This review paper illustrates the main normal and superconducting state properties of magnesium diboride, a material known since the early 1950s but only recently discovered to be superconductive at a remarkably high critical temperature Tc = 40 K for a binary compound. What makes MgB2 so special? Its high Tc, simple crystal structure, large coherence lengths, high critical current densities and fields, and transparency of grain boundaries to current promise that MgB2 will be a good material for both large-scale applications and electronic devices. During the last seven months, MgB2 has been fabricated in various forms: bulk, single crystals, thin films, tapes and wires. The largest critical current densities, greater than 10 MA cm−2, and critical fields, 40 T, are achieved for thin films. The anisotropy ratio inferred from upper critical field measurements is yet to be resolved as a wide range of values have been reported, γ = 1.2–9. Also, there is no consensus on the existence of a single anisotropic or double energy gap. One central issue is whether or not MgB2 represents a new class of superconductors, which is the tip of an iceberg awaiting to be discovered. To date MgB2 holds the record for the highest Tc among simple binary compounds. However, the discovery of superconductivity in MgB2 revived the interest in non-oxides and initiated a search for superconductivity in related materialss; several compounds have since been announced to be superconductive: TaB2, BeB2.75, C–S composites, and the elemental B under pressure.

https://iopscience.iop.org/article/10.1088/0953-2048/14/11/201/pdf

Review of the superconducting properties of MgB2

This review paper illustrates the main normal and superconducting state properties of magnesium diboride, a material known since early 1950's, but recently discovered to be superconductive at a remarkably high critical temperature Tc=40K for a binary compound. What makes MgB2 so special? Its high Tc, simple crystal structure, large coherence lengths, high critical current densities and fields, transparency of grain boundaries to current promises that MgB2 will be a good material for both large scale applications and electronic devices. During the last seven month, MgB2 has been fabricated in various forms, bulk, single crystals, thin films, tapes and wires. The largest critical current densities >10MA/cm2 and critical fields 40T are achieved for thin films. The anisotropy ratio inferred from upper critical field measurements is still to be resolved, a wide range of values being reported, between 1.2 and 9. Also there is no consensus about the existence of a single anisotropic or double energy gap. One central issue is whether or not MgB2 represents a new class of superconductors, being the tip of an iceberg who awaits to be discovered. Up to date MgB2 holds the record of the highest Tc in its class. However, the discovery of superconductivity in MgB2 revived the interest in non-oxides and initiated a search for superconductivity in related materials, several compounds being already announced to become superconductive: TaB2, BeB2.75, C-S composites, and the elemental B under pressure.

Review of superconducting properties of MgB2

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

This review focuses on the superconducting properties of MgB2 that are relevant for power applications. The reversible mixed state parameters are the most important, since they define the limiting conditions for loss-free currents: the transition temperature, the upper critical field and the depairing current. They also determine the flux pinning energy, the pinning force and the elastic properties of the flux line lattice and, therefore, strongly influence the critical current densities. The magnetic properties of magnesium diboride are anisotropic and influenced by the two different energy gaps of the σ- and π-bands. Whereas the transition temperature could not be enhanced significantly during the past five years, the upper critical field was considerably increased by impurity scattering or doping. Flux pinning is very weak in MgB2 single crystals and was only improved by irradiation techniques so far. In polycrystalline samples, grain boundary pinning seems to play the dominant role. High critical currents close to the theoretical limit were found in c-axis oriented thin films. The anisotropy of the upper critical field strongly reduces the critical currents in untextured MgB2 at high magnetic fields, where the supercurrents become highly percolative, since not all grains are superconducting anymore. The performance of polycrystalline wires and tapes was significantly improved during the past few years by increasing the upper critical field and by reducing its anisotropy. Pinning seems to be nearly optimized in many forms of this material, but the connectivity between the grains might be further improved.

https://iopscience.iop.org/article/10.1088/0953-2048/20/12/R01/pdf

Magnetic properties and critical currents of MgB2

Fine grained polycrystalline samples of MgB2 superconductor were synthesized from the elements to contain < 5 % of impurity phases, according to x-ray powder diffractometry. The superconductive transition was sharp with a midpoint Tc = 38.5 K. The magnetization in the vortex state was studied as a function of applied field H, temperature T and time t. From the equilibrium magnetization, the London penetration depth was obtained. The supercurrent density J(T,H,t) in the vortex state (derived from the irreversible magnetization) decreases approximately linearly with T, in contrast to the quasi-exponential fall-off in high-Tc superconductors. The current is highly stable in time, with normalized decay rates S = - d ln(J)/d ln(t) well below those in high-Tc materials. These results are compared with those of other superconductors.

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High temporal stability of supercurrents in MgB2 materials

The presence of strong vortex fluctuation effects in two families of layered high-temperature superconductors (${\mathrm{HgBa}}_{2}$${\mathrm{CuO}}_{4+\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{Tl}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10+\mathrm{\ensuremath{\delta}}}$) is established from experimental studies of the equilibrium magnetization in the mixed state using the theory of Bulaevskii et al. Detailed information is obtained within the framework of this theory on the London penetration depth ${\ensuremath{\lambda}}_{\mathit{a}\mathit{b}}$, upper critical field ${\mathit{H}}_{\mathit{c}2}$, and Ginzburg-Landau parameter ${\mathrm{\ensuremath{\kappa}}}_{\mathit{a}\mathit{b}}$ (with magnetic field perpendicular to the copper oxide planes) of these materials.

Vortex fluctuations, magnetic penetration depth, and Hc2 in Hg- and Tl-based high-Tc superconductors.

The upper critical field {ital H}{sub {ital c}2} and other equilibrium properties of a magnetically aligned HgBa{sub 2}Ca{sub 2}Cu{sub 3}O{sub 8+{delta}} superconductor have been investigated. Experimental results for the reversible magnetization, both with {bold H}{parallel}{ital c} and {bold H}{parallel}{ital ab}, are analyzed using the theoretical formalism of Hao {ital et} {ital al}. [Phys. Rev. B 43, 2844 (1991)] for type-II superconductors. Near {ital T}{sub {ital c}}, the slopes {ital dH}{sub {ital c}2}/{ital dT} of the upper critical field are {minus}1.6 T/K and {minus}12.1 T/K for fields parallel and perpendicular to the {ital c} axis, respectively. These correspond to coherence lengths (extrapolated to {ital T}=0) of {xi}{sub {ital a}{ital b}}(0)=15 A and {xi}{sub {ital c}}=1.9 A. This gives a lower bound on the superconductive anisotropy parameter {gamma}=({ital m}{sub {ital c}}/{ital m}{sub {ital a}{ital b}}){sup 1/2}{ge}8.

Equilibrium superconducting properties of grain-aligned HgBa2Ca2Cu3O8+ delta.

Fluctuation analysis in the limit of high magnetic fields was performed on three epitaxial thin films of YBa[sub 2]Cu[sub 3]O[sub 7[minus][delta]] for various oxygen deficiencies [delta][lt]0.3. On the 90-K plateau, the three-dimensional (3D) limit yielded an [ital H][sub [ital c]2]([ital T]) slope of [minus]1.7 T/K for [ital H][parallel][ital c], consistent with previous observations of transport and magnetic properties. Moreover, the 3D scaling showed better convergence than the 2D scaling, which gave relatively low values of [ital H][sub [ital c]2]. In contrast, the transitions were not adequately described by either scaling for [ital T][sub [ital c]] off the 90-K plateau; it is speculated that this is due to an extrinsic broadening of the transitions, possibly due to the lack of a complete percolation path of the ortho-[ital I] phase ([delta]=0).

Upper-critical fields of YBa2Cu3O7- delta epitaxial thin films with variable oxygen deficiency delta.

The equilibrium magnetization was studied in magnetically aligned Hg-based cuprate superconductors with a crystal structure containing one, two, and three adjacent Cu-O layers. The mixed state magnetization was measured with the magnetic field applied perpendicular to the layers, along with low field Meissner effect and normal state susceptibility studies for volume correction factors. The internally consistent analysis is used to identify systematics as the number {open_quote}{open_quote}{ital n}{close_quote}{close_quote} of Cu-O layers increases. The study reveals a linear increase in the slope of upper critical field {minus}{ital dH}{sub {ital c}2}/{ital dT} with {open_quote}{open_quote}{ital n}{close_quote}{close_quote}. Most importantly, we find a nearly constant carrier doping per Cu-O layer. This result is compared with other studies, e.g., Rietveld analysis of neutron diffractometry, and its implications are discussed. {copyright} {ital 1996 The American Physical Society.}

J. G. Ossandon

Papers

High temporal stability of supercurrents in MgB2 materials

Vortex fluctuations, magnetic penetration depth, and Hc2 in Hg- and Tl-based high-Tc superconductors.

Equilibrium superconducting properties of grain-aligned HgBa2Ca2Cu3O8+ delta.

Upper-critical fields of YBa2Cu3O7- delta epitaxial thin films with variable oxygen deficiency delta.

Comparative study of the characteristic length scales and fields of Hg-based high-Tc superconductors.