Pressure and High-Tc Superconductivity in Sulfur Hydrides

The paper discusses fundamentals of record-TC superconductivity discovered under high pressure in sulfur hydride. The rapid increase of TC with pressure in the vicinity of Pcr ≈ 123GPa is interpreted as the fingerprint of a first-order structural transition. Based on the cubic symmetry of the high-TC phase, it is argued that the lower-TC 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 TC are here inapplicable. A modified approach is formulated and shown to provide realistic values for TC and to determine the relative contributions of optical and acoustic branches. The isotope effect (change of TC upon Deuterium for Hydrogen substitution) originates from high frequency phonons and differs in the two phases. The decrease of TC following its maximum in the high-TC 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.