We study the structural and vibrational properties of the high-temperature superconducting sulfur trihydride and trideuteride in the high-pressure $Im\overline{3}m$ and $R3m$ phases by first-principles density-functional-theory calculations. On lowering pressure, the rhombohedral transition $Im\overline{3}m\to R3m$ is expected, with hydrogen-bond desymmetrization and occurrence of trigonal lattice distortion. With both Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, in hydrostatic conditions we find that, contrary to what is suggested in some recent experiments, if the rhombohedral distortion exists it affects mainly the hydrogen bonds, whereas the resulting cell distortion is minimal. We estimate that the occurrence of a stress anisotropy of approximately $10\%$ could explain this discrepancy. Assuming hydrostatic conditions, we calculate the critical pressure at which the rhombohedral transition occurs. Quantum and anharmonic effects, which are relevant in this system, are included at nonperturbative level with the stochastic self-consistent harmonic approximation. Within this approach, we determine the transition pressure by calculating the free-energy Hessian, a method that allows to estimate the critical pressure with much higher precision (and much lower computational cost) compared with the free-energy “finite-difference” approach previously used. Using PBE and BLYP, we find that quantum anharmonic effects are responsible for a strong reduction of the critical pressure with respect to the one obtained with the classical harmonic approach. Interestingly, for the two functionals, even if the transition pressures at classical harmonic level differ by 83 GPa, the transition pressures including quantum anharmonic effects differ only by 23 GPa. Moreover, we observe a prominent isotope effect, as we estimate higher transition pressure for ${\mathrm{D}}_3\mathrm{S}$ than for ${\mathrm{H}}_3\mathrm{S}$. Finally, within the stochastic self-consistent harmonic approximation, with PBE we calculate the anharmonic phonon spectral functions in the $Im\overline{3}m$ phase. The strong anharmonicity of the system is confirmed by the occurrence of very large anharmonic broadenings leading to complex non-Lorentzian line shapes. Generally, for the high-energy hydrogen bond-stretching modes, the anharmonic phonon broadening is of the same magnitude of the electron-phonon one. However, for the vibrational spectra at zone center, accessible, e.g., by infrared spectroscopy, the broadenings are very small (linewidth at most around 2 meV) and anharmonic phonon quasiparticles are well defined.

• Received 22 February 2018
• Revised 11 May 2018

DOI:https://doi.org/10.1103/PhysRevB.97.214101