High-temperature superconductivity in hydrides

Over the past six years (2015–2021), many superconducting hydrides with critical temperatures $T_{\rm c}$ up to $+15^{\circ }$C, which are currently record high, have been discovered. Now, we can already say that a special field of superconductivity has developed: 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 interactions, especially when the anharmonicity of phonons is taken into account. We investigate the isotope effect, the effect of a magnetic field (up to 60–70 T) on the critical temperature and critical current in the hydride samples, and the dependence of $T_{\rm c}$ on the pressure and the degree of doping. The divergences between the theory and experiment are of interest, especially in the regions of phase stability and in the behavior of the upper critical magnetic fields at low temperatures. We present a retrospective analysis of data from 2015–2021 and describe promising directions for future research on hydride superconductivity.