Pressure and high-Tc superconductivity in sulfur hydrides

The paper discusses fundamentals of record-T-C superconductivity discovered under high pressure in sulfur hydride. The rapid increase of T-C with pressure in the vicinity of P-cr approximate to 123GPa is interpreted as the fingerprint of a first-order structural transition. Based on the cubic symmetry of the high-T-C phase, it is argued that the lower-T-C phase has a different periodicity, possibly related to an instability with a commensurate structural vector. In addition to the acoustic branches, the phonon spectrum of H3S contains hydrogen modes with much higher frequencies. Because of the complex spectrum, usual methods of calculating T-C are here inapplicable. A modified approach is formulated and shown to provide realistic values for T-C and to determine the relative contributions of optical and acoustic branches. The isotope effect ( change of T-C upon Deuterium for Hydrogen substitution) originates from high frequency phonons and differs in the two phases. The decrease of T-C following its maximum in the high-T-C phase is a sign of intermixing with pairing at hole-like pockets which arise in the energy spectrum of the cubic phase at the structural transition. On-pockets pairing leads to the appearance of a second gap and is remarkable for its non-adiabatic regime: hydrogen mode frequencies are comparable to the Fermi energy.