local ordering of the oxygen ions in the basal ${\mathrm{CuO}}_{\mathit{x}}$ plane, leading to a charge transfer between the ${\mathrm{CuO}}_{\mathit{x}}$ and ${\mathrm{CuO}}_2$ planes. It is the same effect that leads to the rise in ${\mathit{T}}_{\mathit{c}}$ observed earlier in orthorhombic ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ (x>0.35). The mechanism of the local ordering and the concept of oxygen ions ordering in a structure with tetragonal symmetry are discussed.

The exact ground-state energy ${\mathit{E}}_0$(Φ) is calculated for a one-dimensional copper-oxide model defined on a ring of finite length L, threaded by an external flux Φ. It includes on-site and nearest-neighbor intersite Coulomb repulsion V, as well as a nonzero bare ‘‘oxide’’ gap ${\mathrm{\Delta }}_0$ between the orbitals in the unit cell. The correlation exponent ${\mathit{K}}_{\mathrm{\rho }}$ of the corresponding low-energy Hamiltonian shows that singlet (extended s-wave) superconductivity has the most rapidly diverging susceptibility as T→0 (${\mathit{K}}_{\mathrm{\rho }}$>1). This superconducting phase is located close to a phase-separation instability of the model, indicated by ${\mathit{K}}_{\mathrm{\rho }}$→∞. Longer range of the Coulomb interaction tends to frustrate phase separation, enhances the range of V for which ${\mathit{K}}_{\mathrm{\rho }}$>1, and slightly broadens the regime of V where 1<${\mathit{K}}_{\mathrm{\rho }}$<∞.

The resistivity and Hall effect have been measured in a number of samples of as-grown, oxygen deficient, c-axis-oriented ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{x}}$ thin films, both as a function of temperature and oxidation state. The temperature dependence of the longitudinal resistivity and Hall coefficient were generally similar to films prepared by ex-situ oxidation processes with the R-T and 1/${\mathit{R}}_{\mathit{H}}$-T characteristics nearly linear and cot${\mathrm{\theta }}_{\mathit{H}}$∝${\mathit{T}}^2$. Small deviations from these laws were investigated and a quadratic fit obtained for the resistivity data and a cubic fit for cot${\mathrm{\theta }}_{\mathit{H}}$ but with dominant linear and quadratic terms, respectively. From the empirical data, expressions for the effective carrier relaxation times and mobilities were obtained and compared with other possible scattering mechanisms. In contrast to films reoxidized after growth, we find that for the as-grown films the Hall mobility ${\mathrm{\mu }}_{\mathit{H}}$ increases sharply and cot${\mathrm{\theta }}_{\mathit{H}}$ decreases with increasing oxygen content. This is discussed in terms of different oxidation conditions that lead to different lattice defects for the two cases.

The crystal structures of underdoped, optimally doped, and overdoped ${\mathrm{TlSr}}_2$(${\mathit{R}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ca}}_{\mathit{x}}$)${\mathrm{Cu}}_2$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (R=Lu or Tl) are refined from neutron powder-diffraction data. Carrier concentrations in this system are estimated from simple ionic consideration using the refined occupation numbers. The plot of ${\mathit{T}}_{\mathit{c}}$ vs carrier concentration shows the characteristic bell-shaped dependence. The in-plane bond length Cu-O(1) is affected by only the change of carrier concentration and provides a measurement of the doping level, while the apical bond length Cu-O(2) is affected by both the change of carrier concentration and the amount of cation substitution. If we take the effect of cation substitution into account, these bond lengths change ‘‘linearly’’ with carrier concentration over the entire range from the underdoped, through the optimally doped, to the overdoped region.