Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

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 the past few years magneto-optical flux imaging (MOI) has come to take an increasing role in the investigation and understanding of critical current densities in high-Tc superconductors (HTS). This has been related to the significant progress in quantitative high-resolution magneto-optical imaging of flux distributions together with the model-independent determination of the corresponding current distributions. We review in this article the magneto-optical imaging technique and experiments on thin films, single crystals, polycrystalline bulk ceramics, tapes and melt-textured HTS materials and analyse systematically the properties determining the spatial distribution and the magnitude of the supercurrents. First of all, the current distribution is determined by the sample geometry. Due to the boundary conditions at the sample borders, the current distribution in samples of arbitrary shape splits up into domains of nearly uniform parallel current flow which are separated by current domain boundaries, where the current streamlines are sharply bent. Qualitatively, the current pattern is described by the Bean model; however, changes due to a spatially dependent electric field distribution which is induced by flux creep or flux flow have to be taken into account. For small magnetic fields, the Meissner phase coexists with pinned vortex phases and the geometry-dependent Meissner screening currents contribute to the observed current patterns. The influence of additional factors on the current domain patterns are systematically analysed: local magnetic field dependence of jc(B), current anisotropy, inhomogeneities and local transport properties of grain boundaries. We then continue to an overview of the current distribution and current-limiting factors of materials, relevant to technical applications like melt-textured samples, coated conductors and tapes. Finally, a selection of magneto-optical experiments which give direct insight into vortex pinning and depinning mechanisms are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/65/5/202/pdf

Magneto-optical studies of current distributions in high-Tc superconductors

Magneto-optical investigations of the flux distributions in high-Tc superconductors are reviewed. The various techniques (which are all based on the Faraday effect) are compared with each other concerning resolution and working range of temperature and external magnetic field. A short description of the historical development of the magneto-optical methods is given and the existing equipment is classified. Various aspects of flux visualization are presented acid special observations made by means of magneto-optical techniques are shown. The capability of the magneto-optical techniques to observe dynamic processes allows observation of flux motion due to thermal activation or even quantum creep, and under the influence of transport currents. It is shown that magneto-optical techniques are a unique tool to show that flux patterns are extremely sensitive to the presence of defects.

https://iopscience.iop.org/article/10.1088/0953-2048/8/4/002/pdf

Magneto-optical investigations of superconductors

Observation of in-plane anisotropy of vortex pinning by inclined columnar defects

Using the high-resolution Faraday technique, domain patterns of flux penetration in heavy-ion-irradiated YBa 2 Cu 3 O 7-δ thin films are obtained. To compare the influence of different projectiles, the samples were irradiated with 25-MeV oxygen ions, 230-MeV nickel ions, and 1-GeV lead ions with various fluences perpendicular to the sample surface and hence parallel to the c axis of the materials. The irradiation with 16 O produces point-defect cascades mainly perpendicular to the path of the projectile whereas the irradiation using 58 Ni ions creates spherical regions of amorphized material along the path

Enhancement of critical current densities by heavy-ion irradiation in YBa2Cu3O7- delta observed using the high-resolution Faraday effect.

Linear defects were introduced in high-temperature superconductors (HTSC{close_quote}s) by high-energy heavy-ion irradiation. Flux penetration into partly crossed and parallel irradiated HTSC{close_quote}s was observed by magneto- optics. The obtained flux distributions show that the critical current density {ital j}{sub {ital c}} in cross-irradiated HTSC{close_quote}s is larger by a factor up to 14 than in parallel irradiated HTSC{close_quote}s. {copyright} {ital 1996 The American Physical Society.}

Direct observation of stronger flux-line pinning of crossed compared to parallel linear defects.

The Hall effect of epitaxial YBa 2 Cu 3 O 7-x (T c ≃90 K) and Bi 2 Sr 2 CaCu 2 O y (T c ≃80 K) films has been investigated. In both compounds the Hall coefficients R H (B∥c axis) in the normal phase is positive and exhibits a strong temperature dependence, which is more pronounced in YBa 2 Cu 3 O 7-x than in Bi 2 Sr 2 CaCu 2 O y . On the basis of a renormalized two-dimensional tight-binding band structure the normal-state Hall coefficient R H has been calculated as a function of doping concentration and temperature using the relaxation-time approximation

Hall effect of epitaxial YBa2Cu3O7-x and Bi2Sr2CaCu2Oy films: Interpretation of the Hall effect on the basis of a renormalized tight-binding model.

We report on the visualization of vortex patterns by means of the high-resolution Bitter-decoration technique in ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathit{x}}$ single crystals containing columnar defects generated via high-energy heavy-ion irradiation. By irradiating only a part of each sample, a simultaneous decoration of irradiated and nonirradiated parts was possible. The columnar defects lead to a complete destruction of translational order, whereas the vortex lattice in the nonirradiated parts exhibits hexagonal ordering. Analyses of the decoration images yield translational correlation lengths of 1.5 to 2 flux spacings in the nonirradiated areas and about 0.5 flux spacings in the irradiated areas.

M. Leghissa

Papers

Observation of in-plane anisotropy of vortex pinning by inclined columnar defects

Enhancement of critical current densities by heavy-ion irradiation in YBa2Cu3O7- delta observed using the high-resolution Faraday effect.

Direct observation of stronger flux-line pinning of crossed compared to parallel linear defects.

Hall effect of epitaxial YBa2Cu3O7-x and Bi2Sr2CaCu2Oy films: Interpretation of the Hall effect on the basis of a renormalized tight-binding model.

Observation of a disordered vortex state in Bi2Sr2CaCu2O8+x single crystals containing columnar defects.