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Showing papers on "High-temperature superconductivity published in 1993"


Journal ArticleDOI
01 May 1993-Nature
TL;DR: In this article, the authors provided support for this conjecture, with the discovery of superconductivity above 130 K in a material containing HgBa2Ca2Cu3O1+x (with three CuO2 layers per unit cell), Hg Ba2CaCu2O6+X (with two O2 layers) and an ordered superstructure comprising a defined sequence of the unit cells of these phases.
Abstract: THE recent discovery1 of superconductivity below a transition temperature (Tc) of 94 K in HgBa2CuO4+δ has extended the repertoire of high-Tc superconductors containing copper oxide planes embedded in suitably structured (layered) materials. Previous experience with similar compounds containing bismuth and thallium instead of mercury suggested that even higher transition temperatures might be achieved in mercury-based compounds with more than one CuO2 layer per unit cell. Here we provide support for this conjecture, with the discovery of superconductivity above 130 K in a material containing HgBa2Ca2Cu3O1+x (with three CuO2 layers per unit cell), HgBa2CaCu2O6+x (with two CuO2 layers) and an ordered superstructure comprising a defined sequence of the unit cells of these phases. Both magnetic and resistivity measurements confirm a maximum transition temperature of ∼ 133 K, distinctly higher than the previous established record value of 125–127 K observed in Tl2Ba2Ca2Cu3O10 (refs 2,3). The discovery in 1986 of the first copper oxide superconductor stimulated an explosion of research activity that continues to the present day. The early years of high-temperature superconductivity were characterized by the rapid discovery of many new materials with increasingly high transition temperatures. The record now stands at ~133 K, attributed to a mercury-containing compound reported by Schilling et al. in 1993, although the dream of achieving room-temperature superconductivity has yet to be fulfilled.

1,378 citations


Journal ArticleDOI
01 Mar 1993-Nature
TL;DR: In this article, the same authors reported the synthesis of the related compound HgBa2CuO4+δ (Hg-1201), with only one CuO2 layer per unit cell, and showed that it is superconducting below 94 K.
Abstract: FOLLOWING the discovery1 of high-transition-temperature (high-Tc) superconductivity in doped La2CuO4, several families of related compounds have been discovered which have layers of CuO2 as the essential requirement for superconductivity: the highest transition temperatures so far have been found for thallium-bearing compounds2. Recently the mercury-bearing compound HgBa2Rcu2O6+δ (Hg-1212) was synthesized3 (where R is a rare-earth element), with a structure similar to the thallium-bearing superconductor TlBa2CaCu2O7 (Tl-1212), which has one T1O layer and two CuO2 layers per unit cell, and a Tc of 85 K (ref. 2). But in spite of its resemblance to Tl-1212, Hg-1212 was found not to be superconducting. Here we report the synthesis of the related compound HgBa2CuO4+δ (Hg-1201), with only one CuO2 layer per unit cell, and show that it is superconducting below 94 K. Its structure is similar to that of Tl-1201 (which has a Tc of < 10 K)4, but its transition temperature is considerably higher. The availability of a material with high Tc but only a single metal oxide (HgO) layer may be important for technological applications, as it seems that a smaller spacing between CuO2 planes leads to better superconducting properties in a magnetic field5.

919 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that there is a strong tendency for dilute holes in an antiferromagnet to phase separate, leading to high-temperature superconductivity.
Abstract: There is a strong tendency for dilute holes in an antiferromagnet to phase separate. (This is a generic feature of doping into a commensurate correlated insulating state.) We review the general and model-specific theoretical arguments that support this conclusion for neutral holes. In the presence of long-range Coulomb interactions, there is frustrated phase separation leading to large-amplitude, low-energy fluctuations in the hole density at intermediate length scales, provided the dielectric constant is sufficiently large. We describe extensive experimental evidence showing that such “clumping” of the holes is an important feature of the cuprate superconductors. We also summarize theoretical results which suggest that frustrated phase separation may account for the anomalous properties of the normal state and give rise to high-temperature superconductivity.

506 citations


Journal ArticleDOI
16 Jul 1993-Science
TL;DR: A quantitative analysis of a recent model of high-temperature superconductors based on an interlayer tunneling mechanism can account well for the observed magnitudes of the high transition temperatures in these materials and implies a gap that does not change sign, can be substantially anisotropic, and has the same symmetry as the crystal.
Abstract: A quantitative analysis of a recent model of high-temperature superconductors based on an interlayer tunneling mechanism is presented. This model can account well for the observed magnitudes of the high transition temperatures in these materials and implies a gap that does not change sign, can be substantially anisotropic, and has the same symmetry as the crystal. The experimental consequences explored so far are consistent with the observations.

384 citations


BookDOI
01 Jan 1993

268 citations


Journal ArticleDOI
05 Feb 1993-Science
TL;DR: A high-temperature superconducting-receiver system for use in nuclear magnetic resonance (NMR) microscopy is described, and it is demonstrated that thermal noise in the receiver coil is the factor that limits resolution.
Abstract: A high-temperature superconducting-receiver system for use in nuclear magnetic resonance (NMR) microscopy is described. The scaling behavior of sources of sample and receiver-coil noise is analyzed, and it is demonstrated that Johnson, or thermal, noise in the receiver coil is the factor that limits resolution. The behavior of superconductors in the environment of an NMR experiment is examined, and a prototypical system for imaging biological specimens is discussed. Preliminary spin-echo images are shown, and the ultimate limits of the signal-to-noise ratio of the probe are investigated.

212 citations


Journal ArticleDOI
TL;DR: In this paper, a mean field type theory is developed for the insulating RVB state and high temperature superconductivity in doped La2CuO4 and other high-Tc oxides.

203 citations


Journal ArticleDOI
TL;DR: In this article, the BaPb1-xBix03 phase has perovskite related structures and superconductivity was observed over the range x ≅ 0.05-0.3.

161 citations


Journal ArticleDOI
TL;DR: SrRuO3 thin films were deposited on (100) LaAlO3 using pulsed laser deposition as discussed by the authors, and the films were oriented normal to the substrate surface with a high degree of inplane orientation with respect to the major axes.
Abstract: SrRuO3 thin films were deposited on (100) LaAlO3 using pulsed laser deposition. The films were (001) oriented normal to the substrate surface with a high degree of in‐plane orientation with respect to the substrate’s major axes. An ion beam minimum yield of 2.5% was obtained for the films, indicating high crystallinity. The films exhibited metallic behavior with a room temperature resistivity of ∼200 mW cm. A kink in the resistivity, corresponding to a ferromagnetic phase transition, was observed at ∼160 K. It was found that SrRuO3 is structurally and chemically compatible with the YaB2Cu3O7−d (YBCO) superconductors. High quality YBCO films were obtained on SrRuO3 LaAlO3. Multilayers of YBCO/SrRuO3 were successfully fabricated.

143 citations


Journal ArticleDOI
TL;DR: The Meissner effect of polycrystalline Bi high-temperature superconductors is studied using a special superconducting-quantum-interference-device magnetometer and the data are consistent with orbital paramagnetic moments due to spontaneous currents.
Abstract: We have studied the low-field Meissner effect of polycrystalline Bi high-temperature superconductors using a special superconducting-quantum-interference-device magnetometer. In certain samples a surprising feature was observed: Instead of the usual diamagnetic moment a paramagnetic moment develops in the field cooling mode below ${\mathit{T}}_{\mathit{c}}$ for fields H1 Oe. The data are consistent with orbital paramagnetic moments due to spontaneous currents. Such currents may originate in so-called \ensuremath{\pi} contacts in the weak-link network of polycrystalline material. In some of these samples also an anomaly in the low-field microwave absorption was observed, which is obviously correlated with the existence of spontaneous currents.

126 citations


Journal ArticleDOI
TL;DR: In this paper, the structure and superconducting properties of the infinite-layer compound A 1− x CuO 2− z (A=Ca 1− y Sr y ) have been investigated by high-resolution electron microscopy as well as magnetization and resistivity measurements.
Abstract: Microstructure and superconducting properties of the infinite-layer compound A 1− x CuO 2− z (A=Ca 1− y Sr y ) have been investigated by high-resolution electron microscopy as well as magnetization and resistivity measurements. The alkaline earth deficient samples always contain defect-layers inserted almost randomly into the parent simple structure, where we suggest that the A cation vacancies are concentrated. High-resolution electron microscopy observations reveal that oxygen deficiency can simultaneously occur within the central CuO 2 sheet of the defect layer for the sake of charge compensation for the A deficiency. p-type superconductivity with a maximum T c of 110 K is realized if the oxygen defects are filled in by application of high oxygen pressure on high-pressure synthesis ( z ∼0). On the other hand, n-type superconductivity also occurs in the same structure when oxygen deficency is increased so that z > x by a heat-treatment in a reducing atmosphere under high pressure. The fundamental relationship between structure and superconductivity is discussed on the basis of the demonstrated structural uniqueness of the title compound.

Journal ArticleDOI
TL;DR: The fluctuations of vortices in Josephson-coupled layered superconductors are shown to have a profound effect on values of the temperature-dependent penetration depth, Ginzburg-Landau parameter, and upper critical field extracted from reversible magnetization data below the critical temperature.
Abstract: The fluctuations of vortices in Josephson-coupled layered superconductors are shown to have a profound effect on values of the temperature-dependent penetration depth, Ginzburg-Landau parameter, and upper critical field extracted from reversible magnetization data below the critical temperature.

Journal ArticleDOI
TL;DR: Sr-Ca-Cu-O samples which exhibited bulk superconductivity and contained phases of layer structures with long-range periodicities of (10.2+3.4m) A (where m=0, 1 and 2) were obtained using a high-pressure technique.
Abstract: Sr-Ca-Cu-O samples which exhibited bulk superconductivity and contained phases of layer structures with long-range periodicities of (10.2+3.4m) A (where m=0, 1 and 2) were obtained using a high-pressure technique. Phases contained in the samples were investigated by electron diffraction, transmission electron microscopy and X-ray powder diffraction. Members with n = 2, 3 and 4 of a homologous series written as “02(n−1)n” were proposed for these new superconducting phases.

Journal ArticleDOI
TL;DR: In this paper, single-grain-boundary junctions in cuprate superconductors were studied and it was shown that they behave as weak links, qualitatively similar to the YBa2Cu3O7−δ superconductor.
Abstract: We have studied single‐grain‐boundary junctions in the neodymium‐, bismuth‐, and thallium‐based cuprate superconductors and find that they behave as weak links, qualitatively similar to the YBa2Cu3O7−δ superconductor. In general, the grain boundary critical current is determined by flux flow for small misorientation angles and by Josephson junctionlike coupling for large angles. The latter is verified by the observation of voltage oscillations with an external magnetic field in superconducting quantum interference devices built using single‐grain‐boundary junctions of these materials. The commonality of behavior of grain boundaries in all of the high temperature cuprate superconductors suggests that the weak link is most likely associated with the structure of the grain boundary and the evidence points increasingly to dislocations, which describe the topology of the boundary.

Journal ArticleDOI
TL;DR: In this article, the authors describe partially established prerequisites of liquid phase epitaxy (LPE) of high-Tc superconductors, so that layer-by-layer growth and thus single-crystalline epitaxial layers of NdBCO could be achieved for the first time.

Journal ArticleDOI
TL;DR: Inelastic neutron scattering yielded the first information on superconductivity-induced frequency shifts for q¬=;0 phonons in YBa 2 Cu 3 O x .
Abstract: Inelastic neutron scattering yielded the first information on superconductivity-induced frequency shifts for q¬=;0 phonons in YBa 2 Cu 3 O x . For branches starting from the Raman-active mode at 340 cm -1 (10.2 THz), the shifts were round to decrease only slowly with increasing momentum transfer (x=7.0) or even exhibit a maximum at finite q (x=6.92) when going along the [100] and [010] directions. They were independent or q in the [001] direction

Journal ArticleDOI
TL;DR: Superconducting fluctuations in strongly anisotropic planar superconductors substantially affect the resistivity above the transition temperature, resulting in a wide temperature range above T(c), the main effect of these fluctuations is to create a virtual gap in the electronic spectrum, causing an increase in resistivity.
Abstract: Superconducting fluctuations in strongly anisotropic planar superconductors substantially affect the resistivity above the transition temperature. In a wide temperature range above T(c), the main effect of these fluctuations is to create a virtual gap in the electronic spectrum, causing an increase in resistivity. As a result the resistivity shows a maximum close to the transition temperature. Closer to the transition temperature the correction to the resistivity becomes negative and grows.as 1/(T - T(c))2, WhiCh is followed by the usual (T - T(c))1/2 law still closer to the transition temperature. This observation may help to understand the unusual behavior of the resistivity in the c direction in high-T(c) cuprates.

Journal ArticleDOI
TL;DR: Taking account of quantum fluctuations, the shape of the melting line is given by a universal function which is different from a simple power law in 1-T/T c and is in excellent agreement with recent experiments on YBa 2 Cu 3 O 7-δ single crystals.
Abstract: In the new high-T c superconductors both thermal as well as quantum fluctuations are large. The latter smear the vortex cores over a distance of the order of the coherence length and thereby strongly affect the melting transition. Taking account of quantum fluctuations, the shape of the melting line is given by a universal function which is different from a simple power law in 1-T/T c and is in excellent agreement with recent experiments on YBa 2 Cu 3 O 7-δ single crystals. Above a crossover field of the order of a few tesla the resulting high-temperature phase is a quantum liquid

Book
01 Mar 1993
TL;DR: In this article, the authors discuss the electrodynamics of granular superconductors, particularly where grain boundaries (either natural or synthetic) act as Josephson weak-links, responsible for residual dissipation and for unwanted dependence of the electromagnetic properties on ambient magnetic fields and on elevated power level.
Abstract: These lectures are concerned with the application of high temperature superconductors to both passive and active high-frequency devices.The central issue addressed is the electrodynamics of granular superconductors, particularly where grain boundaries (either natural or synthetic) act as Josephson weak-links. Grain boundaries are responsible for residual dissipation and for unwanted dependence of the electromagnetic properties on ambient magnetic fields and on elevated power level. Properly controlled, similar weak-links are the key to high sensitivity dc and rf SQUIDS at readily accessible temperatures, and to modulators, mixers and detectors. Such structures may conveniently lead to superconductive electronic devices as well as coherent sources of radiation in the very far infrared.

Journal ArticleDOI
TL;DR: The results of ultrasonic, sonic and infrasonic experiments in high-Tc superconductors (HTSC) are reviewed in this paper, where some other related fields of investigation are also mentioned.
Abstract: The results of ultrasonic, sonic and infrasonic experiments in high-Tc superconductors (HTSC) are reviewed. Some other related fields of investigation are also mentioned.

Journal ArticleDOI
TL;DR: High-frequency measurements of the ceramic sample at room temperature show a loss peak and suggest a relaxation process for the polarization mechanism with characteristic time T=0.5×10 -9 s, which is near the electrical diffusivity time.
Abstract: A study of the dielectric response as a function of frequency (${10}^{2--}$${10}^{6}$ Hz) and temperature (4.2--300 K) in ceramic and c-axis-oriented single-crystal samples of ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ reveals dielectric constants g${10}^{3}$ at low frequencies in both cases but in different temperature regimes. High-frequency (0.2--20 GHz) measurements of the ceramic sample at room temperature show a loss peak and suggest a relaxation process for the polarization mechanism with characteristic time \ensuremath{\tau}=0.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ s, which is near the electrical diffusivity time. For the single crystal the large polarizability results from a thermally activated process with an activation energy of 0.28 eV and an attempt frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ of about ${10}^{9}$ Hz at 300 K. Our results show that the high dielectric constant may be a common feature of the 1:2:3-structure oxide family, and that the previously discovered ordering of the Cu spins at T\ensuremath{\sim}300 K in ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ may be accompanied by near ferroelectric polarizability.

Journal ArticleDOI
12 Mar 1993-Science
TL;DR: This article discusses a 2-day workshop which was held by researchers attempting to find new superconducting materials, including synthesizing compounds which have the CuO[sub 2] planes in different environments, and general guidelines for finding newsuperconductors.
Abstract: This article discusses a 2-day workshop which was held by researchers attempting to find new superconducting materials. Topics discussed including synthesizing compounds which have the CuO[sub 2] planes in different environments, the superconducting properties of the bismuthates, fulleride superconductors, nitride synthesis and properties, molecular beam epitaxy techniques for fabricating oxide structures, etc. General guidelines for finding new superconductors are given as follows. Materials should be multicomponent structures with more than two sites per unit cell, where one or more sites not involved in the conduction band can be used to introduce itinerant charge carriers. Compositions should be near the metal-insulator Mott transition. On the insulating side of the Mott transition, the localized states should have spin-1/2 ground states and antiferromagnetic ordering the parent compound. The conduction band should be formed from antibonding tight-binding states that have a high degree of cation-anion hybridization near the Fermi level. There should be no extended metal-metal bonds. Structural features that are desirable include two-dimensional extended sheets or clusters with controllable linkage, or both.

Journal ArticleDOI
TL;DR: The results of the presented analysis suggest that further femtosecond-spectroscopy measurements may reveal more information about the superconducting anisotropic energy gap and band structure, pairing mechanism, quasiparticle-vortex interactions, and vortex energy structure in high-temperature superconductors.
Abstract: This paper discusses the mechanism of the nonequilibrium optical response of high-temperature superconductors below [ital T][sub [ital c]]. Optical-response studies include pulsed-photoresponse measurements and modulated-reflectivity (transmission) measurements using femtosecond spectroscopy. A model is presented to explain the mechanism of the optical response based on the nonequilibrium dynamic transitions of electrons (quasiparticles and Cooper pairs) and phonons. These nonequilibrium transitions may cause flux motion due to activation by high-energy quasiparticles and phonons in the frame of BCS theory; moreover, these transitions may also change the kinetic inductance due to the reduction in the superconducting-electron density. Relaxation of the high-energy quasiparticles (generated by photons) through the electron-phonon and electron-electron scattering is rather fast: on the order of a picosecond, however, the speed limit of the photoresponse is governed by the phonon escape time. The results of the presented analysis suggest that further femtosecond-spectroscopy measurements may reveal more information about the superconducting anisotropic energy gap and band structure, pairing mechanism, quasiparticle-vortex interactions, and vortex energy structure in high-[ital T][sub [ital c]] superconductors. The results also strongly suggest that with proper optimization of device parameters (geometry and thermodynamic properties for fast heat removal, increasing pinning site density, critical current density, etc.), high speed (onmore » the order of a ps response time), and sensitive detectors covering a broad electromagnetic spectrum (e.g., from ultraviolet to far infrared and beyond) can be developed.« less

Journal ArticleDOI
TL;DR: In this paper, an extended critical state model which includes the effects of bulk critical current density, equilibrium magnetization and surface barrier is developed for the magnetization of superconductors.

BookDOI
01 Apr 1993
TL;DR: In this paper, structural aspects and Cu mixed valence in Bi- and TI-based cuprate superconductors are discussed. But the authors focus on the superconducting properties of the cuprates and other oxides.
Abstract: Structural aspects and Cu mixed valence in Bi- and TI-based cuprate superconductors (B. Raveau) superconductivity in cuprates and other oxides (H.R. Ott) organic superconductors (T. Ishiguro) superconducting granular films (S-I. Kobayashi) breaking the log-jam in many-body physics - fermi surfaces without fermi liquids (P.W. Anderson) Mott transition in the Hubbard model (B.S. Shastry) fundamentals of resonating valence bond (RVB) theory and its applications to high-Tc superconductivity (G. Baskaran) anyons and superconductivity (S. Das Sarma) superconducting pairing in layered superconductors (S.S. Jha) crystal field excitations in high-Tc superconducting materials (A. Furrer) superconductivity in high magnetic fields from a microscopic theory (A.K. Rajagopal) non-equilibrium superconductivity (R. Tidecks) NMR study in highly correlated systems - heavy fermion and high-Tc superconductors (K. Asayama) superconductivity and magnetism in heavy fermion compounds (F. Steglich) transport properties in the mixed state of high temperature superconductors (A. Freimuth) tunnelling spectroscopy of copper oxide superconductors (J. Akimitsu) pulsed laser and cylindrical magnetron sputter deposition of epitaxial metal oxide thin films (T. Venkatesan).

Journal ArticleDOI
TL;DR: In this article, the formation of the liquid phase facilitated the decomposition of BaCO3 and crystallization of the YBCO grains in the BaO-CuO thin film system.
Abstract: Processing atmosphere and precursor effects on liquid phase formation were investigated in the BaO–CuO thin film system. Liquid phase was observed at a significantly lower temperature (∼620 °C) under N2 atmosphere with carboxylate solution precursors. In the processing of the YBCO oxide superconductors, formation of the liquid phase facilitated the decomposition of BaCO3 and crystallization of the YBCO grains. Larger grains and greater (00l) preferred orientation were also observed in the YBCO films prepared with the presence of the liquid phase.

Journal ArticleDOI
TL;DR: In this article, the phase responsible for superconductivity was identified as the 1212 phase with a space group of P4/mmm and lattice constants of a ∼ 38 A and c ∼ 120 A.
Abstract: Bulk superconductivity up to 92 K has been achieved in the mercury-containing curprate (Tl05Hg05)Sr2(Ca1−xYx)Cu2 O7−δ when x=03 Based on X-ray and electron diffraction and electron probe microanalyzer results, we identify the phase responsible for the superconductivity to be similar to that of (Tl05Pb05)Sr2CaCu2O7 (so-called 1212 phase) with a space group of P4/mmm and lattice constants of a ∼ 38 A and c ∼ 120 A Moreover, neither superlattice nor intergrowth along the a∗ and c∗ directions were observed by electron diffraction An increase in Ca2+ doping, 05⩽x⩽03, into the Y3+ sites results in a maximum superconducting transition temperature (Tc) at around 92 K for x=03 For compositions x

Journal ArticleDOI
TL;DR: In this article, a review is given of theories of high-temperature superconductors in which the current is carried by bipolarons, which form a condensed Bose gas below T c and a non-degenerate gas above it.
Abstract: A review is given of theories of high-temperature superconductors in which the current is carried by bipolarons, which form a condensed Bose gas below T c and a non-degenerate gas above it. Such theories were first proposed by Schafroth, Alexandrov, Ranninger and de Jongh; the present author has, for the copper oxide materials, proposed spin bipolarons. Experimental work has, however, shown no magnetic moments in the superconducting and “spin glass” ranges of composition; a modification of the spin bipolaron model is proposed to take account of these observations. Other aspects of the model are discussed, particularly heat conduction and the effect of disorder. A comparison is made with the cubic bismuth materials.

Journal ArticleDOI
TL;DR: The microscopic model presented here reduces to the phenomenological Ginzburg-Landau, Lawrence-Doniach, and anisotropic London models in the appropriate limits, and is used to examine the role of dimensionality and interlayer scattering on the magnetic properties of layered superconductors.
Abstract: We develop a microscopic model of layered superconductors, designed specifically for the high-${\mathit{T}}_{\mathit{c}}$ cuprates, which is valid at all temperatures below the degeneracy temperature and for all relevant length scales. The model is based on the original idea of Bulaevskii, and consists of a stack of two-dimensional conducting planes coupled via interlayer diffusion of charge carriers. The microscopic model presented here reduces to the phenomenological Ginzburg-Landau, Lawrence-Doniach, and anisotropic London models in the appropriate limits. We derive the main equations of the interlayer diffusion model, then use the model to examine the role of dimensionality and interlayer scattering on the magnetic properties of layered superconductors.

Journal ArticleDOI
TL;DR: Monte Carlo simulations of the uniformly frustrated three-dimensional [ital XY] model are carried out, as a model for vortex-line fluctuations in a high-[ital T][sub [ital c]] superconductor in an external magnetic field, finding two sharp phase transitions.
Abstract: We carry out Monte Carlo simulations of the uniformly frustrated three-dimensional XY model, as a model for vortex-line fluctuations in a high-${\mathit{T}}_{\mathit{c}}$ superconductor in an external magnetic field. A density of vortex lines of f=1/25 is considered. We find two sharp phase transitions. The low-T superconducting phase is an ordered vortex-line lattice. The high-T normal phase is a vortex-line liquid, with much entangling, cutting, and loop excitations. An intermediate phase is found, which is characterized as a vortex-line liquid of disentangled, approximately straight, lines. In this phase, the system displays superconducting properties in the direction parallel to the magnetic field, but normal behavior in planes perpendicular to the field. A detailed analysis of the vortex structure function is carried out.