Band/Dos character and Superconductivity of CeH 18 . To assess superconducting properties of CeH18, we first evaluate its electronic band structure, taking 400 GPa as a representative case study. Calculated results clearly indicate the metallic nature of CeH18 with several band crossing the Fermi level, as shown in the left panel of Figure 3(a). Results in the right panel of Figure 3(a) show that the hydrogen atoms make a substantial contribution to the electronic density of states (DOS) near the Fermi level, which is almost identical to the DOS contributed by the electrons from Ce. It is seen that the DOS is essentially flat around the Fermi energy, which is notably different from the DOS of LaH10 that hosts van Hove singularity around the Fermi energy 19. To examine the changes of the band-filling states, we have calculated the band structures at different pressures, and the results (see Figure S2) show that the hole-bands at the X–point, along the Z–X path, and at the Y–point move downward with rising pressure, indicating a systematic pressure driven electron transfer, which provides an explanation for the decreasing trend of Tc with increasing pressure. We next examine the phonon and electron-phonon coupling in CeH18. Calculated phonon dispersion results are shown in the left panel of Figure 3(b). No imaginary phonon modes are present in the entire Brillouin zone, indicating the dynamic stability of this crystal structure. We then computed the Eliashberg spectral function α2F (ω), from which the electron-phonon coupling parameter can be obtained via a simple integration in the frequency domain.37–40 The resulting integrated electron-phonon coupling parameter λ = 2.3 is quite large and comparable to the value of λ = 2.2 for H3S.17 It is noted that such strong electron-phonon couplings make various approximate weak-coupling Tc formulas generally unreliable, and an accurate description necessitates direct numerical solutions to the Eliashberg equations.37–40 We have employed this approach to calculate superconducting energy gap and transition temperature using the typical Coulomb pseudopotential µ⋆ = 0.10; we also checked results with µ⋆ = 0.13 to estimate a reasonable range of Tc values. The resulting Tc of 309-329 K (for µ⋆ = 0.10 and 0.13) at 350 GPa, where CeH18 is stable, is well above the room temperature and represents the highest hitherto reported Tc among binary superhydrides.
Superconductivity of MH 18 . To explore systematic trends and elucidate the underlying mechanisms for superconductivity in the predicted extreme superhydrides, we have calculated key electronic, phonon and electron-phonon coupling parameters and the resulting Tc values from solving the Eliashberg equations of selected MH18 compounds. We also have calculated, for the purpose of comparison, under the same parameters employing the same computational approach for the I41/amd phase of solid hydrogen that is known to stabilize in the pressure range of interest here.41 Moreover, we have systematically examined energetic and phonon dispersion aspects of the MH18 compounds beyond their stability fields indicate in Figure1(b), and we have identified several metastable phases that extend the structural viability to lower pressures with enhanced superconducting transition temperatures. All the key parameters and properties for the identified stable and metastable phases of MH18 and hydrogen in I41/amd phase are summarized in Table I with the Tc data plotted in Figure 4.
Calculated results show that the electron-phonon coupling parameter λ and the resulting Tc vary considerably among the MH18 superhydrides at the same pressure points (see Table I and Figure 4). This phenomenon reflects the broadly variable lattice dynamics and electronic states in different MH18 compounds, despite that they all share the same stoichiometry and clathrate structures. These contrasting properties indicate substantial differences in their bonding strengths and charge distributions, which are manifested in the large disparities of their characteristic vibrational frequencies and electronic density of states at the Fermi level as listed in Table I.
It is noted that the MH18 compounds host Tc values that distribute over a large range, from 50 K for Fddd-AcH18 at 700 GPa up to 329 K for Fddd-CeH18 at 350 GPa (Tc quoted for discussion are all taken at µ⋆ = 0.10). These results offer important clues for understanding the trends in Tc values that approach the result of the I41/amd phase of solid hydrogen at high pressures. Among the extreme superhydrides, CeH18 exhibits the highest Tc in the entire pressure range, and this compound hosts H−H distances in the range of 0.85–1.17 Å that is close to that of AMH (1.0 Å) at 500 GPa. These results show that these newly identified extreme MH18 superhydrides represent a series of compounds that approach AMH in superconducting properties, confirming Ashcroft’s original conjecture.11 We have calculated the projected phonon density of states (PHDOS) from Ce and H atoms. The results given in the middle panel of Figure 3(b) show that the main contributions to the EPC come from the mid– and high–frequency hydrogen vibrations in the range of 500–2500 cm−1. It is also seen from the results in Figure 4 that most MH18 compounds exhibit monotonically decreasing Tc with increasing pressure with the exception of Fddd-ThH18 that hosts a slightly upward trend in its Tc versus rising pressure. This pressure induced reduction of Tc is reminiscent of the behavior of solid hydrogen at higher pressures (700-1,000 GPa),5 which is consistent with the idea that chemical pre-compression in hydrogen compounds would shift material behaviors toward lower pressures. These insights are helpful for rational exploration and elucidation of optimal superconducting superhydrides.
Taking potential effects into consideration. Additional effects, such as spin-orbit coupling (SOC), magnetism and electron correlation, may affect the estimated Tc of the predicted MH18 compounds. We have taken CeH18 and ThH18 as case studies to assess the effect of SOC. Our calculations reveal that the Tc values are insensitive to SOC (see Table I), which is consistent with the nearly identical band structures with and without the SOC (Figure 3a). We have examined the energetics of the magnetic structures of the predicted MH18 compounds by considering six possible magnetic configurations (one ferromagnetic and five antiferromagnetic configurations). The results show that the nonmagnetic state is the most stable for all the predicted MH18 com pounds. We have not considered electron correlation effects on the EPC due to a lack of available computational tools for this purpose. We note, however, that previous studies17,19−21 have shown that the experimental results on several superhydrides (e.g., La, Y, Th, and Ca hydrides15, 22–25,29,30,42) are well described by the theoretical results obtained within the current EPC computation scheme without considering the electron correlation effects. On this basis, it is expected that the results in the present work offer a reasonably accurate description of the superconductivity in the newly predicted MH18 compounds.
In summary, we have identified a series of MH18 compounds containing the highest atomic hydrogen content among metal hydrides reported to date. These extreme superhydrides comprise unique H36 clathrate units stabilized at high pressures starting around 300–400 GPa. Favorable conditions of electronic density of states near the Fermi level and lattice vibrational modes that set large phonon energy scale and strong electron-phonon coupling in CeH18 generate high Tc of 329 K at 350 GPa. Meanwhile, other MH18 compounds exhibit a wide range of Tc with variable electronic, phonon and electron-phonon coupling combinations. These results offer insights into intricate mechanisms for superconductivity in superhydrides, establishing a promising platform for further exploration and optimization of diverse superhydrides that approach and may even exceed high-temperature superconductivity predicted for atomic metallic hydrogen.