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Imaging local magnetic fields produced by nano- and micrometer-scale superconductors has become a vital tool that can not only reveal crucial information on the vortex dynamics and order parameters of the superconducting materials but also visualize the working mechanism of superconducting devices made for quantum information. Here, we performed measurements of the magnetic field distributions of mesoscopic superconducting structures with various geometries by combining a thin ferromagnetic metal layer as a magneto-optical sensing element that responds to the environmental magnetic fields and a custom-made sensitive Sagnac interferometer. The sensitivity of the technique enables the observation of magnetic flux jumps due to individual vortex entries into nanostructured superconductors. In addition, with the control of incident power at a focused laser spot, we induce thermally driven movement of vortices that leaves a trace of a microscopic optical heating pattern. [ABSTRACT FROM AUTHOR]

Under the spell of BCS-electron–phonon theory [M. Tinkham, Introduction to Superconductivity, 2nd ed. (McGraw Hill, New York, 1996)], during the last 6 years experimentalists have purportedly discovered a plethora of high temperature conventional superconductors among pressurized hydrides [Pickard et al., Ann. Rev. Condens. Matter Phys. 11, 57 (2020) and R. F. Service, Science 373, 954 (2021)], and theorists have been busy predicting and explaining those findings [Lv et al., Matter Radiat. Extremes 5, 068101 (2020); Flores-Livas et al., Phys. Rep. 856, 1 (2020); and Boeri et al., J. Phys. Condens. Matter. (to be published)]. The alternative theory of hole superconductivity (see https://jorge.physics.ucsd.edu/hole.html for a list of references) predicts instead that no superconductivity can exist in these materials. In this Tutorial, I will first argue that, unclouded by the prejudice of BCS's validity, the existing experimental evidence for superconductivity in pressurized hydrides does not withstand scrutiny. Once it is established that superconductivity in pressurized hydrides is a myth and not a reality, the claim to validity of BCS-electron–phonon theory as a descriptor of superconductivity of real materials will be forever shattered, and an alternative theory will become imperative. I will explain the fundamentals of the theory of hole superconductivity, developed over the past 32 years [see https://jorge.physics.ucsd.edu/hole.html and J. E. Hirsch, Phys. Lett. A 134, 451 (1989)], and why it is compelling. Crucially, it explains the Meissner effect, that I argue the conventional theory does not. It applies to all superconducting materials and provides guidelines in the search for high temperature superconductors that are very different from those provided by BCS-electron–phonon theory. Light elements are predicted to be irrelevant to warm superconductivity because according to this theory the electron–phonon interaction plays no role in superconductivity. [ABSTRACT FROM AUTHOR]