Design of moderate-pressure superconductivity in a ternary hydride system†

Xue Li*^a, Nan Wang^a, Yuan Ma^c, JingKai Bi^b and Hanyu Liu*^c
aHenan Institute of Advanced Technology, Zhengzhou University, Zhengzhou 450001, China. E-mail: lx2021@zzu.edu.cn
^bInstitute of Quantum Materials and Physics, Henan Academy of Sciences, Zhengzhou 450001, China
^cKey Laboratory of Material Simulation Methods and Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, China. E-mail: hanyuliu@jlu.edu.cn

First published on 7th July 2025

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1. Introduction

A long-sought goal in condensed matter physics is hunting for high-temperature and even room-temperature superconductors. Recent discoveries have suggested that phonon-mediated hydrides have been regarded as promising alternatives to achieve favorable superconductivity.^1–8 It is encouraging to see that several hydrides exhibit high-temperature superconductivity, including H₃S,^9–11 YH₆,¹² YH₉,¹³ LaH₁₀,^14–18 CaH₆,^19–21 (La,Y)H₁₀,²² (La,Ce)H₉,^23,24 and other related compounds.^25,26 The superconductivity among these superhydrides benefits from the hydrogen-dominant electronic density of states at the Fermi level. However, high pressures (>∼100 GPa) are necessary to stabilize such high hydrogen content in hydrides, hindering the further applications of hydrides. Hydrides with stable near-ambient pressure have thus currently become one of the focuses in the superconducting field.^27,28

Previous studies have shown that few-hydrogen metallic hydrides are promising for maintaining stability under ambient pressure due to the capture of H atoms in the metallic interstices. Shi et al. discovered a series of few-hydrogen metal-bonded perovskites possessing considerable superconductivity.^29,30 Furthermore, recent studies have also indicated that some hydrides based on existing structural prototypes exhibit superconductivity under low pressure.³¹ For example, a family with compositions XY₂H₆ and XYH₃, featuring perovskite-like structures, was also identified to exhibit higher superconductivity at low pressure.^32–36 Gao et al. unveiled numerous A15-type superconducting hydrides at low pressures.^37,38 Based on this, the design of hydrides from different structural prototypes is suggested as an alternative route to achieve high-temperature superconductivity at lower pressure, enriching the family of phonon-mediated superconductors.

In this work, we further explore promising superconducting hydrides with these high-symmetry structures that could be stable at low pressure. Considering electronegativity/mass plays a critical role in enhancing superconducting temperatures,^39,40 we introduce group I/IIA metal atoms with less electronegativity and a lighter mass to form a cubic hydrogen alloy framework. Meanwhile, the heavier III/IVB metal atoms are considered to be saturated in the center position of the structures. This screening strategy is expected to increase the superconducting transition temperature and reduce the required stabilising pressure in a ternary hydride system. After the high-throughput simulations, we identified a series of superconducting hydrides at low pressures of 0, 10, and 50 GPa. In particular, the T_c of LiTiH₆ is up to 86 K, above the temperature of liquid nitrogen (77 K). Our results provide a way to optimize the stabilization pressure and superconducting performance of hydrides.

2. Computational methods

The geometry optimizations were performed within the framework of density functional theory (DFT) implemented in the Vienna ab initio simulation package (VASP)⁴¹ with the Perdew–Burke–Ernzerhof (PBE)^42,43 generalized gradient approximation (GGA) as the exchange–correlation function. The kinetic cutoff energy was set to 400 eV to ensure that the enthalpy was well-converged. The electron–phonon coupling (EPC) interaction calculations were performed using the Quantum ESPRESSO package based on the linear response theory.⁴⁴ We chose a cutoff energy of 40 Ry and a q-point mesh of 6 × 6 × 6. A much denser k-point mesh of 12 × 12 × 12 was used to ensure k-point sampling convergence. The superconducting temperatures (T_c) among the newly proposed hydrides were estimated using the Allen–Dynes-modified McMillan equation⁴⁵ with a Coulomb pseudopotential μ* of 0.1.

3. Results and discussion

We performed high-throughput calculations to identify high-temperature superconducting hydrides based on the structural prototype of ABH₃ with Pmm symmetry, ABH₆ with Pm symmetry, and AB₂H₆ with Fmm symmetry at 0, 10, and 50 GPa, as presented at the top of Fig. 1. Different combinations of alkali metals, alkaline earth metals, and transition metals were considered in these structures, as shown at the bottom of Fig. 1. The heavier elements saturated at the center position of the structures. The elements with less electronegativity and a lighter mass are responsible for forming cubic hydrogen alloy frameworks. We evaluated dynamic stability among these different compounds. After systemic calculations, 53 dynamically stable compounds with absent imaginary frequency were identified, which are marked by green and blue countermarks in Fig. 1. For dynamically stable ternary hydrides, we further investigated their electronic properties, including projected electronic band structure and density of states (DOS). For different structural prototypes, the electronic structures of typical compounds are sketched in Fig. 2. These hydrides exhibit obvious metallic behavior due to the presence of electronic states at the Fermi level. The contributions of different atoms to the total DOS are also depicted in the above figures. The projected bands onto different elements are also shown in corresponding band structures.

3.1. Pm ABH₆

Our work shows that 11 ternary hydrides with Pm symmetry were stable within 50 GPa, of which ten exhibited expected superconductivity. Here, we will use LiTiH₆ as an example for discussion. As shown in Fig. 2, Ti and H atoms contribute significantly to the DOS at the Fermi level. The DOS value of Ti atoms is about twice that of H atoms at the Fermi level, suggesting possible stronger electron–phonon coupling. Meanwhile, the calculated band structure also reveals that the Fermi level is mainly dominated by the contributions of Ti and H atoms, which is consistent with the conclusion of DOS. After determining the metallicity, we performed electron–phonon coupling (EPC) simulations to investigate potential superconductivity. The calculated EPC strength-weighted phonon curves, projected phonon density of states (PHDOS), Eliashberg spectral function α²F(ω)/ω, and EPC parameter λ for LiTiH₆ are shown in Fig. 3(b). The results suggest that low-frequency phonon modes associated with metal atom vibrations dominated the increasing EPC parameter λ. We further decomposed λ and found that the low-frequency vibrations distributed below 16 THz account for 52% of the total λ of 2.3 at 50 GPa. Key material and superconducting parameters for Pm ABH₆ hydrides at several pressures are listed in Table S1 (ESI†). LiTiH₆ exhibits the highest T_c, reaching 87 K under 50 GPa. We also investigated the evolution of T_c with pressure for LiTiH₆, as shown in Fig. 4. The calculated λ decreased from 3.1 at 40 GPa to 1.8 at 75 GPa, while ω_log increased from 343 to 738 K, resulting in the increase in T_c value from 63 to 100 K. In addition, the T_c values of LiZrH₆ and LiHfH₆ are estimated to be 82 and 80 K at pressures of 50 GPa, respectively, higher than that of liquid nitrogen (Table S1, ESI†).

3.2. Pmm ABH₃

In this section, 18 configurations with Pmm symmetry were identified to be dynamically stable within 50 GPa, of which ten were found to be potential superconductors. One example is the BeZrH₃ phase, which was estimated to achieve the highest T_c value of 41 K among the studied ABH₃ systems. The electronic property of the BeZrH₃ phase was investigated at 50 GPa, as displayed in Fig. 2. The calculated DOS suggests that BeZrH₃ exhibits excellent metallic behavior, arising from the appearance of electronic states at the Fermi level. The Zr atoms contribute significantly to the total DOS at the Fermi energy level, indicating the potential for superconducting characteristics. Further, projected band structure calculations also confirmed the role of Zr atoms as a major contribution, which is consistent with the analysis for the aforementioned DOS. In order to understand the favorable superconductivity in BeZrH₃, we calculated the PHDOS and Eliashberg spectral function, as depicted in Fig. 3. It is evident that the high-frequency and low-frequency phonon modes are dominated by the vibrations of H and metal atoms, respectively. Low-frequency vibrations of Zr atoms distributed below 8 THz contribute 67% to the total λ, and the 8–25 THz frequency derived from Be atoms vibrations contributes 23% to the total λ. We also tested the pressure dependence of T_c. The EPC parameter λ decreased from 2.3 at 40 GPa to 1.6 at 75 GPa, while ω_log increased from 252 to 344 K, resulting in a slight increase in the T_c from 40 to 42 K (see Fig. 4). Compared with the above-mentioned metal-bonded perovskites MgHCu₃, the predicted BeZrH₃ possesses moderate hydrogen content, which ensures stability and better superconductivity at lower pressure.

3.3. Fmm AB₂H₆

For Fmm-like AB₂H₆ structures, we found that 24 hydrides could remain dynamically stable at low pressures of below 50 GPa, of which 19 hydrides possess favorable metallic character. Combined with projected band structures and DOS, it is evident that the electronic states at the Fermi level are mainly dominated by the contributions of Zr atoms, indicating favorable EPC strength for superconductivity. Furthermore, we evaluated the T_c value among stable metal hydrides. The results reveal that 19 hydrides exhibit potential superconductivity, and MgZr₂H₆ could reach the highest value of 27 K at 50 GPa. The EPC parameter λ of MgZr₂H₆ at 50 GPa is estimated to be 0.8, and the λ in different phonon modes is also depicted in Fig. 3. As a result, the pronounced contribution to the EPC parameter comes from the modes associated with Zr atom vibrations, contributing 73% to the total λ. Meanwhile, we also studied the evolution of T_c with pressure for MgZr₂H₆ (see Fig. 4). The calculated λ decreased from 1.3 at 40 GPa to 1.0 at 75 GPa, while ω_log increased from 273 to 334 K, resulting in a decrease in the T_c value from 28 to 25 K.

4. Conclusion

In summary, we performed high-throughput calculations to search for ternary superconducting hydrides at moderate pressure based on high-symmetry prototype structures. Our work covered 288 ternary hydrides and ultimately identified that 53 compounds could remain dynamically stable within 50 GPa, of which 39 exhibited favorable metallicity. Further EPC calculations predicted that 39 compounds could be potential superconductors. Excitingly, three phases exhibited expected superconducting transition temperatures exceeding the boiling point of liquid nitrogen at 50 GPa, including LiTiH₆ (87 K), LiZrH₆ (82 K), and LiHfH₆ (80 K). With the increase in pressure, LiTiH₆ could reach the highest T_c value of 100 K under 75 GPa. Our study discovered a series of candidates displaying promising superconductivity among Pm ABH₆, Pmm ABH₃, and Fmm AB₂H₆ systems at moderate pressure. These results may help find additional superconducting hydrides that are stable at low pressure.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The data supporting this article have been included as part of the ESI.†

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12304031, 12404007, 52288102, and 52090024), the Joint Fund of Science and Technology R&D Plan of Henan Province (Grant No. 242301420031), and the National Supercomputing Center in Zhengzhou.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5tc00832h

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