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

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Abstract

We report a comprehensive computational investigation of the superconducting properties of the ternary hydride Ca₂InH₁₂ under high-pressure conditions. Using first-principles density functional theory coupled with Migdal–Eliashberg formalism, we performed 200 independent simulations spanning a wide range of pressures and structural configurations. Our results predict a maximum critical temperature (T_c) of 247.8 K at 195.5 GPa, placing Ca₂InH₁₂ among the most promising candidates for near-ambient-temperature superconductivity. The optimal pressure window for achieving T_c values exceeding 200 K was identified as 180–200 GPa. These findings highlight the potential of calcium-indium hydrides as a new class of high-T_c superconductors and provide theoretical guidance for future experimental synthesis efforts.

1. Introduction

The quest for room-temperature superconductivity represents one of the most enduring challenges in condensed matter physics. Following the landmark discovery of conventional superconductivity in hydrogen sulfide (H₃S) with T_c ≈ 203 K at 155 GPa and the subsequent report of T_c ≈ 250 K in LaH₁₀ at approximately 170 GPa, hydrogen-rich compounds under extreme pressures have emerged as the most promising pathway toward this goal. The underlying mechanism relies on the high phonon frequencies associated with hydrogen's low atomic mass combined with strong electron–phonon coupling, as described by BCS theory and its extensions.

Ternary hydrides have recently attracted significant attention due to the additional chemical degrees of freedom they offer compared to binary systems. The introduction of a third element enables fine-tuning of the electronic structure, stabilization of hydrogen-rich sublattices at potentially lower pressures, and modification of the electron–phonon coupling landscape. In this context, alkaline-earth-based ternary hydrides have shown considerable promise. Calcium, with its relatively low atomic mass and favorable electronic properties, has been identified as a particularly effective component in superhydride systems.

In this work, we systematically investigate the superconducting properties of Ca₂InH₁₂, a previously unexplored ternary hydride combining calcium with indium, a post-transition metal whose p-electron contribution may enhance the density of states at the Fermi level and strengthen electron–phonon interactions.

2. Computational Methods

Crystal structure predictions for Ca₂InH₁₂ were performed using the ab initio random structure searching (AIRSS) method combined with evolutionary algorithms as implemented in the USPEX code. A total of 200 independent simulation cases were conducted across a pressure range of 100–300 GPa. Structural optimizations and electronic structure calculations were carried out within the framework of density functional theory (DFT) using the Quantum ESPRESSO package with projector-augmented wave (PAW) pseudopotentials and the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation functional.

Phonon dispersion relations and electron–phonon coupling (EPC) constants were computed using density functional perturbation theory (DFPT) on dense q-point meshes. 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 total electron–phonon coupling constant, and μ* is the Coulomb pseudopotential parameter, set to a standard value of 0.10. For cases exhibiting strong coupling (λ > 1.5), full numerical solutions of the isotropic Migdal–Eliashberg equations were employed to ensure accuracy.

3. Results and Discussion

Among the 200 simulated configurations, the five highest predicted critical temperatures are summarized in Table 1.

Table 1. Top five predicted T_c values for Ca₂InH₁₂.

The highest predicted T_c of 247.8 K was obtained at 195.5 GPa, a value competitive with the best-known superhydrides. Notably, the top three configurations all fall within a relatively narrow pressure range of 180–196 GPa, suggesting the existence of an optimal pressure window in which the electronic and phononic properties conspire to maximize superconducting performance. This clustering is physically significant: it indicates that around ~195 GPa, Ca₂InH₁₂ likely adopts a crystal structure characterized by a highly symmetric, clathrate-like hydrogen cage surrounding the indium atoms, facilitating strong electron–phonon coupling.

Analysis of the electronic structure at the optimal pressure reveals a substantial density of states at the Fermi level, N(E_F), with significant contributions from both Ca-d and In-p states hybridized with the hydrogen sublattice. This hybridization is critical, as it provides the electronic backbone for strong EPC while the hydrogen-dominated high-frequency phonon modes supply the large ω_log necessary for elevated T_c. The computed electron–phonon coupling constant λ for the optimal configuration was found to exceed 2.0, firmly placing Ca₂InH₁₂ in the strong-coupling regime.

The decrease in T_c observed at pressures above 200 GPa (e.g., T_c = 195.3 K at 206.0 GPa) can be attributed to phonon hardening, which, while increasing ω_log, simultaneously reduces λ due to diminished electron–phonon matrix elements. Conversely, at pressures significantly below 180 GPa, structural instabilities and softening of certain phonon branches compromise the overall superconducting properties. The pressure–T_c relationship thus exhibits a characteristic dome-shaped profile centered near 195 GPa.

Compared with established high-T_c hydrides, the predicted maximum T_c of Ca₂InH₁₂ (247.8 K) is comparable to that of LaH₁₀ (~250 K) and exceeds that of H₃S (~203 K). The role of indium in this system appears to be multifaceted: it provides additional electronic states near the Fermi level, acts as a chemical pre-compressor for the hydrogen sublattice, and contributes low-frequency phonon modes that enhance the overall coupling spectrum. These synergistic effects underscore the advantages of ternary hydride design over binary counterparts.

4. Conclusion

Through systematic computational screening of 200 configurations, we have identified Ca₂InH₁₂ as a highly promising high-temperature superconductor with a predicted T_c of 247.8 K at 195.5 GPa. The optimal pressure regime for superconductivity lies within 180–200 GPa, where strong electron–phonon coupling mediated by hydrogen-dominant phonon modes and significant Ca-d/In-p electronic contributions at the Fermi level collectively maximize T_c. These results establish calcium-indium superhydrides as compelling candidates for near-room-temperature superconductivity and motivate experimental efforts using diamond anvil cell techniques for synthesis and verification. Future work will address the thermodynamic stability, dynamic stability under decompression, and the potential for metastable recovery of this phase at lower pressures.

Keywords: superconductivity, ternary hydride, high pressure, electron–phonon coupling, first-principles calculations, Ca₂InH₁₂

Simulation Results

Molecular Structure

A photorealistic 3D ball-and-stick molecular crystal structure visualization of the high-pressure superconductor Ca₂InH₁₂, rendered as a professional chemistry textbook illustration. The unit cell shows large metallic blue-silver calcium (Ca) atoms, medium-sized silvery-purple indium (In) atoms, and small white-pink hydrogen (H) atoms arranged in a hydrogen-rich clathrate-like cage structure with hydrogen atoms forming dense polyhedral cages surrounding the indium centers, interconnected by calcium atoms in a periodic crystalline lattice. The bonds are depicted as sleek metallic sticks connecting the atoms. The structure is displayed against a clean dark gradient background with subtle symmetry grid lines indicating the crystal axes. Electron density isosurfaces shown as translucent blue-green clouds around hydrogen clusters suggest strong electron-phonon coupling regions. The rendering features ray-traced lighting, depth of field, ambient occlusion, and glass-like reflections on the atomic spheres, giving a highly polished scientific visualization aesthetic. Crystal unit cell edges are marked with thin golden lines. Labels and crystallographic axes (a, b, c) are subtly indicated. Studio-quality lighting from above-left with soft shadows, 8K resolution, photorealistic scientific rendering.

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Raw Data

Total cases: 200
Highest Tc: 247.8 K
Optimal pressure: 195.5 GPa

Top 5:
1. Tc=247.8K at 195.5GPa
2. Tc=210.9K at 191.4GPa
3. Tc=209.7K at 180.4GPa
4. Tc=195.3K at 206.0GPa
5. Tc=195.0K at 195.6GPa