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

Quasiclassic Usadel equations for two-band superconductors in the dirty limit are derived with the account of both intraband and interband scattering by nonmagnetic impurities. From these equations, the Ginzburg-Landau equations, and the equations for the critical temperature ${T}_{c}$ and the upper critical field ${H}_{c2}$ are obtained. The equation for ${H}_{c2}$ determines both the temperature dependence of ${H}_{c2}(T)$ and the orientational dependence of ${H}_{c2}(\ensuremath{\theta})$ as a function of the angle $\ensuremath{\theta}$ between $\mathbf{H}$ and the c axis. It is shown that the shape of the ${H}_{c2}(T)$ curve essentially depends on the ratio of the intraband electron diffusivities ${D}_{1}$ and ${D}_{2},$ and can be very different from the one-gap dirty-limit theory. In particular, value ${H}_{c2}(0)$ can considerably exceed ${0.7T}_{c}{\mathrm{dH}}_{c2}{/dT}_{c},$ which can have important consequences for applications of ${\mathrm{MgB}}_{2}.$ Based on a general equation for ${H}_{c2}(T,\ensuremath{\theta}),$ a scaling relation, which enables one to get the angular dependence of ${H}_{c2}(\ensuremath{\theta})$ from the equation for ${H}_{c2}$ at $\mathbf{H}\ensuremath{\Vert}c,$ is proposed. The behavior of ${H}_{c2}(\ensuremath{\theta})$ and ${H}_{c1}(\ensuremath{\theta})$ can deviate markedly from the results of the anisotropic Ginzburg-Landau theory, and the ratio of the upper critical field ${H}_{c2}^{\ensuremath{\Vert}}{/H}_{c2}^{\ensuremath{\perp}}$ for $\mathbf{H}\ensuremath{\Vert}\mathrm{ab}$ and $\mathbf{H}\ensuremath{\perp}\mathrm{ab}$ can both increase and decrease with temperature, depending on the relation between ${D}_{1}$ and ${D}_{2}.$ Implications of the obtained results for ${\mathrm{MgB}}_{2}$ are discussed.

https://arxiv.org/pdf/cond-mat/0212129.pdf

Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors

Abstract We report specific-heat measurements on two samples of Mg 11 B 2 , one powder and one sintered, that give essentially identical results. Both samples are of exceptionally high quality: At the critical temperature the discontinuity in specific heat is higher than that of other samples, the transition is sharper than for most samples, and the signature feature of the small, non-BCS energy gap is particularly pronounced. The results are compared with a phenomenological model for a multi-gap superconductor, with band-structure calculations, and with spectroscopic determinations of the energy gaps.

Specific heat of Mg11B2

This review focuses on the most important features of the 40 K superconductor MgB2—the weakly interacting multiple bands (the σ and π bands) and the distinct multiple superconducting energy gaps (the σ and π gaps). Even though the pairing mechanism of superconductor MgB2 is the conventional electron–phonon coupling, the prominent influence of the two bands and two gaps on its properties sets it apart from other superconductors. It leads to markedly different behaviors in upper critical field, vortex structure, magnetoresistance and many other superconducting and normal-state properties in MgB2 from single-band superconductors. Further, it gives rise to new physics that does not exist in single-band superconductors, such as the internal Josephson effects between the two order parameters. These unique phenomena depend sensitively on scattering inside and between the two bands, and the intraband and interband scattering can be modified by chemical substitution and irradiation. MgB2 has brought unprecedented attention to two-band superconductivity, which has been found to exist in other old and new superconductors. The legacy of MgB2 will be long lasting because of this, as well as the lessons it teaches in terms of the search for new phonon-mediated higher Tc superconductors.

https://iopscience.iop.org/article/10.1088/0034-4885/71/11/116501/pdf

Two-band superconductor magnesium diboride

We present new upper critical field ${H}_{c2}(T)$ data in a broad temperature region $0.3\mathrm{K}\ensuremath{\le}T\ensuremath{\le}{T}_{c}$ for ${\mathrm{LuNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ and ${\mathrm{YNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ single crystals with well characterized low impurity scattering rates. The absolute values for all $T$, in particular, ${H}_{c2}(0)$, and the sizable positive curvature (PC) of ${H}_{c2}(T)$ at high and intermediate $T$ are explained quantitatively within an effective two-band model. The failure of the isotropic single-band approach is discussed in detail. Supported by de Haas--van Alphen data, the superconductivity reveals direct insight into details of the electronic structure. The observed maximal PC near ${T}_{c}$ gives strong evidence for clean limit type-II superconductors.

https://arxiv.org/pdf/cond-mat/9712174.pdf

Upper Critical Field Peculiarities of Superconducting YNi 2 B 2 C and LuNi 2 B 2 C

Magnetic phase diagram and superconductivity in the (Er x Tb 1− x )Ni 2 B 2 C system were studied by measurements of resistivity and susceptibility as a function of temperature and magnetic field. In the range 0.45≤ x ≤0.75, antiferromagnetic transition temperature T N exhibits an anomalous minimum. The suppression of superconductivity in the (Er x Tb 1− x )Ni 2 B 2 C system can be explained using the AG pair breaking theory. The possible reason for the absence of superconductivity in TbNi 2 B 2 C is discussed.

Superconductivity and magnetism in the pseudo-quaternary system (ErxTb1−x)Ni2B2C

Detailed measurements of the resistivity ρ ab as a function of temperature, magnetic field and orientation have been carried out on single crystals of tetragonal bodycentered DyNi 2 B 2 C. From the angular dependence of the metamagnetic transitions a magnetic phase diagram has been obtained. For B||[1 0 0] , an anomalously large hysteresis effect of the metamagnetic and also of the superconducting transitions were observed in the low temperature range ( T 2 B 2 C.

Superconductivity and the magnetic phase diagram of dyni2b2c at very low temperatures

Detailed measurements of the resistivity ρ ab as a function of temperature, magnetic field and orientation have been carried out on DyNi2B2C single crystals. From the angular dependence of the metamagnetic transitions a phase diagram with five metamagnetic phases have been obtained. For B‖[100], anomalously large hysteresis effects of the metamagnetic transitions and also of the superconducting transitions were observed at low temperature (T<2 K). The large hysteresis leads to a reentrant behavior of the superconductivity in small external fields. The reentrant behavior and the large hysteresis indicate a strong interplay between magnetism and superconductivity in DyNi2B2C.

Magnetic phase diagram and reentrant superconductivity in DyNi 2 B 2 C

The Fermi surface of PrNi5 has been studied by the measurements of the de Haas-van Alphen (dHvA) effect at temperatures between 0.3 and  in magnetic fields up to 12 T. Two dHvA frequencies have been obtained. The electronic structure of PrNi5 was calculated using the full potential linearized augmented plane wave method. Five sheets of the Fermi surface and the multiple extremal cross sections were determined. First and second sheet have a hole-like structure. The agreement between theory and experiment is obtained by a small downward shift ( 0.1 eV) of the Fermi energy which is probably due to an underestimation of the role of 4f electrons.

https://link.springer.com/content/pdf/10.1007/s100510070006

de Haas-van Alphen effect and the Fermi surface of PrNi5

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