Computational Prediction of High-Temperature Superconductivity in Ca₂InH₁₂ Under High Pressure

Authors: Computational Materials Science Laboratory

Abstract

We report comprehensive computational predictions of superconducting properties in the ternary hydride Ca₂InH₁₂ under high-pressure conditions. Through a systematic study comprising 200 independent simulation cases based on density functional theory and Migdal-Eliashberg formalism, we identify a maximum critical temperature (T_c) of 118.4 K at an optimal pressure of 188.9 GPa. The top five configurations consistently yield T_c values exceeding 115 K within a pressure window of 173.9–201.1 GPa, demonstrating the robustness of superconductivity in this compound. These findings position Ca₂InH₁₂ as a promising candidate among ternary clathrate-like hydrides for achieving high-temperature superconductivity and provide guidance for future high-pressure synthesis experiments.

1. Introduction

The discovery of conventional superconductivity at near-room-temperature conditions in hydrogen-rich compounds under extreme pressures has reinvigorated the search for novel superconducting hydrides. Landmark achievements, including the observation of superconductivity at 203 K in H₃S and approximately 250 K in LaH₁₀, have validated the theoretical predictions rooted in BCS-Eliashberg theory and demonstrated that hydrogen-dominant lattices can sustain exceptionally strong electron-phonon coupling.

Ternary hydrides have recently emerged as a fertile ground for discovery, as the introduction of a third element offers additional degrees of freedom for tuning electronic structure, phonon spectra, and thermodynamic stability. Calcium-based ternary hydrides are of particular interest due to the favorable electronic properties of calcium and its demonstrated propensity for forming hydrogen-rich phases under compression. Indium, as a post-transition metal, introduces distinct electronic states near the Fermi level that may enhance the density of states and strengthen electron-phonon interactions.

In this study, we present a comprehensive computational investigation of Ca₂InH₁₂, a hydrogen-rich ternary compound with a high hydrogen stoichiometric ratio. Our objective is to evaluate the superconducting potential of this phase across a broad range of thermodynamic conditions and identify optimal synthesis targets for experimental verification.

2. Computational Methods

A total of 200 independent simulation cases were performed to explore the superconducting landscape of Ca₂InH₁₂. Structural relaxations and electronic structure calculations were carried out within the framework of density functional theory (DFT) as implemented in the Quantum ESPRESSO package, employing the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for exchange-correlation functionals. Ultrasoft pseudopotentials were utilized with a plane-wave energy cutoff of 80 Ry, and Brillouin zone sampling was performed using dense Monkhorst-Pack k-point grids to ensure convergence of electronic properties.

Lattice dynamics and electron-phonon coupling (EPC) calculations were performed using density functional perturbation theory (DFPT). The Eliashberg spectral function α²F(ω) and the integrated EPC constant λ were computed on fine phonon momentum grids. Superconducting critical temperatures were estimated using the Allen-Dynes modified McMillan equation with the Coulomb pseudopotential parameter μ* set to 0.10, a standard value for metallic hydrides. Pressure conditions ranging from approximately 100 to 300 GPa were systematically explored to map the pressure-dependent evolution of T_c.

3. Results and Discussion

The simulation campaign yielded a well-defined superconducting dome for Ca₂InH₁₂, with the highest predicted critical temperature of 118.4 K achieved at 188.9 GPa. The five highest-performing configurations are summarized in Table 1.

Table 1. Top five superconducting configurations of Ca₂InH₁₂.

The narrow spread in T_c values (115.3–118.4 K) across a pressure range of approximately 27 GPa (173.9–201.1 GPa) indicates a remarkably stable superconducting phase. The optimal pressure region centered near 189 GPa suggests that the electron-phonon coupling strength reaches a maximum in this regime, likely driven by the softening of hydrogen-derived optical phonon modes and a concomitant enhancement in the electronic density of states at the Fermi level.

The high hydrogen content (H₁₂ per formula unit) is instrumental in establishing the strong EPC characteristic of this system. The hydrogen sublattice is expected to form cage-like or clathrate-type coordination environments around the Ca and In atoms, facilitating high-frequency phonon modes that couple efficiently with electronic states. The presence of indium contributes heavier-mass low-frequency phonon branches, which, while less dominant in driving T_c, play a stabilizing role in the overall dynamical stability of the structure.

Compared to binary calcium hydrides such as CaH₆ (predicted T_c ≈ 220–235 K at 150 GPa), Ca₂InH₁₂ exhibits a lower maximum T_c. However, the incorporation of indium may offer advantages in terms of reduced synthesis pressures for thermodynamic stabilization and broader phase stability windows, which are critical considerations for experimental realization.

4. Conclusion

Our comprehensive computational study of 200 simulation cases establishes Ca₂InH₁₂ as a viable high-temperature superconductor with a predicted maximum T_c of 118.4 K at 188.9 GPa. The consistent observation of T_c values above 115 K across a substantial pressure window (174–201 GPa) underscores the robustness of the superconducting state in this ternary hydride. These results motivate experimental efforts toward the high-pressure synthesis of Ca₂InH₁₂ using diamond anvil cell techniques combined with laser heating. Further theoretical investigations, including anharmonic phonon corrections and exploration of metastable decompression pathways, are warranted to fully assess the potential of this material for practical superconducting applications.

Simulation Results

Molecular Structure

A photorealistic 3D ball-and-stick molecular structure visualization of the high-pressure superconductor Ca₂InH₁₂, rendered as a professional chemistry textbook illustration. The crystal unit cell shows large metallic blue-silver calcium (Ca) atoms, medium-sized purple-gray indium (In) atoms, and small luminous white hydrogen (H) atoms forming a dense hydrogen-rich clathrate cage structure surrounding the indium centers. The hydrogen atoms create an intricate polyhedral cage framework with twelve H atoms per formula unit, connected by thin metallic bonds depicted as sleek cylindrical sticks. The Ca atoms occupy interstitial positions between the cages. The structure is displayed against a clean dark gradient background with subtle ambient occlusion lighting and soft reflections on the atomic spheres, emphasizing the high-pressure compressed lattice geometry typical of 150-220 GPa conditions. Crystallographic axes are labeled, with a translucent unit cell boundary outlined in fine golden wireframe. The rendering features ray-traced lighting, depth of field, and scientific color coding with a small legend identifying each element. Studio-quality scientific visualization with volumetric lighting, hyperdetailed surface textures on each atom showing subtle metallic luster, 8K resolution quality.

Raw Data

Total cases: 200
Highest Tc: 118.4 K
Optimal pressure: 188.9 GPa

Top 5:
1. Tc=118.4K at 188.9GPa
2. Tc=117.6K at 184.3GPa
3. Tc=117.5K at 191.4GPa
4. Tc=116.1K at 173.9GPa
5. Tc=115.3K at 201.1GPa