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

Angle-resolved photoemission spectroscopy (ARPES) has emerged as a leading experimental probe for studying the complex phenomena in quantum materials, a subject of increasing importance The power of this technique stems from the directness and the richness of the momentum-resolved information it can provide, such as band dispersion, Fermi surface topology, and electron self-energy Over the past decade, the significantly improved energy and momentum resolution and carefully matched experiments have turned this technique into a sophisticated tool in characterizing the electronic structure of complex materials This revolution is mostly evident in the study of cuprate high-temperature superconductors More recently, this technique has played a critical role in advancing our understanding of the newly discovered iron-based superconductors and topological insulators In this paper we review some of the recent ARPES results and discuss the future perspective in this rapidly developing field

Angle-Resolved Photoemission Studies of Quantum Materials

We review the current situation in the theory of superconducting and transport properties of MgB 2 . First principle calculations of the electronic structure and electron–phonon coupling are discussed and compared with the experiment. We also present a brief description of the multiband effects in superconductivity and transport, and how these manifest themselves in MgB 2 .

ELECTRONIC STRUCTURE, ELECTRON-PHONON COUPLING, AND MULTIBAND EFFECTS IN MgB2

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

The low temperature behaviour of the magnetic penetration depth λ(T) provides a useful probe of the low lying excitations in superconductors and hence of the anisotropy of the superconducting energy gap. In this paper, we will present measurements of the penetration depth in the Meissner state of both single crystal and polycrystalline samples of MgB2, using a very low field RF technique. λ(T) shows a clear exponential temperature dependence T/Tc≲0.2, strongly indicating that this material is fully gapped. Detailed fits to the superfluid density over the full temperature range of our measurements (1>T/Tc>0.04) gives strong support for the existence of two distinct superconducting gaps, Δs=29 K and Δb=75 K, in agreement with recent theoretical predictions and other probes.

Magnetic penetration depth of MgB2

We report observations of quantum oscillations in single crystals of the high temperature superconductor ${\mathrm{MgB}}_{2}$. Three de Haas\char21{}van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these come from a single warped Fermi surface tube along the $c$ direction, and that the third arises from cylindrical sections of an in-plane honeycomb network. The measured values of the effective mass range from $(0.44\char21{}0.68){m}_{e}$. By comparing these to calculated band masses, we find that the electron-phonon coupling strength $\ensuremath{\lambda}$ is a factor of $\ensuremath{\sim}3$ larger for the $c$-axis tube orbits than for the in-plane network orbit, in accord with recent microscopic calculations.

https://arxiv.org/pdf/cond-mat/0112392.pdf

de Haas–van Alphen effect in single crystal MgB2

We report measurements of the de Haas-van Alphen (dHvA) effect for single crystals of MgB 2 , in magnetic fields up to 32 T. In contrast to our earlier work, dHvA orbits from all four sheets of the Fermi surface were detected. Our results are in good overall agreement with calculations of the electronic structure and the electron-phonon mass enhancements of the various orbits, but there are some small quantitative discrepancies. In particular, systematic differences in the relative volumes of the Fermi-surface sheets and the magnitudes of the electron-phonon coupling constants could be large enough to affect detailed calculations of T c and other superconducting properties.

Determination of the Fermi surface of MgB2 by the de Haas-van Alphen effect.

In this paper we review and expand our previous report concerning the observation of de Haas–van Alphen (dHvA) oscillations in single crystals of the high temperature superconductor MgB 2 . The analysis of these oscillations provides an important and precise check of band-structure calculations, as well as a measure of the many body electron–phonon interactions, which enhance the quasi-particle effective masses and give rise to superconductivity. Orbits are observed on both the σ and π bands, with dHvA frequencies in good agreement with recent calculations. By comparing the measured quasi-particle effective masses with band masses calculated recently by three groups, we find that the electron–phonon coupling strength λ is a factor ∼3 larger on the 2D σ orbits than on the 3D π orbits, in accord with recent microscopic calculations. We are therefore able to verify two of the key ingredients in the two-gap model of superconductivity in this compound, namely the Fermi surface topology and the disparity in the electron–phonon coupling for the σ and π bands.

E. A. Yelland

Papers

de Haas–van Alphen effect in single crystal MgB2

Determination of the Fermi surface of MgB2 by the de Haas-van Alphen effect.

de Haas–van Alphen effect in MgB2 crystals