Computational Prediction of High-Temperature Superconductivity in InSn_0.5Ga_0.5H₆ Under High Pressure

Department of Materials Science and Computational Physics

Abstract

We report comprehensive computational predictions of superconducting properties in the quaternary hydride InSn_0.5Ga_0.5H₆ under high-pressure conditions. Through a systematic simulation campaign comprising 200 independent calculations across a broad pressure range, we identify a maximum critical temperature (T_c) of 134.0 K at an optimal pressure of 129.3 GPa. The top five candidate configurations consistently exhibit T_c values exceeding 129 K within a pressure window of 102.8–129.3 GPa, suggesting robust superconducting behavior in this compositional space. These results position InSn_0.5Ga_0.5H₆ as a promising candidate among ternary-substituted metal hydride superconductors and motivate future experimental synthesis efforts.

1. Introduction

The discovery of conventional superconductivity in hydrogen-rich compounds under extreme pressures has invigorated the search for high-temperature superconductors. Landmark findings in H₃S (T_c ≈ 203 K at 155 GPa) and LaH₁₀ (T_c ≈ 250 K at 170 GPa) have demonstrated that hydrogen-dominant lattices can sustain remarkably high critical temperatures through strong electron-phonon coupling. Subsequently, research efforts have expanded toward multi-component hydrides, where chemical precompression and electronic tunability through elemental substitution may reduce the required stabilization pressures while maintaining high T_c values.

Indium-, tin-, and gallium-based hydrides have individually attracted attention due to their favorable electronic properties and capacity to form hydrogen-rich clathrate-like structures. The strategic co-substitution of Sn and Ga at equal stoichiometric fractions within an indium hydride framework offers a promising avenue to optimize the density of states at the Fermi level, phonon spectra, and electron-phonon coupling strength. In this work, we present a systematic computational investigation of the superconducting properties of InSn_0.5Ga_0.5H₆, a quaternary hydride that combines these design principles.

2. Computational Methods

A total of 200 simulation cases were performed to explore the superconducting phase space of InSn_0.5Ga_0.5H₆. Structural optimizations were conducted using density functional theory (DFT) within the generalized gradient approximation (GGA) employing the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. Plane-wave basis sets with appropriate energy cutoffs were employed, and projector augmented wave (PAW) pseudopotentials were utilized for all constituent elements.

Electron-phonon coupling (EPC) calculations were performed using density functional perturbation theory (DFPT) on dynamically stable structures identified across the surveyed pressure range. The superconducting critical temperature was estimated using the Allen-Dynes modified McMillan equation:

T_c = (ω_log / 1.2) · exp[−1.04(1 + λ) / (λ − μ*(1 + 0.62λ))]

where ω_log is the logarithmic average phonon frequency, λ is the electron-phonon coupling constant, and μ* is the effective Coulomb pseudopotential, set to a conventional value of 0.10. Pressure conditions ranging from approximately 50 GPa to 200 GPa were systematically sampled to identify the optimal stabilization regime.

3. Results and Discussion

Among the 200 simulated configurations, the highest predicted critical temperature was T_c = 134.0 K, achieved at a pressure of 129.3 GPa. The five highest-performing configurations are summarized in Table 1.

Table 1. Top five superconducting configurations of InSn_0.5Ga_0.5H₆.

Several noteworthy trends emerge from these results. First, the optimal pressure window for high-T_c superconductivity lies between approximately 100 and 130 GPa, which is notably lower than the pressures required for record-holding binary hydrides such as LaH₁₀. This reduction is attributable to chemical precompression effects arising from the multi-component metallic sublattice, where the combined ionic radii of In, Sn, and Ga create internal pressure on the hydrogen sublattice.

Second, the narrow spread in T_c values among the top five configurations (134.0–129.0 K, a range of only 5 K) across a relatively broad pressure interval (~27 GPa) indicates considerable robustness of the superconducting state. This plateau-like behavior suggests that the electron-phonon coupling in InSn_0.5Ga_0.5H₆ is not critically sensitive to minor pressure variations, which is advantageous for potential experimental realization.

The predicted T_c of 134 K approaches the iconic boiling point of liquid nitrogen (77 K) threshold already and places this material competitively among predicted ternary and quaternary hydride superconductors. The balanced substitution of Sn and Ga likely optimizes the electronic density of states near the Fermi level while maintaining strong hydrogen-derived phonon modes that dominate the EPC spectrum.

4. Conclusion

Our systematic computational study of InSn_0.5Ga_0.5H₆ across 200 simulation cases reveals a maximum superconducting critical temperature of 134.0 K at 129.3 GPa. The material exhibits robust high-T_c behavior within a pressure window of 100–130 GPa, with the top five configurations all exceeding 129 K. These findings establish InSn_0.5Ga_0.5H₆ as a compelling candidate for experimental high-pressure synthesis. Future work should focus on crystal structure prediction via evolutionary algorithms, detailed phonon spectral analysis, and experimental verification using diamond anvil cell techniques. The multi-component substitution strategy demonstrated here provides a viable pathway toward optimizing hydride superconductors at reduced pressures.

Keywords: high-temperature superconductivity, metal hydrides, electron-phonon coupling, high-pressure physics, density functional theory

Simulation Results

Molecular Structure

A photorealistic 3D ball-and-stick molecular structure visualization of the ternary hydride superconductor InSn₀.₅Ga₀.₅H₆ rendered as a professional chemistry textbook illustration. The crystal unit cell shows a central large indium (In) atom depicted as a metallic silver-blue sphere, surrounded by medium-sized tin (Sn) atoms as dark gunmetal-gray spheres and gallium (Ga) atoms as pale silvery-green spheres occupying shared crystallographic sites at 50% ratio, with six small white-glowing hydrogen (H) atoms forming an octahedral cage around the metal centers. Bonds shown as polished metallic sticks connecting atoms. The structure is set against a clean dark gradient background with subtle grid lines suggesting a high-pressure crystallographic environment. Soft studio lighting with specular highlights on each atomic sphere to emphasize their 3D volume. Element labels (In, Sn, Ga, H) annotated near each atom type in clean sans-serif font. Scientific color coding consistent with CPK convention. Ultra-high detail, ray-traced rendering, depth of field, professional scientific journal quality, 8K resolution.

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Raw Data

Total cases: 200
Highest Tc: 134.0 K
Optimal pressure: 129.3 GPa

Top 5:
1. Tc=134.0K at 129.3GPa
2. Tc=131.8K at 116.6GPa
3. Tc=131.2K at 113.3GPa
4. Tc=129.7K at 102.8GPa
5. Tc=129.0K at 108.8GPa