Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

In order to enable optical systems to operate with a high degree of compactness and reliability it is necessary to combine large number of optical functions in small monolithic structures. A development, somewhat reminiscent of that that took place in Integrated Electronics, is now beginning to take place in optics. The initial challenge in this emerging field, known appropriately as "Integrated Optics", is to demonstrate the possibility of performing basic optical functions such as light generation, coupling, modulation, and guiding in Integrated Optical configurations. The talk will review the main theoretical and experimental developments to date in Integrated Optics. Specific topics to be discussed include: Material considerations, guiding mechanisms, modulation, coupling and mode losses. The fabrication and applications of periodic thin film structures will be discussed.

Integrated optics

Melt‐textured growth of polycrystalline YBa2Cu3O7−δ superconductor using directional solidification created an essentially 100% dense structure consisting of long, needle‐ or plate‐shaped crystals preferentially aligned parallel to the a‐b conduction plane. The new microstructure, which completely replaces the previous granular and random structure in the sintered precursor, exhibits dramatically improved transport Jc values at 77 K of ∼17 000 A/cm2 in zero field and ∼4000 A/cm2 at H=1 T (as compared to ∼500 and ∼1 A/cm2, respectively, for the as‐sintered structure), with the severe field dependence of Jc (‘‘weak‐link’’ problem) no longer evident in the new melt‐textured material. The improvement in Jc is attributed to the combined effects of densification, alignment of crystals, and formation of cleaner grain boundaries. Microstructure and distribution of various phases present in the melt‐textured material are discussed in relation to the superconducting properties.

High critical currents in Y‐Ba‐Cu‐O superconductors

We have extended Bean’s critical state model to explicitly include anisotropic critical currents. Measurements at 30 K of the critical currents parallel to the Cu‐O planes but with vortex motion either parallel or across twin boundaries show twin boundaries are probably not an important cause of vortex pinning. In the critical state, current flow perpendicular to the Cu‐O planes is about 30 times smaller than flow parallel to these planes.

Anisotropic critical currents in Ba2YCu3O7 analyzed using an extended Bean model

Using torque magnetometry, the superconducting anisotropy of a single crystal of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{Ca}}_{1}$${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ has been measured in the temperature range 775lTl83 K (${T}_{c}$=85 K) The data provide direct experimental evidence for a giant anisotropy A London analysis provides an excellent description of the results and establishes a temperature-independent value of 3\ifmmode\times\else\texttimes\fi{}${10}^{3}$ for the superconducting effective-mass anisotropy

Giant superconducting anisotropy in Bi2Sr2Ca1Cu2O8+ delta.

Electronic structure and energetics of (0001) and (11\ifmmode\bar\else\textasciimacron\fi{}02) surfaces of sapphire, \ensuremath{\alpha}-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$, were calculated using the self-consistent-field discrete variational (DV) method in the local-density framework. Clusters of a size of 70--120 atoms embedded in the semi-infinite host lattice were used to model the sapphire free surfaces. Calculations were performed on all possible terminating (0001) and (11\ifmmode\bar\else\textasciimacron\fi{}02) surfaces obtained from cleaving a sapphire single crystal. The energetic calculations show that the surface with the lowest cleavage energy is terminated with an Al layer for the (0001) surface, while it is terminated with an O layer for the (11\ifmmode\bar\else\textasciimacron\fi{}02) surface. The concept of the surface building block, useful in determining the surface atomic termination, was proposed. Two unoccupied surface bands derived from the top-layer Al atoms are found within the bulk band gap at 2 and 8 eV below the conduction-band minimum (CBM) for the (0001) surface. For the (11\ifmmode\bar\else\textasciimacron\fi{}02) surface, the occupied valence states derived from 2p states of the top-layer O atoms are found \ensuremath{\sim}4.0 eV below the CBM, which may explain the 4.7-eV energy-loss feature found experimentally on a sapphire (11\ifmmode\bar\else\textasciimacron\fi{}02) surface.

Electronic structure and energetics of sapphire (0001) and (11¯02) surfaces

Detailed Raman studies of the optical phonons in high-quality single-crystal ${\mathrm{PbTiO}}_{3}$ indicate that the mode energies and symmetry assignments in the literature [G. Burns and B. Scott, Phys. Rev. B 7, 3088 (1973)] must be revised. In this study, all k\ensuremath{\simeq}0 optical-phonon modes are directly observed and are shown to obey rigorously the Raman selection rules. The angular dependence of the phonon frequencies indicates that the energy of the lowest-frequency ${\mathit{A}}_{1}$(TO) mode is higher than the energy of the lowest-frequency E(LO) mode at 300 K. This indicates that these two k\ensuremath{\simeq}0 modes will cross at elevated temperature. The ${\mathit{A}}_{1}$(TO) mode exhibits an anomalous line shape, which we attribute to the anharmonic nature of the lattice. The phonon frequencies determine the clamped dielectric constants, ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{a}}$(0) and ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(0), using the Lydanne-Sachs-Teller relation. These values, when compared to those obtained from impedance measurements, indicate no dielectric dispersion in ${\mathrm{PbTiO}}_{3}$ between the MHz region and the Raman region.

Anharmonicity of the lowest-frequency A 1 (TO) phonon in PbTiO 3

X-ray photoelectron-spectroscopy study of oxides of the transuranium elements Np, Pu, Am, Cm, Bk, and Cf

The valence-band structures of the light actinides thorium, uranium, and their dioxides have been investigated by means of x-ray photoemission spectroscopy. This study shows that the electronic structures of Th${\mathrm{O}}_{2}$ and U${\mathrm{O}}_{2}$ are quite similar, except for the presence of $5f$ electrons in U${\mathrm{O}}_{2}$ which lie close to the Fermi level. It is these low-binding-energy $5f$ electrons that give rise to the most dramatic differences in physical properties, notably the magnetism, electrical conductivity, and color. Conduction in U${\mathrm{O}}_{2}$ apparently occurs via holes created by excitation of rather localized $5f$ electrons from the uranium to interstitial oxygen-acceptor sites. Sputtering experiments on thin oxide film and bulk samples show Fermi-level shifts in x-ray photoemission spectra associated with doping changes that result from preferential removal of interstitial ("impurity") oxygen atoms. The deep-trap and polaron conduction models have been reexamined. It is our view, at this time, that neither model can be ruled out. For the pure metal thorium, valence-band spectra were compared with the available density-of-states calculations and satisfactory agreement was obtained. For $\ensuremath{\alpha}\ensuremath{-}\mathrm{uranium}$, no detailed band calculation exists. However, the results agree with the qualitative density-of-states picture presented by Friedel.

D. J. Lam

Papers

Giant superconducting anisotropy in Bi2Sr2Ca1Cu2O8+ delta.

Electronic structure and energetics of sapphire (0001) and (11¯02) surfaces

Anharmonicity of the lowest-frequency A 1 (TO) phonon in PbTiO 3

X-ray photoelectron-spectroscopy study of oxides of the transuranium elements Np, Pu, Am, Cm, Bk, and Cf

X-ray photoelectron studies of thorium, uranium, and their dioxides