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High-temperature superconductivity in hydrides

Over the past six years (2015-2021), many superconducting hydrides with critical temperatures $T_{C}$ up to 250 K, which are currently record highs, have been discovered. Now we can already say that a special field of superconductivity has developed. This is hydride superconductivity at ultrahigh pressures. For the most part, the properties of superhydrides are well described by the Migdal-Eliashberg theory of strong electron-phonon interaction, especially when anharmonicity of phonons is taken into account. The isotope effect, the effect of the magnetic field (up to 60-70 T) on the critical temperature and critical current in the hydride samples, the dependence of $T_{C}$ on the pressure and degree of doping were investigated. The divergences between the theory and experiment are of interest, especially in the field of phase stability and in the behavior of the upper critical magnetic fields at low temperatures. This article presents a retrospective analysis of data of 2015-2021 and describes promising directions for future research of hydride superconductivity.