Abstract
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.
Highlights
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
The function α2(ω)F(ω) is a well-known quantity determining the strength of the electron-phonon interaction, F(ω) is the phonon density of states, Z ≃ 1+λin (1) stands for the band mass renormalization
Summary
Our approach is to separate the phonon spectrum in the two regions of the optical and acoustic phonons and for each of them to introduce their respective average frequencies ω opt and ω ac and the coupling constants λopt and λac. According to[6,13], we estimate λopt ≈ 1.5 and λac ≈ 0.5; these values consistent with the above approximations Using these coupling constants and taking for ω opt and ω ac the values ω opt ≈ 1700 K and ω ac ≈ 450 K (μ* ≈ 0.14 which is close to that for usual superconductors and was calculated in11), we obtain TC0 ≈ 170 K and ∆TCac ≈ 45 K , so that in total TC ≈ 215 K, in quite good agreement with TC ≈ 203 K observed in[4]. This interpretation is in contrast with the scenario[17] of the pockets developing via the Lifshitz 2.5- topological transition as in that case the pockets sizes would grow with pressure
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