Quantum symmetrization transition in superconducting sulfur hydride from quantum Monte Carlo and path integral molecular dynamics

We study the structural phase transition, originally associated with the highest superconducting critical temperature T_c measured in high-pressure sulfur hydride. A quantitative description of its pressure dependence has been elusive for any ab initio theory attempted so far, raising questions on the actual mechanism leading to the maximum of T_c. Here, we estimate the critical pressure of the hydrogen bond symmetrization in the Im \(\bar{3}\) $\overline{3}$ m structure, by combining density functional theory and quantum Monte Carlo simulations for electrons with path integral molecular dynamics for quantum nuclei. We find that the T_c maximum corresponds to pressures where local dipole moments dynamically form on the hydrogen sites, as precursors of the ferroelectric Im \(\bar{3}\) $\overline{3}$ m-R3m transition, happening at lower pressures. For comparison, we also apply the self-consistent harmonic approximation, whose ferroelectric critical pressure lies in between the ferroelectric transition estimated by path integral molecular dynamics and the local dipole formation. Nuclear quantum effects play a major role in a significant reduction (≈50 GPa) of the classical ferroelectric transition pressure at 200 K and in a large isotope shift (≈25 GPa) upon hydrogen-to-deuterium substitution of the local dipole formation pressure, in agreement with the corresponding change in the T_c maximum location.