Conventional/unconventional superconductivity in high-pressure hydrides and beyond: insights from theory and perspectives

The observation of a superconducting critical temperature Tc exceeding 200K in ultra-dense hydrogen sulfide has demonstrated that high-Tc superconductivity can be achieved also in compounds where the superconducting pairing is mediated by phonons. This poses interesting challenges and opportunities. In particular, in this paper, we present a theoretical overview of the following points: Density functional theory has been quite effective in predicting various structures and this was the first time that theory has been successful in predicting novel superconductors. Along this line, we use DFT and many body theory to discuss possible strategies to search for new high-Tc superconductors in light-element compounds at high pressures [20, 34, 36, 37, 43]. The microscopic key elements for high Tc seem to be a high phonon frequency, a peak in the density of states, a large el-ph coupling due to strong bonds, and the avoidance of lattice instabilities for very large couplings. The first two points lead to an appreciable Migdal parameter and to the possibility that non-adiabatic effects may require the generalization of the standard Migdal-Eliashberg theory of superconductivity [32, 33, 45]. In this perspective, it would be important to locate these materials in the Uemura diagram and to measure isotope effect for Tc but also for the effective electron mass and the magnetic susceptibility [31], where the standard ME theory would give zero effect. The possibility of going beyond ME theory adds a new dimension also in the perspective of exporting these concepts to other materials at ambient or low pressure. For example, carbon compounds have a phonon frequency similar to the hydrides and the coupling can also be strong. This points to a search towards fullerene, graphene, or doped graphane. In these materials, especially fullerene, the Fermi energy is very small and the system is certainly in the non-adiabatic regime