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

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 topical review summarizes various features of magnetic penetration depth in unconventional superconductors. Precise measurements of the penetration depth as a function of temperature, magnetic field and crystal orientation can provide detailed information about the pairing state. Examples are given of unconventional pairing in hole- and electron-doped cuprates, organic and heavy fermion superconductors. The ability to apply an external magnetic field adds a new dimension to measurements of penetration depth. We discuss how field-dependent measurements can be used to study surface Andreev bound states, nonlinear Meissner effects, magnetic impurities, magnetic ordering, proximity effects and vortex motion. We also discuss how measurements of penetration depth as a function of orientation can be used to explore superconductors with more than one gap and with anisotropic gaps. Details relevant to the analysis of penetration depth data in anisotropic samples are also discussed.

https://iopscience.iop.org/article/10.1088/0953-2048/19/8/R01/pdf

Magnetic penetration depth in unconventional superconductors

The temperature dependence of the London penetration depth, $\ensuremath{\lambda}(T)$, was measured in both single crystal and polycrystalline ${\mathrm{MgB}}_{2}$ samples by a high-resolution, radio frequency technique. A clear exponential temperature dependence of $\ensuremath{\lambda}(T)$ was observed at low temperature, indicating $s$-wave pairing. A BCS fit to the lowest temperature data gives an in-plane energy gap $\ensuremath{\Delta}$ of $30\ifmmode\pm\else\textpm\fi{}2\mathrm{K}$ $(2\ensuremath{\Delta}{/T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.5\ifmmode\pm\else\textpm\fi{}0.1)$, which is significantly smaller than the standard BCS weak coupling value of 3.5. We find that the data are best described by a two-gap model.

Exponential temperature dependence of the penetration depth in single crystal 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

S. Lee

Papers

Exponential temperature dependence of the penetration depth in single crystal MgB2.

de Haas–van Alphen effect in single crystal MgB2