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Quantum materials are defined by the emergence of new properties resulting from collective quantum effects and by holding promise for their quantum applications. Novel superconductors, from high-Tc cuprates and iron-based superconductors to twisted monolayers, exhibit a higher level of emergent complexity, with a multiband electronic structure playing a pivotal role in their comprehension and potential applications. Here, we provide a brief overview of key multiband effects in these superconductors and topological semimetals, offering guidelines for the theory-assisted development of new quantum materials and devices.

This review article summarizes recent progress in low-temperature properties of binary molybdenum-based alloys and intermetallic compounds, focusing mainly on superconductivity characteristics reflecting novel physics as well as possible applications. We present experimental data proving the two-band/two-gap nature of some superconducting compounds. As argued, the binary Mo–Re alloys with rhenium predominance represent an ideal and rare test system where related compounds with different Re/Mo ratios can be either centrosymmetrical or noncentrosymmetrical, leading in the latter case to possible mixed superconducting pairing. It is demonstrated that two MoC phases, namely, α-MoC and γ-MoC phases, are topologically nontrivial in their bulk and surface band structures, while amorphous MoSi and MoGe superconductors are among highly-promising materials for different superconductivity applications. We conclude the review with a brief discussion of new tendencies in computer modelling of the structure and properties of binary compounds, using as an example recently discovered stoichiometric MoBi2 compound, and practical prospects for already known and studied molybdenum-based superconductors.

The Josephson effect, as an example of a macroscopic quantum phenomenon, reveals itself in the three-layer heterostructures formed by two superconductors coupled by a weak link that usually consists of a 1–2 nm-thick insulating barrier. The traditional way of modelling such-systems’ dynamics is based on an equivalent circuit that comprises three parallel elements: a pure superconducting element with a certain supercurrent-versus-Josephson phase difference dependence, a resistor R, and a capacitor C. In this short review, we analyse the practical problem of reducing the junction capacitance while maintaining or slightly impairing other characteristics. Some arguments are presented to explain why the capacitance should be suppressed and how it will affect performance of superconducting quantum interference devices (SQUIDs) and digital electronics circuits. As a solution for low-capacitance junctions, we propose a weak link made of an amorphous-silicon interlayer doped with nanoscale metallic drops between the two superconducting Mo–Re-alloy electrodes.

The electronic structure of FeSe—the simplest iron-based superconductor (Fe-SC)—conceals a potential of abrupt increase of superconducting tran-sition temperature realized under the pressure or in a single-layer film. This is also a system where the appearing of a spontaneous electronic anisotropy known as the nematicity is formed far above the superconducting transition and is not accompanied with a magnetic ordering. The given review deals with the determining electronic structure of these compounds, its evolution with temperature, pressure, doping, and other impacts, which cause such key phenomena in Fe-SC as nematicity and high-temperature superconductivity.

The discovery of high-temperature superconductors (HTS) has led to understanding that, in order to explain and utilize the phenomenon, completely new physical approaches should be introduced at all scales: microscopic, mesoscopic, macroscopic. Leaving first two scales beyond the scope of the present paper, we focus in the upper limit of the last scale, the study of the magnetic flux dynamics in HTS bulks — the dynamics of the ‘compact vortex structures’. A new direction in the experimental superconducting physics, the investigation of HTS bulks with levitation techniques, which has been elaborated during last years to effectively explore the subject, as well as the new fundamental and applied results obtained there from are overviewed here.

A characteristic general feature of electronic structure of the iron-based superconductors is the strong renormalization of a quasi-particle spectrum, which is associated with strong electron-electron interaction, the components of which remain controversial. We are performed a detailed comparative analysis of the photoemission spectra of iron-based superconductors (FeSe and BKFA) and superconducting cuprates (Bi-2201). The constants of the high-energy and low-energy parts of the self-energy, which determine the renormalization in cuprates and iron-based superconductors, are separated, and the essential role of the electron-phonon interaction in the latter ones is proved. [ABSTRACT FROM AUTHOR]