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.

Superconductivity at 94 K in HgBa 2 Cu0 4+δ

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

Since the first days of high-Tc superconductivity, the materials science and the physics of grain boundaries in superconducting compounds have developed into fascinating fields of research. Unique electronic properties, different from those of the grain boundaries in conventional metallic superconductors, have made grain boundaries formed by high-Tc cuprates important tools for basic science. They are moreover a key issue for electronic and large-scale applications of high-Tc superconductivity. The aim of this review is to give a summary of this broad and dynamic field. Starting with an introduction to grain boundaries and a discussion of the techniques established to prepare them individually and in a well-defined manner, the authors present their structure and transport properties. These provide the basis for a survey of the theoretical models developed to describe grain-boundary behavior. Following these discussions, the enormous impact of grain boundaries on fundamental studies is reviewed, as well as high-power and electronic device applications.

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Grain boundaries in high- T c superconductors

The structure of vortices within an infinite stack of thin superconducting layers is considered and examined in detail in the limit of zero interlayer Josephson coupling The basic building block for the description of three-dimensional (3D) vortex lines is shown to be the 2D pancake vortex, which is a vortex located in only one of the layers; the other layers contain no vortices, but have an important effect in screening the magnetic field generated by currents in the first layer It is shown that 3D vortex lines can be built up by superposing the contributions of stacks of 2D pancake vortices Thermal excitation is shown to break up a single 3D vortex line at a temperature corresponding to the Kosterlitz-Thouless temperature of a single superconducting layer The effect of thermally induced decoupling of the 2D vortex solids in different layers, corresponding to melting only in the direction perpendicular to the layers, is also considered It is shown that Josephson coupling can be neglected in the high-temperature superconductors only under very stringent conditions Although these conditions evidently are not met in ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ and ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{1}$${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8}$, they should be satisfied in superconducting-insulating multilayer systems, such as ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$/${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$

Two-dimensional vortices in a stack of thin superconducting films: A model for high-temperature superconducting multilayers

For H‖c-axis, the magnetic field induced broadening of the resistive transitions of high-Tc superconductors (HTS) is shown to depend strongly on the Cu-O layer spacing. For the highly anisotropic HTS, we show experimental evidence that flux motion results from a thermally activated crossover from three dimensional (3D) vortex lines to 2D independent pancake-like vortices in the Cu-O layers, which is intrinsic to the material and occurs when kBT exceeds the Josephson coupling energy of these layers. At low temperatures, however, thermally activated conventional depinning (which can be sample dependent) or melting in the uncoupled 2D Cu-O layers is also required for flux motion. For YBa2Cu3O7, this dimensional crossover does not occur belowHc2, presumably because the conducting Cu-O chains short-circuit the Josephson interlayer coupling, leading to better superconducting properties in a magnetic field. These results show that strong interlayer coupling is a key to finding good alternatives.

Effect of cu-o layer spacing on the magnetic field induced resistive broadening of high-temperature superconductors

Measurements on epitaxial ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ thin films show that the Hall voltage just below the superconducting transition temperature has sign opposite to the Hall voltage in the normal state. This can result either from quasiparticle effects, or from unusual vortex motion. Because we observe a similar effect in Nb thin films, we argue that vortex motion is responsible. A simple interpretation of the Hall effect then requires that the vortex velocity have a component antiparallel to the transport current. This motion, while contrary to existing flux flow models, could result from vortex motion damping similar to that expected in superfluid $^{4}\mathrm{He}$.

Anomalous Hall effect in superconductors near their critical temperatures.

An unusual loss mechanism has been commonly observed in the high-temperature superconductors in a magnetic field near the zero-field transition temperature {ital T}{sub {ital c}}. The resistive transitions associated with this loss in highly {ital c}-axis-oriented Tl{sub 2}Ba{sub 2}CaCu{sub 2}O{sub {ital x}} thin films are presented as a function of field perpendicular to the {ital c} axis, for the current {ital both} {ital perpendicular} {ital and} {ital parallel} {ital to} {ital the} {ital field}. The data for these orientations are essentially the same over a span of 5 orders of magnitude below the normal-state resistance. Since the {ital macroscopic} Lorentz force is zero for the current parallel to the magnetic field, it can play, at most, a significantly reduced role in this loss mechanism, and our results seriously question any explanation of these losses based on magnetic flux motion.

Lorentz-force independence of resistance tails for high-temperature superconductors in magnetic fields near Tc.

Electrical transport properties of {ital c}-axis-oriented Tl{sub 2}Ba{sub 2}CaCu{sub 2}O{sub 8} thin films have been examined within the context of the Kosterlitz-Thouless (KT) model. The nonlinear current versus voltage and resistivity versus magnetic field characteristics below the KT transition temperature ({ital T}{sub {ital c}}=99.0 K), together with the exponential inverse-square-root temperature dependence of the resistivity just above {ital T}{sub {ital c}}, were consistent with each other and with the theory. The parametrization of the resistivity data well above the transition by Aslamazov-Larkin theory was also consistent with that of the KT theory.

Kosterlitz-Thouless transition in Tl2Ba2CaCu2O8 thin films.

Measurements of the in-plane fluctuation-enhanced conductivity of /ital c/-axis oriented Tl-Ba-Ca-Cu-O thin films have been performed over the temperature range /ital T//sub /ital c// to 240 K. The results were consistent with two-dimensional fluctuation theory and with a linear dependence of the normal resistivity on temperature down to (/ital T//minus//ital T//sub /ital c//)/T/sub c/approx.0.03. A crossover to three-dimensional fluctuations close to /ital T//sub /ital c// was not found. The width of the superconducting transition appears to be a measure of a distance over which layers fluctuate in a correlated manner.

Joonhee Kang

Papers

Effect of cu-o layer spacing on the magnetic field induced resistive broadening of high-temperature superconductors

Anomalous Hall effect in superconductors near their critical temperatures.

Lorentz-force independence of resistance tails for high-temperature superconductors in magnetic fields near Tc.

Kosterlitz-Thouless transition in Tl2Ba2CaCu2O8 thin films.

Fluctuation conductivity of Tl-Ba-Ca-Cu-O thin films