Ferroelectric quantum critical point in superconducting hydrides: The case of H$_3$S

TL;DR

This study maps the phase diagram of H$_3$S under high pressure, revealing a ferroelectric quantum critical point that influences its superconducting properties and critical temperature.

Contribution

It provides the first detailed phase diagram including quantum effects, identifying a ferroelectric quantum critical point in H$_3$S and analyzing its impact on superconductivity.

Findings

Quantum critical point at ~134 GPa identified

Superconducting T_c peak occurs above the ferroelectric QCP

Critical behavior belongs to the 4D Ising universality class

Abstract

H$_3$S sulfur hydride has been widely investigated for its high superconducting critical temperature $T_c$ of 203 K at about $p_c = 155$ GPa. Despite being the precursor of superconducting hydrides, a detailed picture of its phase diagram in an extended temperature and pressure range is still missing. To determine it with inclusion of both thermal and quantum effects, we carry out path integral molecular dynamics combined to a MACE neural network potential trained on BLYP density functional theory configurations. The resulting H$_3$S phase diagram is characterized by the ferroelectric transition between the Im$\bar{3}$m and R3m phases, which originates from a quantum critical point (QCP) located at $p_\mathrm{QCP} \approx 134$ GPa. We show that the experimental $T_c$ peak falls into a paraelectric region of large nuclear quantum fluctuations above the ferroelectric QCP, as measured by local phonon Green's functions resolved in imaginary time, where fluctuating dipole moments are at play. We study the critical behavior of the system in the proximity of the QCP by a finite-size scaling analysis, showing that it belongs to the 4D Ising universality class. We finally discuss its implications for the superconducting state.