Quantum Shift Unlocks Secrets of 203 Kelvin Superconductor Material

Scientists are increasingly focused on understanding the high-temperature superconductivity exhibited by hydrogen-rich compounds like H₃S, which displays a critical temperature of 203 K under extreme pressure. Marco Cherubini, Abhishek Raghav, and Michele Casula, all from the Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, CNRS, Sorbonne Université, have now mapped the extended phase diagram of H₃S, revealing a quantum critical point at approximately 2 GPa. This research is significant because it demonstrates the crucial role of quantum fluctuations in the behaviour of this material and identifies a paraelectric region linked to the observed experimental peak. Their analysis, employing path integral molecular dynamics and machine learning, confirms the system’s critical behaviour aligns with the 4D Ising universality class, offering new insights into the mechanisms potentially enhancing superconductivity in these hydrides.

Ferroelectric criticality defines the Im3m, R3m phase transition in high-pressure H3S, leading to superconductivity

Scientists have uncovered a ferroelectric quantum critical point within the high-temperature superconductor H3S sulfur hydride at approximately 134 GPa. This discovery resolves a long-standing discrepancy between experimental observations and theoretical predictions regarding the pressure at which a crucial phase transition occurs in this material.

The research, combining path integral molecular dynamics with a machine learning interatomic potential trained on density functional theory configurations, provides a detailed phase diagram of H3S across an extended temperature and pressure range. This work clarifies the relationship between structural changes and the emergence of superconductivity, potentially paving the way for enhanced superconducting properties.

The study focused on the transition between the Im 3m and R3m phases of H3S, a shift linked to the displacement of hydrogen atoms between sulfur atoms. Researchers determined that the experimental peak in superconducting critical temperature, previously thought to coincide with this ferroelectric transition, actually falls within a paraelectric region characterized by substantial nuclear quantum fluctuations.

These fluctuations, measured using local phonon Green’s functions in imaginary time, involve fluctuating dipole moments and are located above the newly identified quantum critical point. The team employed finite-size scaling analysis to demonstrate that this critical point belongs to the 4D Ising universality class, a significant finding in condensed matter physics.

By integrating path integral molecular dynamics with machine learning interatomic potentials, the researchers overcame computational limitations inherent in accurately modelling quantum effects in light-atom systems like H3S. Simulations were performed using up to L × L × L primitive cells with L ∈{2, 3, 4}, enabling a precise determination of phase boundaries.

The global proton displacement was defined to distinguish between the Im 3m and R3m symmetries, revealing a scalar order parameter for the ferroelectric transition. This detailed analysis establishes a new understanding of the interplay between ferroelectricity, quantum criticality, and superconductivity in H3S.

The resulting phase diagram, depicted in Figure 1, shows the ferroelectric transition occurring at a pressure of 134 ±2 GPa. Analysis of the order parameter and local observables, as shown in Figure 2, further supports this finding. The research suggests that the dome-shaped evolution of the superconducting critical temperature is influenced by strong quantum fluctuations surrounding the quantum critical point, potentially offering a pathway to enhance superconducting properties through manipulation of these fluctuations. This work provides a crucial step towards understanding and optimizing high-temperature superconductivity in sulfur hydride and related materials.

Computational protocol for simulating sulfur hydride phase behaviour requires accurate interatomic potentials

Path integral molecular dynamics combined with a MACE neural network potential underpins this work investigating the phase diagram of H₃S sulfur hydride. To achieve density functional theory accuracy at reduced computational cost, a machine learning interatomic potential was trained on configurations generated by BLYP calculations.

Subsequent NVT-PIMD simulations were performed at varying volumes and temperatures, specifically T = 1/(k B β), utilising the i-PI package in conjunction with the trained machine learning interatomic potential. Simulations extended to 400ps in length, employing systems comprising L × L × L primitive cells with L ∈ {2, 3, 4} to facilitate accurate phase boundary determination via finite-size scaling.

The distinction between ferroelectric Im3m and paraelectric R3m structures hinges on the average proton positions relative to neighbouring sulfur atoms. A global proton displacement, ∆(j), was defined and evaluated at each PIMD iteration by projecting the vector connecting a hydrogen atom to one of its flanking sulfur atoms onto the direction between the two sulfur atoms.

Summation over all hydrogen atoms within the supercell yielded a scalar order parameter, with a reference orientation established to ensure consistent displacement direction. This order parameter, averaged over the entire PIMD trajectory, alongside its absolute value, were used to identify the ferroelectric transition, evidenced by saturation of the order parameter and suppression of fluctuations, as indicated by a sudden drop in the variance of the order parameter, σ²∆.

To pinpoint the quantum critical point, the research team extrapolated data in temperature and system size, identifying a location at p QCP ≈ 134 ±2 GPa. Local proton displacement, or the local dipole moment, ∆(j)i, was then examined to characterise the transition further. Analysis of its distribution at T = 50 K revealed a shift from a unimodal distribution in the paraelectric phase to a bimodal distribution indicative of pre-formed local dipole moments, fluctuating across a central barrier, and ultimately to a shifted unimodal distribution in the ferroelectric phase, signifying permanent local dipole moment creation.

Quantum criticality and ferroelectric behaviour in compressed hydrogen sulfide are closely linked phenomena

The research details a phase diagram for H₃S, revealing a transition between the Im m and R3m phases originating from a quantum critical point located at 134 ±2 GPa. Finite-size scaling analysis indicates that this quantum critical point belongs to the 4D Ising universality class. Detailed analysis of proton displacement, quantified by the parameter ∆(j), demonstrates a shift from unimodal to bimodal distributions as pressure decreases, indicating the formation of local dipole moments.

The variance of the order parameter, σ²∆, experiences a sudden drop, unambiguously identifying the ferroelectric transition line as a function of temperature. At a temperature of 50 K, the critical pressure for the ferroelectric transition was determined to be 124 ±2 GPa. This value differs from the experimentally observed peak at approximately 155 GPa, aligning with predictions from other theoretical studies.

Nuclear quantum effects are shown to significantly reduce the ferroelectric transition pressure by approximately 50 GPa at 200 K when compared to classical molecular dynamics simulations. The study employed a scalar order parameter, ∆, defined as the average of global displacements over the path integral molecular dynamics trajectory, and an absolute value, ∆abs, to precisely pinpoint the transition.

Local proton displacement, calculated as ∆(j) = r(j) HiSi1 · r(j) Si1Si2 −d(j) Si1Si2/2, was used to probe the ferroelectric transition. Distributions of this parameter at 50 K and varying pressures revealed a progression from unimodal symmetric distributions at high pressures to bimodal shapes indicative of pre-formed local dipole moments. Analysis of soft optical mode frequencies at the 4 Γ point, computed from PIMD phonons, further characterizes the ferroelectric transition and provides insight into the driving modes of the structural change.

Quantum criticality and four-dimensional Ising behaviour in compressed hydrogen sulphide are observed at high pressure

Researchers have mapped the phase diagram of H₃S, a compound crucial for understanding high-temperature superconductivity, incorporating both thermal and quantum effects. This detailed mapping reveals a transition between the Im m and R3m phases originating from a quantum critical point located at approximately 2 GPa.

The experimental peak in the material’s behaviour falls within a paraelectric region characterised by substantial nuclear quantum fluctuations and fluctuating dipole moments. Finite-size scaling analysis indicates that the system near this quantum critical point belongs to the four-dimensional Ising universality class.

This classification provides insight into the critical behaviour of the material and its potential link to the emergence of superconductivity. The study acknowledges limitations related to the approximations inherent in the density functional theory used to train the neural network potential, which could introduce some uncertainty in the calculated phase diagram.

Future research could focus on refining the potential with more accurate data or exploring the impact of different exchange-correlation functionals. These findings establish a clearer understanding of the complex interplay between quantum and thermal effects in H₃S, which is vital for optimising its superconducting properties.

Identifying the quantum critical point and its associated critical behaviour offers a pathway towards manipulating the material’s electronic structure and enhancing its superconducting transition temperature. The connection to the 4D Ising universality class suggests that the superconducting state in H₃S may share characteristics with other systems exhibiting similar critical behaviour, potentially guiding the development of novel superconducting materials.