# Prediction of high-temperature superconductivity in LaH<sub>4</sub> at low pressures

Christopher Renskers, Catalin D. Spataru, Marios Zacharias, Sakun Duwal,

Timothy Elmslie, Peter A. Sharma, Elena R. Margine

► To cite this version:

Christopher Renskers, Catalin D. Spataru, Marios Zacharias, Sakun Duwal, Timothy Elmslie, et al. Prediction of high-temperature superconductivity in LaH<sub>4</sub> at low pressures. Journal of Materials Chemistry C, 2025, 10.1039/d5tc02600h. hal-05294688

HAL Id: hal-05294688

https://hal.science/hal-05294688v1

Submitted on 2 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

Cite this: DOI: 10.1039/d5tc02600h

Received 7th July 2025,
Accepted 7th September 2025

DOI: 10.1039/d5tc02600h

rsc.li/materials-c

# Prediction of high-temperature superconductivity in LaH₄ at low pressures

Christopher Renskers, ID a Catalin D. Spataru, b Marios Zacharias, ID cd Sakun Duwal, e Timothy Elmslie, e Peter A. Sharma e and Elena R. Margine ID *a

Superconducting hydrides have received significant attention in the last decade due to their potential for room-temperature superconductivity. However, achieving high critical temperatures ($T_c$) typically requires extreme pressures exceeding 150 GPa. Recently, a new, low-pressure $R\bar{3}m$-LaH$_4$ phase was observed to form above approximately 20 GPa. Here, we perform first-principles calculations to investigate the electron-phonon interactions and superconducting properties of the new phase across a range of pressures. At the harmonic level, the system is found to be dynamically unstable, but this is remedied through the inclusion of anharmonic effects. We estimate that $T_c$ reaches up to 115 K at 25 GPa, driven by a high density of states at the Fermi level ($N_F$) and soft phonon modes. However, superconductivity is suppressed with increasing pressure, as $T_c$ rapidly decreases to 34 K at 60 GPa and 11 K at 100 GPa, due to a reduction in $N_F$ and phonon hardening.

## 1 Introduction

Room-temperature superconductivity has long been a highly sought after goal in materials science. The discovery of superconductivity in H$_3$S at 203 K and 155 GPa$^1$ marked a pivotal breakthrough, demonstrating that high-$T_c$ superconductivity could be realized in hydrogen-rich systems under pressure. This was soon followed by the realization of near-room-temperature superconductivity in LaH$_{10}$ at 250 K and 170 GPa,$^{2,3}$ firmly establishing binary hydrides as front-runners in the search for high-$T_c$ materials. Yttrium hydrides, such as YH$_6$ and YH$_9$, have since been both predicted and experimentally confirmed to reach $T_c$ values above 240 K at megabar pressures.$^{4,5}$ Other binary hydrides have been experimentally reported to exhibit superconductivity, including CaH$_6$ (215 K at 172 GPa),$^{6,7}$ CeH$_9$ (100 K at 100 GPa),$^{8-10}$ and ThH$_{10}$ (161 K at 175 GPa).$^{11}$ These findings demonstrate that binary hydrides have a strong potential to achieve high-$T_c$, particularly when the hydrogen fraction in a compound exceeds 0.6.$^{12}$ The high phonon frequencies of hydrogen and the lower frequency modes from the heavier ions both couple strongly to result in significant electron-phonon (e-ph) coupling, and, therefore, $T_c$. Although these

superhydrides significantly reduce the pressure needed to dissociate molecular H$_2$ by providing a lattice structure that “chemically pre-compresses” the hydrogen,$^{13}$ the required pressures remain prohibitively high for practical applications.

Among binary hydrides, significant research has focused on the lanthanum hydrides following the report of superconductivity in LaH$_{10}$. $^{2,3,14-27}$ In this case, studies have demonstrated strong e-ph coupling,$^{20}$ stability at lower pressures,$^{17}$ and the importance of anharmonic corrections for achieving dynamical stability.$^{18}$ Recently, several lanthanum hydrides with different La:H ratios have been successfully synthesized in the pressure range of 50 to 180 GPa,$^{28}$ with the cubic La$_4$H$_{23}$ phase shown to exhibit superconductivity with a maximum $T_c$ of 105 K at 118 GPa.$^{29,30}$

Building on these results and motivated by the need to identify hydrogen-rich compounds that can achieve high-$T_c$ superconductivity at lower pressures, some of the present authors investigated the formation of La hydrides in cryomilled elemental lanthanum exposed to ammonia borane$^{31}$. Structural evolution under pressures up to 60 GPa revealed a distortion from the $Fm\bar{3}m$ phase to an $R\bar{3}m$ phase, with the new rhombohedral structure becoming kinetically stable at pressures above approximately 20 GPa. Using the observed excess cell volume and comparison with the equation of state calculated via density functional theory (DFT) for various lanthanum hydrides, the stoichiometry of the $R\bar{3}m$ phase was determined to correspond to LaH$_x$ with $x \sim 4.$$^{31}$

Based on these experimental observations, we perform first-principles calculations to investigate the superconducting properties of the rhombohedral LaH$_4$ structure shown in Fig. 1.

<figure><img src="image_3.png" /></figure>

<footnote>$^a$Department of Physics, Applied Physics, and Astronomy, Binghamton University-SUNY, Binghamton, New York 13902, USA. E-mail: rmargine@binghamton.edu</footnote>

<footnote>$^b$Sandia National Laboratories, Livermore, California 94550, USA</footnote>

<footnote>$^c$Univ Rennes, INSA Rennes, CNRS, Institut FOTON-UMR 6082, Rennes F-35000, France</footnote>

<footnote>$^d$Computation-based Science and Technology Research Center, The Cyprus Institute, Aglantzia 2121, Nicosia, Cyprus</footnote>

<footnote>$^e$Sandia National Laboratories, Albuquerque, New Mexico 87185, USA</footnote>
hydrides, such as the *Im*3*m* phase of H3S, where small 0.01 Å displacements work effectively,45 such small displacement values lead to phonon instabilities in the soft-mode regions near Γ, as shown in Fig. S1.46 With the aid of iterative mixing,42 the convergence of the interatomic force constants was achieved at the 10th iteration, where three successive iterations showed little, to no, change in the anharmonic phonon dispersion. The converged anharmonic force constants were then used to construct the dynamical matrix *via* standard Fourier interpolation on a 6 × 6 × 6 *q*-mesh.

The EPW44,48–50 code was employed to investigate the e–ph interactions and superconducting properties. The electronic wave- functions required for the Wannier–Fourier interpolation51,52 were calculated on a Γ–centered 12 × 12 × 12 *k*-mesh. Nine maximally localized Wannier functions (five *d* orbitals for La and one *s* orbital for each H) were used to describe the electronic structure. The anisotropic full-bandwidth Migdal–Eliashberg equations44,53 were solved with a sparse intermediate representa- tion of the Matsubara frequencies54 on fine uniform 80 × 80 × 80 *k*– and 40 × 40 × 40 *q*-grids with an energy window of ± 0.2 eV around the Fermi level. The semiempirical Coulomb parameter, *μ**, was varied from 0.1–0.2.

<figure><img src="image_4.png" /><figcaption>Fig. 1 Crystal structure of R3m-LaH4 at 25 GPa. The two nonequivalent hydrogen atoms are labeled as H1 and H2 and the shortest H–H distance is indicated as dH–H. The figures were generated with VESTA.47</figcaption></figure>

Our calculations predict a *T*<sub>c</sub> reaching 115 K at 25 GPa, nearly
half that of LaH<sub>10</sub><sup>15,19</sup> and comparable to La<sub>4</sub>H<sub>23</sub>,<sup>29</sup> but at
significantly lower pressures. For instance, a tetragonal LaH<sub>4</sub>
phase was previously predicted to exhibit a *T*<sub>c</sub> of only 10 K at
300 GPa.<sup>15</sup> Our findings reinforce the potential of the lanthanum
hydride family for the development of high-temperature super-
conducting materials at low to ambient pressures.

## 2 Methods

First principle calculations were carried out with the Quantum
ESPRESSO (QE) package.32,33 We employed optimized norm-
conversing Vanderbilt pseudopotentials (ONCVPSP)34 from the
Pseudo Dojo library35 generated with the scalar-relativistic
revised Perdew–Burke–Ernzerhof (PBEsol) parametrization.36
A plane wave kinetic-energy cutoff of 120 Ry for the wavefunc-
tions, and 480 Ry for the charge density and potential, were
used. For the Brillouin-zone integration of the 5-atom unit cell,
we used a Γ-centered 12 × 12 × 12 *k*-mesh37 with a Methfessel–
Paxton38 smearing of 0.02 Ry. The atomic positions and lattice
parameters were optimized until the total energy was converged
within 10<sup>-6</sup> Ry and the force on each atom was less than
10<sup>-4</sup> Ry Å<sup>-1</sup>. The dynamical matrices and the linear variation
of the self-consistent potential were first computed using
density-functional perturbation theory (DFPT)39 on the irredu-
cible set of a regular 6 × 6 × 6 *q*-mesh.

The force constants computed by DFPT were used as a
starting point to calculate phonon anharmonicity *via* the anhar-
monic special displacement method (ASDM)40–42 within the fra-
mework of the self-consistent phonon theory.43 The ASDM is used
as implemented in the Zacharias–Giustino (ZG) code of the EPW
package.44 For our ASDM calculations, we employed finite differ-
ences of amplitude 0.2 Å to iteratively compute the interatomic
force constants of ZG configurations at 300 K in 2 × 2 × 2
supercells. We find that such large displacements in low-
symmetry systems involving light-mass atoms improve numerical
stability and provide a better representation of the anharmonic
behavior, particularly for capturing higher-order contributions
to the effective force constants. In contrast to high-symmetry

## 3 Results and discussion

Guided by experiments, we consider the *R*3*m* rhombohedral phase (space group no. 166) for the LaH₄ structure. Fig. 2(a) shows our X-ray Diffraction (XRD) results for cryomilled La mixed with ammonia borane, measured in a diamond anvil cell at a pressure of 29.1 GPa. The XRD data reveal the co-existence of *R*3*m* and FCC La-hydride phases. Fig. 2(b) shows the cell volume of La-hydride inferred from XRD data as a function of pressure. The experimental cell volume is systemically larger than that of the FCC LaH₃ phase over the investigated pressure range.

Utilizing the experimentally determined unit cell and posi-
tions of the La atoms, the positions of the H atoms were derived
in ref. 31 based on symmetry considerations and atomic
relaxation using DFT. The enthalpy of the predicted rhombo-
hedral R3m LaH4 structure was found to be lower by about
0.2 eV f.u.⁻¹ than that of several alternative, symmetry-broken
LaH4 configurations obtained *via ab initio* molecular dynamics
followed by atomic relaxation. On the other hand, the I4/mmm
proposed in ref. 15 remains thermodynamically more favorable
than the R3m phase in the considered pressure range, as shown
in Fig. S2.⁴⁶ While the R3m phase is not the thermodynamic
ground state, our theoretical calculations (including anharmonic
effects) indicate that it is dynamically stable, meaning it is
kinetically stable in the limit of low temperature. Our experi-
mental data corroborate this, suggesting that the R3m phase is
observable (thermodynamically metastable) at room tempera-
ture. This indicates that it is even more likely to be observable
(kinetically stabilized) at low temperatures, particularly near the
predicted transition temperature Tc. A similar kinetics-based
stabilization mechanism has been shown to overcome the highly
unfavorable thermodynamics of Alane at room temperature.⁵⁵

<figure><img src="image_5.png" /></figure>
<table><caption>**Table 1** Calculated lattice parameters, shortest H-H distance, and atomic coordinates for the conventional cell of LaH₄ at 25, 60, and 100 GPa. The structure adopts the R3m space group with γ = 120° at all pressures</caption><thead><tr><th>Pressure (GPa)</th><th>a = b (Å)</th><th>c (Å)</th><th>d<sub>H-H</sub> (Å)</th><th>Atomic coordinates (fractional)</th></tr></thead><tbody><tr><td rowspan="3">25</td><td rowspan="3">3.54</td><td rowspan="3">9.87</td><td rowspan="3">0.96</td><td>La (3a)</td><td>0.000</td><td>0.000</td><td>0.000</td></tr><tr><td>H1 (6c)</td><td>0.000</td><td>0.000</td><td>0.231</td></tr><tr><td>H2 (6c)</td><td>0.333</td><td>0.666</td><td>0.217</td></tr><tr><td rowspan="3">60</td><td rowspan="3">3.20</td><td rowspan="3">9.89</td><td rowspan="3">0.92</td><td>La (3a)</td><td>0.000</td><td>0.000</td><td>0.000</td></tr><tr><td>H1 (6c)</td><td>0.000</td><td>0.000</td><td>0.215</td></tr><tr><td>H2 (6c)</td><td>0.333</td><td>0.666</td><td>0.213</td></tr><tr><td rowspan="3">100</td><td rowspan="3">2.99</td><td rowspan="3">9.78</td><td rowspan="3">0.88</td><td>La (3a)</td><td>0.000</td><td>0.000</td><td>0.000</td></tr><tr><td>H1 (6c)</td><td>0.000</td><td>0.000</td><td>0.209</td></tr><tr><td>H2 (6c)</td><td>0.333</td><td>0.666</td><td>0.212</td></tr></tbody></table>

The electronic band structure and density of state (DOS) plots in Fig. 3 indicate that the R3m-LaH₄ phase is metallic across all investigated pressures. The DOS at the Fermi level (N<sub>F</sub>) comes from a combination of La and H states with La boasting about 50%, 68%, and 81% increase over H states at 25, 60, and 100 GPa. For hydrogen, the unit formed by the vertically adjacent H2 atoms, as seen in Fig. 1, accounts for the bulk of the hydrogen states at the Fermi level, contributing 86%, 82%, and 81% of the total hydrogen states at the Fermi level, as depicted in the second panel of Fig. 3. At 25 GPa, N<sub>F</sub> reaches its highest value of 0.81 states per eV f.u.<sup>-1</sup>, comparable to values reported

<figure><img src="image_6.png" /><figcaption>**Fig. 3** Electronic band structure with orbital characters, and total and projected density of states (DOS) of LaH₄ at (a)–(c) 25, 60, and 100 GPa. The orbital character is shown in red for H and blue for La states. The total DOS is shown in black, while the projected DOS corresponding to H1, H2, and La atoms are shown with red, dashed red, and blue lines, respectively.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 2** (a) Powder X-ray diffraction data for cryomilled La mixed with ammonia borane, showing the co-existence of R3m and FCC La-hydride phases under high pressure (29.1 GPa). (b) The cell volume of the La-hydride phase inferred from X-ray diffraction data as a function of pressure. DFT simulations of the equation of state are shown for the proposed R3m LaH₄ phase and the FCC LaH₃ phase, as indicated. The data presented in this figure are from ref. 31.</figcaption></figure>

The R3m-LaH₄ phase is predicted to adopt a clathrate structure that is characteristic of other high-temperature superconducting hydrides.<sup>7,18,56–63</sup> The structure consists of a La atom occupying the 3a (0, 0, 0) Wyckoff site and two nonequivalent H atoms, labeled as H1 and H2, located at 6c (0, 0, z₁) and 6c (1/3, 2/3, z₂) Wyckoff sites. The calculated structural parameters at 25, 60, and 100 GPa are provided in Table 1. Each La atom is enclosed in a cage formed by 14 H atoms, as seen in Fig. 1. This matches the crystal structure of R3m-TeH₄ predicted to stabilize above 230 GPa and reach a T<sub>c</sub> of about 70 K.<sup>64</sup> The H-hexagonal rings are slightly buckled at 25 GPa (~0.1 Å) but, as in R3m-TeH₄, become nearly flat at higher pressures. The H1 atoms form a H₂ unit as marked by the red bond in Fig. 1. This bond marks the shortest H-H distance in the structure, with a value d<sub>H-H</sub> of 0.96, 0.92, and 0.88 Å for 25, 60, and 100 GPa, respectively. These bond length values are close to the H-H distance of 1 Å predicted for metallic hydrogen near 500 GPa<sup>65</sup> and 0.86 Å for TeH₄ at 300 GPa,<sup>64</sup> but slightly smaller than 1.1 Å for LaH₁₀ in the 150-300 GPa pressure range<sup>15,66</sup> and 1.3 Å for La₄H₂₃ at 118 GPa.<sup>29</sup>
for other high-T_c La-H phases (e.g., ~0.93 states per eV f.u.⁻¹ for LaH₁₀ at 150 GPa¹⁸ and 0.79 states per eV per La for La₄H₂₃ at 120 GPa²⁹). This high DOS is largely attributed to a flat electronic band around the Γ point. Furthermore, approximately 0.2 eV below the Fermi level, a Van-Hove-like singularity emerges due to another flat band along the L-B₁ and B-Z high-symmetry directions. The presence of these dispersionless bands at 25 GPa induces a significant variation in the DOS in the vicinity of E_F that is captured by the full-bandwidth approach used to solve the superconducting Migdal-Eliashberg equations.⁵³ At higher pressures, the flat bands evolve into parabolic dispersions, resulting in a marked decrease in N_F by approximately 33% at 60 GPa and 46% at 100 GPa, respectively. To note, the effect of spin-orbit coupling on the electronic structure was considered and found to be negligible, as shown in Fig. S3.⁴⁶

To further analyze the electronic structure, we calculated the charge density difference between the LaH₄ structure and the sum of its constituent atoms at 25 and 100 GPa. As shown in Fig. 4(a) and (b), there is a buildup of charge on the hydrogen

atoms, but, surprisingly, no charge depletion around the La atoms. This suggests minimal to no charge transfer between La and H atoms. Meanwhile, charge depletion is observed between two vertically adjacent H₂ atoms, becoming significantly more pronounced at 100 GPa. This trend indicates the formation of H₂ units at higher pressure, resembling molecular hydrogen. This picture is further supported by the electron localization function (ELF) plots in Fig. 4(c) and (d), taken along the (1 1 0) and (0 0 1) planes. Panel (c) reveals the formation of H₂ units between adjacent H₂ atoms, as well as the repulsion between La and H1 atoms, which gives rise to the teardrop-shaped features around the H1 atoms. Panel (d) illustrates how the H atoms arrange into a hexagonal ring surrounding the La atom, highlighting the structural characteristics of R\~3m-LaH₄.

Fig. 5 presents the vibrational properties of LaH₄. At the harmonic level, depicted by the solid gray lines, the structure exhibits dynamic instabilities across all investigated pressures, with the most pronounced negative phonon modes observed at 25 GPa. This behavior is common among many superconducting hydrides and is typically resolved by accounting for quantum anharmonic effects.¹⁸,⁶⁸⁻⁷¹ When applying the ASDM, these instabilities are eliminated, as shown by the solid black lines. Notably, the low-frequency La modes at 25 GPa undergo significant renormalization under the ASDM, which has important implications for the superconducting properties of the material.

The phonon dispersion displays a distinct separation between modes associated with lanthanum and hydrogen.

<figure><img src="image_8.png" /><figcaption>**Fig. 4** Charge density difference between the LaH₄ crystal structure and the sum of its constituent atoms at (a) 25 GPa and (b) 100 GPa. The yellow and green colors represent charge accumulation and depletion regions, respectively, with an isosurface value set to 7 × 10⁻² e Å⁻³. Electron localization function (ELF) for LaH₄ at 25 GPa taken along the (c) (1 1 0) and (d) (0 0 1) Miller planes, respectively, with a contour spacing set to 0.1. All plots were generated with VESTA.⁴⁷</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 5** (a)–(c) Harmonic and anharmonic phonon dispersion, phonon density of states (PHDOS), isotropic Eliashberg spectral function (α²F), and electron-phonon coupling strength (λ) of LaH₄ at 25, 60, and 100 GPa, respectively. The total PHDOS is decomposed with respect to the vibrations of H (red) and La (blue) atoms. The anharmonic phonon dispersions were computed for a temperature of 300 K.</figcaption></figure>

<figure><img src="image_10.png" /></figure>
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 6 (a) Histograms of the energy-dependent distribution of the superconducting gap $\Delta_{nk}$ as a function of temperature in LaH$_{4}$ at 25 and 60 GPa with $\mu^* = 0.10$ (black) and $\mu^* = 0.15$ (blue). The solid lines are guides to the eye. (b) and (c) Momentum-resolved superconducting gap on the Fermi surface in LaH$_{4}$ at 25 and 60 GPa with $\mu^* = 0.10$, generated with FermiSurfer.⁶⁷</figcaption></figure>

The acoustic modes arise solely from the vibration of the La atoms, while the intermediate- and high-frequency modes originate exclusively from the motion of the H atoms. From the comparison of the Eliashberg spectral function ($\alpha^2 F$) and the phonon density of states (PHDOS) in the middle and right panels of Fig. 5, we can see that most of the e-ph coupling comes from the hydrogen phonon modes. At 25 GPa, for example, 66% of the total e-ph coupling constant $\lambda$ of 1.64 comes from the H modes. This $\lambda$ value is comparable to those computed for LaH$_{10}$ (1.78 and 1.86 at 300 GPa$^{15,19}$) and La$_{4}$H$_{23}$ (1.49 at 100 GPa$^{72}$), and almost four times larger than that of a predicted tetragonal LaH$_{4}$ phase (0.43 at 300 GPa$^{15}$). As pressure increases, the phonon frequencies harden across all regions, and the DOS at the Fermi level decreases. These combined effects lead to a reduction in $\lambda$, with values of 0.79 and 0.53 at 60 GPa and 100 GPa, respectively. A similar pressure dependence has been observed in LaH$_{10}$ and La$_{4}$H$_{23}$ superconductors.$^{3,15,29}$

To understand the superconducting properties, we solved the anisotropic full-bandwidth Migdal-Eliashberg equations for a Coulomb parameter $\mu^*$ in the 0.10-0.20 range, consistent with values used in other studies on superconductivity in lanthanum hydrides.$^{15,19,29}$ Fig. 6 presents the energy distribution of the superconducting gap, $\Delta_{nk}$, as a function of temperature along with its momentum-resolved k-dependence on the Fermi surface at select pressure and $\mu^*$ values. Our calculations reveal that LaH$_{4}$ exhibits a single anisotropic gap, with an estimated $T_c^{\text{AME}}$ of 115 K for $\mu^* = 0.10$ at 25 GPa. In comparison, the McMillan (McM) equation,$^{73}$ the Allen-Dynes (AD) formula,$^{74}$ the machine-learned (ML) SISSO model,$^{75}$ and the isotropic Migdal-Eliashberg (iME) formalism yield $T_c^{\text{McM}} = 72.5$ K, $T_c^{\text{AD}} = 85.4$ K, $T_c^{\text{ML}} = 102.7$ K, and $T_c^{\text{iME}} = 117$ K, respectively. To put this into context, $T_c^{\text{iME}}$ was predicted to be 254 K at 300 GPa in LaH$_{10}$,$^{15}$ 95 K at 100 GPa in La$_{4}$H$_{23}$,$^{29}$ and only 10 K at 300 GPa in a tetragonal LaH$_{4}$ phase$^{15}$ for $\mu^* = 0.10$. The estimated $T_c^{\text{AME}}$ in R$\bar{3}m$-LaH$_{4}$ is less than half that of LaH$_{10}$ but slightly higher than that in La$_{4}$H$_{23}$, and more importantly, it could be achieved at significantly lower pressures than in these cases. The critical temperature decreases significantly with pressure, with $T_c^{\text{AME}}$ dropping to 33 K at 60 GPa and 14 K at 100 GPa. Results for different $\mu^*$ values and various approaches for calculating the critical temperature are summarized in Table 2.

As mentioned above, the rapid decrease in $T_c$ with increasing pressure can be directly attributed to a reduction in the DOS at the Fermi level and the hardening of the phonon frequencies. Delving deeper, superconducting hydrides are designed to provide a lattice that promotes the dissociation of molecular H$_{2}$, facilitating the formation of metallic hydrogen under pressure.$^{13}$ Consequently, a reduction in the H-H distance within the H$_{2}$ units may suppress superconductivity, aligning with our observations. As summarized in Table 1, the highest $T_c$ of 115 K is achieved at 25 GPa, where the shortest H-H distance is $d_{H-H} = 0.96$ Å. However, $T_c$ drops sharply as pressure increases, reaching just 11 K at 100 GPa where $d_{H-H} = 0.88$ Å. For reference, the bond length of a H$_{2}$ molecule is approximately 0.74 Å,$^{76}$ while the H-H distance in metallic hydrogen is predicted to be around 1 Å at 500 GPa.$^{65}$ This trend, along with the increased charge depletion between the H$_{2}$ units at higher pressures, suggests that hydrogen may transition toward a

<table><caption>**Table 2** Properties of LaH$_{4}$ at 25, 60, and 100 GPa: density of states at the Fermi level ($N_{F}$), logarithmic average phonon frequency ($\omega_{\text{log}}$), total electron-phonon coupling strength ($\lambda$), semiempirical Coulomb parameter ($\mu^*$), and superconducting critical temperature ($T_c$). The $T_c$ values are calculated using different methodologies: McMillan equation ($T_c^{\text{AME}}$), Allen-Dynes formula ($T_c^{\text{AD}}$), machine-learned SISSO mode ($T_c^{\text{ML}}$), isotropic Migdal-Eliashberg formalism ($T_c^{\text{iME}}$), and anisotropic Migdal-Eliashberg formalism ($T_c^{\text{AME}}$)</caption><thead><tr><th>Pressure (GPa)</th><th>N<sub>F</sub> (states per eV f.u.<sup>-1</sup>)</th><th>ω<sub>log</sub> (meV)</th><th>λ</th><th>μ<sup>*</sup></th><th>T<sub>c</sub><sup>McM</sup> (K)</th><th>T<sub>c</sub><sup>AD</sup> (K)</th><th>T<sub>c</sub><sup>ML</sup> (K)</th><th>T<sub>c</sub><sup>iME</sup> (K)</th><th>T<sub>c</sub><sup>AME</sup> (K)</th></tr></thead><tbody><tr><td rowspan="3">25</td><td rowspan="3">0.81</td><td rowspan="3">50.6</td><td rowspan="3">1.64</td><td>0.10</td><td>72.5</td><td>85.4</td><td>102.7</td><td>117</td><td>115</td></tr><tr><td>0.15</td><td>62.8</td><td>71.5</td><td>85.1</td><td>103</td><td>102</td></tr><tr><td>0.20</td><td>53.1</td><td>59.1</td><td>68.7</td><td>93</td><td>92</td></tr><tr><td rowspan="3">60</td><td rowspan="3">0.54</td><td rowspan="3">48.7</td><td rowspan="3">0.79</td><td>0.10</td><td>26.0</td><td>27.4</td><td>25.3</td><td>29</td><td>34</td></tr><tr><td>0.15</td><td>17.8</td><td>18.6</td><td>16.2</td><td>21</td><td>24</td></tr><tr><td>0.20</td><td>10.9</td><td>11.2</td><td>10.3</td><td>16</td><td>15</td></tr><tr><td rowspan="3">100</td><td rowspan="3">0.44</td><td rowspan="3">56.1</td><td rowspan="3">0.53</td><td>0.10</td><td>9.8</td><td>10.1</td><td>7.3</td><td>9</td><td>11</td></tr><tr><td>0.15</td><td>4.4</td><td>4.5</td><td>3.0</td><td>9</td><td>9</td></tr><tr><td>0.20</td><td>1.3</td><td>1.3</td><td>0.9</td><td>—</td><td>6</td></tr></tbody></table>
<figure><img src="image_13.png" /></figure>

molecular H₂-like state rather than a metallic phase under compression.

## 4 Conclusion

We carried out an *ab initio* study to explore the superconducting potential of a new low-pressure rhombohedral LaH₄ phase. Our results show that the inclusion of anharmonic corrections is crucial for stabilizing the crystal structure, highlighting the importance of these effects when investigating lanthanum hydrides under pressure. Furthermore, we find that the superconducting temperature can reach up to 115 K at 25 GPa but decreases rapidly with increasing pressure, a common trend in hydride superconductors. Besides experimentally confirming superconductivity of the rhombohedral phase in the 25–100 GPa range, it would be interesting to explore whether this phase could be stabilized down to ambient pressure. These results are exciting as they contribute to the ongoing search for hydrogen-rich compounds capable of achieve high-temperature superconductivity at lower pressures.

## Conflicts of interest

There are no conflicts to declare.

## Data availability

The data supporting this article is included in the manuscript. Supplementary information is available. See DOI: https://doi.org/10.1039/d5tc02600h.

## Acknowledgements

We would like to thank Dr. Vitalie Stavila for useful discussions. C. R. and E. R. M. acknowledge support from the National Science Foundation (NSF) under award no. DMR-2035518. This work used the Frontera supercomputer at the Texas Advanced Computing Center *via* the Leadership Resource Allocation (LRAC) award DMR22004 and the Expanse system at the San Diego Supercomputer Center through the ACCESS allocation TG-DMR180071. M. Z. acknowledges funding by the European Union (project ULTRA-2DPK/HORIZON-MSCA-2022-PF/01/ grant agreement no. 101106654) and computational resources from the EuroHPC Joint Undertaking and supercomputer LUMI https://lumi-supercomputer.eu/, hosted by CSC (Finland) and the LUMI consortium through a EuroHPC Extreme Scale Access call. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy (DOE)'s National Nuclear Security Administration under contract no. DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the U.S. Government. The XRD work was performed on APS beam time award from the Advanced Photon Source, a U.S. DOE Office of Science user facility operated for the DOE Office of

Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. HPCAT operations are supported by DOE-NNSA's Office of Experimental Sciences.

## References

1. A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov and S. I. Shylin, Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system, *Nature*, 2015, **525**, 73.

2. M. Somayazulu, M. Ahart, A. K. Mishra, Z. M. Geballe, M. Baldini, Y. Meng, V. V. Struzhkin and R. J. Hemley, Evidence for Superconductivity above 260 K in Lanthanum Superhydride at Megabar Pressures, *Phys. Rev. Lett.*, 2019, **122**, 027001.

3. A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari, L. Balicas, F. F. Balakirev, D. E. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz and M. I. Eremets, Superconductivity at 250 K in lanthanum hydride under high pressures, *Nature*, 2019, **569**, 528.

4. P. P. Kong, V. S. Minkov, M. A. Kuzovnikov, S. P. Besedin, A. P. Drozdov, S. Mozaffari, L. Balicas, F. F. Balakirev, V. B. Prakapenka, E. Greenberg, D. A. Knyazev and M. I. Eremets, Superconductivity up to 243 K in yttrium hydrides under high pressure, *Nat. Commun.*, 2021, **12**, 5075.

5. A. V. Troyan, A. O. Lyakhov, A. O. Kurnosov, I. A. Abrikosov, A. O. Shorikov, A. O. Ivanovskii, A. V. Baranov and A. V. Chulkov, Anomalous High-Temperature Superconductivity in YH6, *Adv. Mater.*, 2021, **33**, 2006832.

6. Z. Li, X. He, C. Zhang, X. Wang, S. Zhang, Y. Jia, S. Feng, K. Lu, J. Zhao, J. Zhang, B. Min, Y. Long, R. Yu, L. Wang, M. Ye, Z. Zhang, V. Prakapenka, S. Chariton, P. A. Ginsberg, J. Bass, S. Yuan, H. Liu and C. Jin, Superconductivity above 200 K discovered in superhydrides of calcium, *Nat. Commun.*, 2022, **13**, 2863.

7. L. Ma, K. Wang, Y. Xie, X. Yang, Y. Wang, M. Zhou, H. Liu, X. Yu, Y. Zhao, H. Wang, G. Liu and Y. Ma, High-Temperature Superconducting Phase in Clathrate Calcium Hydride CaH6 up to 215 K at a Pressure of 172 GPa, *Phys. Rev. Lett.*, 2022, **128**, 167001.

8. N. P. Salke, M. M. Davari Esfahani, Y. Zhang, I. A. Kruglov, J. Zhou, Y. Wang, E. Greenberg, V. B. Prakapenka, J. Liu, A. R. Oganov and J.-F. Lin, Synthesis of clathrate cerium superhydride CeH9 at 80–100 GPa with atomic hydrogen sublattice, *Nat. Commun.*, 2019, **10**, 4453.

9. W. Chen, D. V. Semenok, X. Huang, H. Shu, X. Li, D. Duan, T. Cui and A. R. Oganov, High-Temperature Superconducting Phases in Cerium Superhydride with a $T_c$ up to 115 K below a Pressure of 1 Megabar, *Phys. Rev. Lett.*, 2021, **127**, 117001.

10. Z.-Y. Cao, S. Choi, L.-C. Chen, P. Dalladay-Simpson, H. Jang, F. A. Gorelli, J.-F. Yan, S.-G. Jung, G. Huang, L. Yu, Y. Lee, J. Kim, T. Park and X.-J. Chen, *Probing superconducting gap in CeH<sub>9</sub> under pressure*, *arXiv*, 2024, preprint, arXiv:2401.12682 cond-mat.supr-con, DOI: 10.48550/arXiv.2401.1268.
<figure><img src="image_14.png" /></figure>

11 D. V. Semenok, A. G. Kvashnin, A. G. Ivanova, V. Svitlyk, V. Y. Fominski, A. V. Sadakov, O. A. Sobolevskiy, V. M. Pudalov, I. A. Troyan and A. R. Oganov, Superconductivity at 161 K in thorium hydride ThH10: Synthesis and properties, *Mater. Today*, 2020, **33**, 36.

12 I. A. Wrona, P. Niegodajew and A. P. Durajski, A recipe for an effective selection of promising candidates for high-temperature superconductors among binary hydrides, *Mater. Today Phys.*, 2024, **46**, 101499.

13 N. W. Ashcroft, Hydrogen Dominant Metallic Alloys: High Temperature Superconductors?, *Phys. Rev. Lett.*, 2004, **92**, 187002.

14 Z. M. Geballe, H. Liu, A. K. Mishra, M. Ahart, M. Somayazulu, Y. Meng, M. Baldini and R. J. Hemley, Synthesis and stability of lanthanum superhydrides, *Angew. Chem., Int. Ed.*, 2018, **57**, 688.

15 H. Liu, I. I. Naumov, R. Hoffmann, N. W. Ashcroft and R. J. Hemley, Potential high-$T_c$ superconducting lanthanum and yttrium hydrides at high pressure, *Proc. Natl. Acad. Sci. U. S. A.*, 2017, **114**, 6990.

16 H. Liu, I. I. Naumov, Z. M. Geballe, M. Somayazulu, J. S. Tse and R. J. Hemley, Dynamics and superconductivity in compressed lanthanum superhydride, *Phys. Rev. B*, 2018, **98**, 100102.

17 D. Sun, V. S. Minkov, S. Mozaffari, Y. Sun, Y. Ma, S. Chariton, V. B. Prakapenka, M. I. Eremets, L. Balicas and F. F. Balakirev, High-temperature superconductivity on the verge of a structural instability in lanthanum superhydride, *Nat. Commun.*, 2021, **12**, 6863.

18 I. Errea, F. Belli, L. Monacelli, A. Sanna, T. Koretsune, T. Tadano, R. Bianco, M. Calandra, R. Arita, F. Mauri and J. A. Flores-Livas, Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride, *Nature*, 2020, **578**, 66.

19 C. Wang, S. Yi and J.-H. Cho, Multiband nature of room-temperature superconductivity in $LaH_{10}$ at high pressure, *Phys. Rev. B*, 2020, **101**, 104506.

20 Y. L. Wu, X. H. Yu, J. Z. L. Hasaien, F. Hong, P. F. Shan, Z. Y. Tian, Y. N. Zhai, J. P. Hu, J. G. Cheng and J. Zhao, Ultrafast dynamics evidence of strong coupling superconductivity in $LaH_{10} \pm \delta$, *Nat. Commun.*, 2024, **15**, 9683.

21 Z. Wu, Y. Sun, A. P. Durajski, F. Zheng, V. Antropov, K.-M. Ho and S. Wu, Effect of doping on the phase stability and superconductivity in $LaH_{10}$, *Phys. Rev. Mater.*, 2023, **7**, L101801.

22 M. Caussé, G. Geneste and P. Loubeyre, Superionicity of $H^\delta$ in $LaH_{10}$ superhydride, *Phys. Rev. B*, 2023, **107**, L060301.

23 K. K. Ly and D. M. Ceperley, Stability and distortion of fcc $LaH_{10}$ with path-integral molecular dynamics, *Phys. Rev. B*, 2022, **106**, 054106.

24 Y. Watanabe, T. Nomoto and R. Arita, Quantum and temperature effects on the crystal structure of superhydride $LaH_{10}$: A path integral molecular dynamics study, *Phys. Rev. B*, 2022, **105**, 174111.

25 X. Liang, A. Bergara, X. Wei, X. Song, L. Wang, R. Sun, H. Liu, R. J. Hemley, L. Wang, G. Gao and Y. Tian,

Prediction of high-$T_c$ superconductivity in ternary lanthanum borohydrides, *Phys. Rev. B*, 2021, **104**, 134501.

26 A. K. Verma, P. Modak, F. Schrodi, A. Aperis and P. M. Oppeneer, Prediction of an unusual trigonal phase of superconducting $LaH_{10}$ stable at high pressures, *Phys. Rev. B*, 2021, **104**, 174506.

27 Y. Ge, F. Zhang and R. J. Hemley, Room-temperature superconductivity in boron- and nitrogen-doped lanthanum superhydride, *Phys. Rev. B*, 2021, **104**, 214505.

28 D. Laniel, F. Trybel, B. Winkler, F. Knoop, T. Fedotenko, S. Khandarkhaeva, A. Aslandukova, T. Meier, S. Chariton, K. Glazyrin, V. Milman, V. Prakapenka, I. A. Abrikosov, L. Dubrovinsky and N. Dubrovinskaia, High-pressure synthesis of seven lanthanum hydrides with a significant variability of hydrogen content, *Nat. Commun.*, 2022, **13**, 6987.

29 J. Guo, D. Semenok, G. Shutov, D. Zhou, S. Chen, Y. Wang, K. Zhang, X. Wu, S. Luther, T. Helm, X. Huang and T. Cui, Unusual metallic state in superconducting A15-type $La4H23$, *Natl. Sci. Rev.*, 2024, **11**, nwa149.

30 S. Cross, J. Buhot, A. Brooks, W. Thomas, A. Kleppe, O. Lord and S. Friedemann, High-temperature superconductivity in $La_4H_{23}$ below 100 GPa, *Phys. Rev. B*, 2024, **109**, L020503.

31 S. Duwal, V. Stavila, C. Spataru, M. Shivanna, P. Allen, T. Elmslie, C. T. Seagle, J. Jeffries, N. Velisavljevic, J. Smith, P. Chow, Y. Xiao, M. Somayazulu and P. A. Sharma, *Enhancement of hydrogen absorption and hypervalent metal hydride formation in lanthanum using cryogenic ball milling*, arXiv, 2025, preprint, arXiv:2506.23980, DOI: **10.48550/arXiv.2506.23980**.

32 P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. auri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari and R. M. Wentzcovitch, QUANTUM ESPRESSO: a modular and opensource software project for quantum simulations of materials, *J. Phys.: Condens. Matter*, 2009, **21**, 395502.

33 P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. D. Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawamura, H.-Y. Ko, A. Kokalj, E. Küçükbenli, M. Lazzeri, M. Marsili, N. Marzari, F. Mauri, N. L. Nguyen, H.-V. Nguyen, A. O. de-la Roza, L. Paulatto, S. Poncé, D. Rocca, R. Sabatini, B. Santra, M. Schlipf, A. P. Seitsonen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari, N. Vast, X. Wu and S. Baroni, Advanced capabilities for materials modelling with Quantum ESPRESSO, *J. Phys.: Condens. Matter*, 2017, **29**, 465901.

34 D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, *Phys. Rev. B: Condens. Matter Mater. Phys.*, 2013, **88**, 085117.
<figure><img src="image_15.png" /></figure>

35 M. van Setten, M. Giantomassi, E. Bousquet, M. Verstraete, D. Hamann, X. Gonze and G.-M. Rignanese, The Pseudo-Dojo: Training and grading a 85 element optimized norm-conserving pseudopotential table, *Comput. Phys. Commun.*, 2018, **226**, 39.

36 J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou and K. Burke, Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, *Phys. Rev. Lett.*, 2008, **100**, 136406.

37 H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, *Phys. Rev. B*, 1976, **13**, 5188.

38 M. Methfessel and A. T. Paxton, High-precision sampling for Brillouin-zone integration in metals, *Phys. Rev. B: Condens. Matter Mater. Phys.*, 1989, **40**, 3616.

39 S. Baroni, S. de Gironcoli, A. Dal Corso and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, *Rev. Mod. Phys.*, 2001, **73**, 515.

40 M. Zacharias and F. Giustino, One-shot calculation of temperature-dependent optical spectra and phononinduced band-gap renormalization, *Phys. Rev. B*, 2016, **94**, 075125.

41 M. Zacharias and F. Giustino, Theory of the special displacement method for electronic structure calculations at finite temperature, *Phys. Rev. Res.*, 2020, **2**, 013357.

42 M. Zacharias, G. Volonakis, F. Giustino and J. Even, Anharmonic lattice dynamics via the special displacement method, *Phys. Rev. B*, 2023, **108**, 035155.

43 N. R. Werthamer, Self-consistent phonon formulation of anharmonic lattice dynamics, *Phys. Rev. B*, 1970, **1**, 572.

44 H. Lee, S. Poncé, K. Bushick, S. Hajinazar, J. Lafuente-Bartolome, J. Leveillee, C. Lian, J.-M. Lihm, F. Macheda, H. Mori, H. Paudyal, W. H. Sio, S. Tiwari, M. Zacharias, X. Zhang, N. Bonini, E. Kioupakis, E. R. Margine and F. Giustino, Electron-phonon physics from first principles using the EPW code, *npj Comput. Mater.*, 2023, **9**, 156.

45 S. B. Mishra, H. Mori and E. R. Margine, *Electronphonon vertex correction effect in superconducting H₃S*, arXiv, 2025, preprint, arXiv:2507.01897 cond-mat.supr-con, DOI: 10.48550/arXiv.2507.01897.

46 See Fig. S1-S3.

47 K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, *J. Appl. Crystallogr.*, 2011, **44**, 1272.

48 F. Giustino, M. L. Cohen and S. G. Louie, Electronphonon interaction using Wannier functions, *Phys. Rev. B*, 2007, **76**, 165108.

49 E. R. Margine and F. Giustino, Anisotropic Migdal-Eliashberg theory using Wannier functions, *Phys. Rev. B*, 2013, **87**, 024505.

50 S. Poncé, E. Margine, C. Verdi and F. Giustino, EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions, *Comput. Phys. Commun.*, 2016, **209**, 116.

51 N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, *Rev. Mod. Phys.*, 2012, **84**, 1419.

52 G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibáñez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Poncé, T. Ponweiser, J. Qiao, F. Thöle, S. S. Tsirkin, M. Wierzbowska, N. Marzari, D. Vanderbilt, I. Souza, A. A. Mostofi and J. R. Yates, Wannier90 as a community code: new features and applications, *J. Phys.: Condens. Matter*, 2020, **32**, 165902.

53 R. Lucrezi, P. P. Ferreira, S. Hajinazar, H. Mori, H. Paudyal, E. R. Margine and C. Heil, Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides, *Commun. Phys.*, 2024, **7**, 33.

54 H. Mori, T. Nomoto, R. Arita and E. R. Margine, Efficient anisotropic Migdal-Eliashberg calculations with an intermediate representation basis and Wannier interpolation, *Phys. Rev. B*, 2024, **110**, 064505.

55 V. Stavila, S. Li, C. Dun, M. A. T. Marple, H. E. Mason, J. L. Snider, J. E. r Reynolds, F. El Gabaly, J. D. Sugar, C. D. Spataru, X. Zhou, B. Dizdar, E. H. Majzoub, R. Chatterjee, J. Yano, H. Schlöombeg, B. V. Lotsch, J. J. Urban, B. C. Wood and M. D. Allendorf, Defying Thermodynamics: Stabilization of Alane Within Covalent Triazine Frameworks for Reversible Hydrogen Storage, *Angew. Chem., Int. Ed.*, 2021, **60**, 25815.

56 F. Peng, Y. Sun, C. J. Pickard, R. J. Needs, Q. Wu and Y. Ma, Hydrogen Clathrate Structures in Rare Earth Hydrides at High Pressures: Possible Route to Room-Temperature Superconductivity, *Phys. Rev. Lett.*, 2017, **119**, 107001.

57 P. Kong, V. S. Minkov, M. A. Kuzovnikov, A. P. Drozdov, S. P. Besedin, S. Mozaffari, L. Balicas, F. F. Balakirev, V. B. Prakapenka, S. Chariton, D. A. Knyazev, E. Greenberg and M. I. Eremets, Superconductivity up to 243 K in the yttrium-hydrogen system under high pressure, *Nat. Commun.*, 2021, **12**, 5075.

58 Y. Li, J. Hao, H. Liu, J. S. Tse, Y. Wang and Y. Ma, Pressure-stabilized superconductive yttrium hydrides, *Sci. Rep.*, 2015, **5**, 9948.

59 X. Feng, J. Zhang, G. Gao, H. Liu and H. Wang, Compressed sodalite-like mgh6 as a potential hightemperature superconductor, *RSC Adv.*, 2015, **5**, 59292.

60 J. Zhao, B. Ao, S. Li, T. Gao and X. Ye, Phase Diagram and Bonding States of Pu-H Binary Compounds at High Pressures, *J. Phys. Chem. C*, 2020, **124**, 7361.

61 Y.-L. Hai, N. Lu, H.-L. Tian, M.-J. Jiang, W. Yang, W.-J. Li, X.-W. Yan, C. Zhang, X.-J. Chen and G.-H. Zhong, Cage Structure and Near Room-Temperature Superconductivity in TbHn (n = 1-12), The, *J. Phys. Chem. C*, 2021, **125**, 3640.

62 D. V. Semenok, D. Zhou, A. G. Kvashnin, X. Huang, M. Galasso, I. A. Kruglov, A. G. Ivanova, A. G. Gavriliuk, W. Chen, N. V. Tkachenko, A. I. Boldyrev, I. Troyan, A. R. Oganov and T. Cui, Novel Strongly Correlated Euroium Superhydrides, The, *J. Phys. Chem. Lett.*, 2021, **12**, 32.

63 W. Sun, X. Kuang, H. D. J. Keen, C. Lu and A. Hermann, Second group of high-pressure high-temperature lanthanide polyhydride superconductors, *Phys. Rev. B*, 2020, **102**, 144524.
<figure><img src="image_16.png" /></figure>

64 X. Zhong, H. Wang, J. Zhang, H. Liu, S. Zhang, H.-F. Song, G. Yang, L. Zhang and Y. Ma, Tellurium hydrides at high pressures: High-temperature superconductors, *Phys. Rev. Lett.*, 2016, **116**, 057002.

65 N. W. Ashcroft, Metallic Hydrogen: A High-Temperature Superconductor?, *Phys. Rev. Lett.*, 1968, **21**, 1748.

66 H. W. T. Morgan and A. N. Alexandrova, Structures of LaH<sub>10</sub>, EuH<sub>9</sub>, and UH<sub>8</sub> superhydrides rationalized by electron counting and Jahn–Teller distortions in a covalent cluster model, *Chem. Sci.*, 2023, **14**, 6679.

67 M. Kawamura, Fermisurfer: Fermi-surface viewer providing multiple representation schemes, *Comput. Phys. Commun.*, 2019, **239**, 197.

68 I. Errea, M. Calandra and F. Mauri, First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hydride compounds, *Phys. Rev. Lett.*, 2013, **111**, 177002.

69 I. Errea, M. Calandra, C. J. Pickard, J. Nelson, R. J. Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma and F. Mauri, High-pressure hydrogen sulfide from first principles: A strongly anharmonic phonon-mediated superconductor, *Phys. Rev. Lett.*, 2015, **114**, 157004.

70 P. Hou, F. Belli, R. Bianco and I. Errea, Quantum anharmonic enhancement of superconductivity in P63/mmc ScH6 at high pressures: A first-principles study, *J. Appl. Phys.*, 2021, **130**, 175902.

71 M. Dogan, S. Oh and M. L. Cohen, High temperature superconductivity in the candidate phases of solid hydrogen, *J. Phys.: Condens. Matter*, 2022, **34**, 15LT01.

72 J. J. Gilman, Lithium Dihydrogen Fluoride—An Approach to Metallic Hydrogen, *Phys. Rev. Lett.*, 1971, **26**, 546.

73 W. L. McMillan, Transition temperature of strongcoupled superconductors, *Phys. Rev.*, 1968, **167**, 331.

74 P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, *Phys. Rev. B*, 1975, **12**, 905.

75 S. R. Xie, G. R. Stewart, J. J. Hamlin, P. J. Hirschfeld and R. G. Hennig, Functional form of the superconducting critical temperature from machine learning, *Phys. Rev. B*, 2019, **100**, 174513.

76 K. P. Huber and G. Herzberg, Constants of diatomic molecules, *Molecular Spectra and Molecular Structure: IV. Constants of Diatomic Molecules*, Springer, US, Boston, MA, 1979, pp. 8–689.