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

Abstract

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 \emph{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$\bar{3}$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$\bar{3}$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 ($\approx$ 50 GPa) of the classical ferroelectric transition pressure at 200K and in a large isotope shift ($\approx$ 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.