Quantum Crystal Structure in the 250 K Superconducting Lanthanum Hydride

TL;DR

This paper demonstrates that quantum atomic fluctuations stabilize a high-symmetry crystal structure in LaH$_{10}$ across a wide pressure range, explaining its high-temperature superconductivity at 250 K and challenging classical predictions.

Contribution

It shows that quantum effects are essential for accurately predicting the stable crystal structure and superconducting properties of LaH$_{10}$ hydrides, which classical methods fail to capture.

Findings

Quantum fluctuations stabilize the Fm-3m structure across 137-218 GPa.

The structure exhibits a colossal electron-phonon coupling of ~3.5.

Quantum effects simplify the energy landscape, confirming the structure as the true ground state.

Abstract

The discovery of superconductivity at 200 K in the hydrogen sulfide system at large pressures [1] was a clear demonstration that hydrogen-rich materials can be high-temperature superconductors. The recent synthesis of LaH$_{10}$ with a superconducting critical temperature (T$_{\text{c}}$) of 250 K [2,3] places these materials at the verge of reaching the long-dreamed room-temperature superconductivity. Electrical and x-ray diffraction measurements determined a weakly pressure-dependent T$_{\text{c}}$ for LaH$_{10}$ between 137 and 218 gigapascals in a structure with a face-centered cubic (fcc) arrangement of La atoms [3]. Here we show that quantum atomic fluctuations stabilize in all this pressure range a high-symmetry Fm-3m crystal structure consistent with experiments, which has a colossal electron-phonon coupling of $\lambda\sim3.5$. Even if ab initio classical calculations neglecting quantum atomic vibrations predict this structure to distort below 230 GPa yielding a complex energy landscape with many local minima, the inclusion of quantum effects simplifies the energy landscape evidencing the Fm-3m as the true ground state. The agreement between the calculated and experimental T$_{\text{c}}$ values further supports this phase as responsible for the 250 K superconductivity. The relevance of quantum fluctuations in the energy landscape found here questions many of the crystal structure predictions made for hydrides within a classical approach that at the moment guide the experimental quest for room-temperature superconductivity [4,5,6]. Furthermore, quantum effects reveal crucial to sustain solids with extraordinary electron-phonon coupling that may otherwise be unstable [7].

Tables

Table 1. Extended Data Table 1:   Summary of calculated superconducting T c c {}_{\text{c}} . Values are within different approaches ranging from empirical to fully ab initio : McMillan equation (T c c {}_{\text{c}} μ ∗ = 0.1 M ​ c subscript superscript absent M 𝑐 superscript 𝜇 0.1 {}^{\text{M}c}_{\mu^{*}=0.1} ), Allen-Dynes modified McMillan equation (T c c {}_{\text{c}} μ ∗ = 0.1 A ​ D subscript superscript absent A 𝐷 superscript 𝜇 0.1 {}^{\text{A}D}_{\mu^{*}=0.1} ), anisotropic treatment of Migdal-Éliashberg (T c c {}_{\text{c}} M ​ E a ​ n ​ i superscript subscript absent 𝑎 𝑛 𝑖 M 𝐸 {}_{ani}^{\text{M}E} ) and SCDFT (T SCDFT c superscript subscript absent c SCDFT {}_{\text{c}}^{\rm SCDFT} ). Values of λ 𝜆 \lambda and ω l ​ o ​ g subscript 𝜔 l 𝑜 𝑔 \omega_{\text{l}og}  are also given.

System	Pressure (GPa)	$\lambda$	${\omega }_{\text{l}og}$ (meV)	T${}_{\text{c}}$${}_{{\mu }^{\ast }=0.1}{}^{}{}_{}{}^{\text{M}c}$ (K)	T${}_{\text{c}}$${}_{{\mu }^{\ast }=0.1}{}^{}{}_{}{}^{\text{A}D}$ (K)	T${}_{\text{c}}$${}_{}{}^{\text{M}E}{}_{ani}{}^{}$ (K)	T${}_{}{}^{\mathrm{SCDFT}}{}_{\text{c}}{}^{}$ (K)
LaH10	129	3.62	76.4	171.8	252.6	255.3	230
LaH10	163	2.67	96.4	197.1	247.0	242.8	225
LaH10	214	2.06	115.5	196.3	235.9	237.9	210
LaH10	264	1.73	126.6	189.5	219.2	216.9	201
LaD10	159	3.14	63.5	135.0	184.2	180.4	171
LaD10	210	2.21	81.7	145.5	176.5	172.9	158
LaD10	260	1.80	92.2	142.2	164.6	157.9	151

Table 2. Extended Data Table 2: R 𝑅 R - 3 ​ m 3 𝑚 3m LaH 10 and F ​ m 𝐹 𝑚 Fm - 3 ​ m 3 𝑚 3m LaH 10 Wycokff positions. The table summarizes the occupied Wyckoff positions for the two structures. We describe the Wyckoff positions in crystal coordinates so that the [ x , y , z ] 𝑥 𝑦 𝑧 \left[x,y,z\right] coordinate should be understood as a x ​ 𝐚 + y ​ 𝐛 + z ​ 𝐜 𝑥 𝐚 𝑦 𝐛 𝑧 𝐜 x\mathbf{a}+y\mathbf{b}+z\mathbf{c} atomic position with 𝐚 𝐚 \mathbf{a} , 𝐛 𝐛 \mathbf{b} , 𝐜 𝐜 \mathbf{c} the lattice vectors. For the R 𝑅 R - 3 ​ m 3 𝑚 3m phase we use the rhombohedral lattice (R), where the three lattice vectors have the same length ( a = b = c 𝑎 𝑏 𝑐 a=b=c ) and the angle between them is the same ( α = β = γ 𝛼 𝛽 𝛾 \alpha=\beta=\gamma ). The F ​ m 𝐹 𝑚 Fm - 3 ​ m 3 𝑚 3m  phase is described both in this rhombohedral description (R) and, for comparison, in the standard cubic conventional lattice (C). In the F ​ m 𝐹 𝑚 Fm - 3 ​ m 3 𝑚 3m  the lanthanum atom is described by the 4b sites, two hydrogen atoms occupy the 8c sites, and the remaining 8 hydrogen atoms occupy the 32f sites. Most of the atomic positions are fixed by symmetry and overall the F ​ m 𝐹 𝑚 Fm - 3 ​ m 3 𝑚 3m  structure can be described by one single free parameter ( ϵ italic-ϵ \epsilon ). In the R 𝑅 R - 3 ​ m 3 𝑚 3m the lanthanum atom is locked in the 3b sites, two pairs of hydrogen atoms occupy the 6c sites, and the remaining 6 hydrogen atoms occupy the 18h sites. In this case symmetry allows for more freedom, and overall the structure of the R 𝑅 R - 3 ​ m 3 𝑚 3m phase can be described by 4 free parameters ( ϵ a subscript italic-ϵ 𝑎 \epsilon_{a} , ϵ b subscript italic-ϵ 𝑏 \epsilon_{b} , ϵ x subscript italic-ϵ 𝑥 \epsilon_{x} and ϵ y subscript italic-ϵ 𝑦 \epsilon_{y} ).

$Fm$-$3m$ (C)		$Fm$-$3m$ (R)		$R$-$3m$ (R)
1 La 4b	$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	1 La 4b	$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	1 La 3b	$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]$
2 H 8c	$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]$	2 H 8c	$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]$	2 H 6c	[${ϵ}_a,{ϵ}_a,{ϵ}_a$]
	$[\frac{3}{4},\frac{3}{4},\frac{3}{4}]$		$[\frac{3}{4},\frac{3}{4},\frac{3}{4}]$		[-${ϵ}_a$,-${ϵ}_a$,-${ϵ}_a$]
8 H 32f	[$ϵ$,$ϵ$,$ϵ$]	8 H 32f	[$ϵ$,$ϵ$,$ϵ$]	2 H 6c	[${ϵ}_b$,${ϵ}_b$,${ϵ}_b$]
	[-$ϵ$,-$ϵ$,-$ϵ$]		[-$ϵ$,-$ϵ$,-$ϵ$]		[-${ϵ}_b$,-${ϵ}_b$,-${ϵ}_b$]
	[$ϵ$,$ϵ$,-$ϵ$]		[-$ϵ$,-$ϵ$,3$ϵ$]	6 H 18h	[-${ϵ}_x$,-${ϵ}_x$,$3{ϵ}_y$]
	[$ϵ$,-$ϵ$,$ϵ$]		[-$ϵ$,3$ϵ$,-$ϵ$]		[-${ϵ}_y$,$3{ϵ}_x$,-${ϵ}_x$]
	[-$ϵ$,$ϵ$,$ϵ$]		[3$ϵ$,-$ϵ$,-$ϵ$]		[$3{ϵ}_y$,-${ϵ}_x$,-${ϵ}_x$]
	[-$ϵ$,-$ϵ$,$ϵ$]		[$ϵ$,$ϵ$,-3$ϵ$]		[${ϵ}_x$,${ϵ}_x$,-$3{ϵ}_y$]
	[-$ϵ$,$ϵ$,-$ϵ$]		[$ϵ$,-3$ϵ$,$ϵ$]		[${ϵ}_x$,-$3{ϵ}_y$,${ϵ}_x$]
	[$ϵ$,-$ϵ$,-$ϵ$]		[-3$ϵ$,$ϵ$,$ϵ$]		[-$3{ϵ}_y$,${ϵ}_x$,${ϵ}_x$]

Table 3. Extended Data Table 3: Crystal structure details for relevant phases . Lattice parameters and atomic coordinates for LaH 10 ( I ​ m ​ m ​ m 𝐼 𝑚 𝑚 𝑚 Immm ) and LaH 10 ( C ​ 2 𝐶 2 C2 ) at 150 GPa and LaH 11 P ​ 4 / n ​ m ​ m 𝑃 4 𝑛 𝑚 𝑚 P4/nmm at 100 GPa. These pressures are estimated classically. The positions below give vanishing forces at classical level.

Composition (Space group)	Lattice parameters	Wyckoff positions
LaH10 ($Immm$)	$a=3.58303$ Å	La	2c	[0.50000, 0.50000, 0.00000]
	$b=3.61834$ Å	H	8m	[0.75841, 0.00000, 0.11649]
	$c=5.08749$ Å	H	8l	[0.00000, 0.75742, 0.87548]
		H	4j	[0.50000, 0.00000, 0.74572]
LaH10 ($C2$)	$a=6.15468$ Å	La	4c	[0.49244, 0.00070, 0.25292]
	$b=3.60628$ Å	H	4c	[0.13978, 0.24567, -0.05243]
	$c=7.23776$ Å	H	4c	[0.09798, 0.24122, 0.45027]
	$\beta =55.71434$°	H	4c	[0.36015, 0.25590, 0.05238]
		H	4c	[0.40204, 0.26021, 0.54971]
		H	4c	[-0.09751, 0.00051, -0.05100]
		H	4c	[0.86810, 0.00071, 0.43706]
		H	4c	[0.88713, 0.00076, 0.69398]
		H	4c	[0.87083, 0.00068, 0.19089]
		H	4c	[0.73058, 0.00043, 0.88088]
		H	4c	[0.76156, 0.00071, 0.36763]
LaH11 ($P4/nmm$)	$a=3.87435$ Å	La	2c	[0.25000, 0.25000, 0.78577]
	$b=3.87435$ Å	H	4e	[0.00000, 0.00000, 0.50000]
	$c=5.27636$ Å	H	8i	[0.25000, -0.02052, 0.17824]
		H	8i	[0.25000, 0.55418, 0.35160]
		H	2a	[0.75000, 0.25000, 0.00000]

Equations

$$\frac{{\partial }^{2}E(\mathcal{R})}{\partial \mathcal{R}\partial \mathcal{R}}=\mathbf{\Phi }+\stackrel{(3)}{\Phi }\mathbf{\Lambda }{\left[1-\stackrel{(4)}{\Phi }\mathbf{\Lambda }\right]}^{-1}\stackrel{(3)}{\Phi }.$$

$${\alpha }^{2}F(\omega )$$

$${\Delta }_s\left(ϵ\right)=\mathcal{Z}\left(ϵ\right){\Delta }_s\left(ϵ\right)-\int d{ϵ}^{\prime }\mathcal{K}\left(ϵ,{ϵ}^{\prime }\right)\frac{\tanh \left[\frac{\beta E\left({ϵ}^{\prime }\right)}{2}\right]}{2E\left({ϵ}^{\prime }\right)}{\Delta }_s\left({ϵ}^{\prime }\right),$$

$$\mu (ϵ,{ϵ}^{\prime })=\sum _{n,m}\iint d^3(k{k}^{\prime })V_{n\mathbf{k},m{\mathbf{k}}^{\prime }}^{RPA}\frac{\delta (ϵ-{ϵ}_{n\mathbf{k}})}{N({ϵ}_{n\mathbf{k}})}\delta ({ϵ}^{\prime }-{ϵ}_{m{\mathbf{k}}^{\prime }}).$$

$${\Sigma }_{n\mathbf{k}}(i{\omega }_i)$$

$${\Delta }_{n\mathbf{k}}(i{\omega }_i)$$

$$\times |G_{m\mathbf{k}+\mathbf{q}}(i{\omega }_{\mu }+i{\omega }_i){|}^2{\Delta }_{m\mathbf{k}+\mathbf{q}}(i{\omega }_{\mu }+i{\omega }_i).$$

$$V_{mn}^{\mathrm{ph}}(\mathbf{q},i{\omega }_{\mu })=\sum _{\nu }|g_{nm}^{\nu }(\mathbf{q}){|}^2{D}_{\nu }(\mathbf{q},i{\omega }_{\mu }),$$

$$|g_{nm}^{\nu }(\mathbf{q}){|}^2=\frac{{\sum }_{\mathbf{k}}|g_{n\mathbf{k},m\mathbf{k}+\mathbf{q}}^{\nu }{|}^2\delta ({ϵ}_{n\mathbf{k}}-E_F)\delta ({ϵ}_{m\mathbf{k}+\mathbf{q}}-E_F)}{{\sum }_{\mathbf{k}}\delta ({ϵ}_{n\mathbf{k}}-E_F)\delta ({ϵ}_{m\mathbf{k}+\mathbf{q}}-E_F)},$$

Full text

The potential of metallic hydrogen as a high-T${}_{\text{c}}$ superconductor [8, 9] was identified few years after the development of the Bardeen-Cooper-Schrieffer (BCS) theory, which explained superconductivity through the electron-phonon coupling mechanism. The main argument was that T${}_{\text{c}}$ can be maximized for light compounds due to their high vibrational frequencies. In view of the large pressures needed to metallize hydrogen [10], chemical precompression with heavier atoms [11, 12] was suggested as a pathway to decrease the pressure needed to reach metallicity and, thus, superconductivity. These ideas have bloomed thanks to modern ab initio crystal structure prediction methods based on density-functional theory (DFT) [5, 13, 14]. Hundreds of hydrogen-rich compounds have been predicted to be thermodynamically stable at high pressures and, by calculating the electron-phonon interaction parameters, their T${}_{\text{c}}$’s have been estimated [4, 5]. The success of this symbiosis between DFT crystal structure predictions and T${}_{\text{c}}$ calculations is exemplified by the discovery of superconductivity in H3S at 200 K [1, 15, 16]. The prospects for discovering warm hydrogen-based superconductors in the next years are thus high, in clear contrast with other high-T${}_{\text{c}}$ superconducting families such as cuprates or pnictides [17, 18], where the lack of a clear understanding of the superconducting mechanism hinders an in silico guided approach.

DFT predictions in the La-H system proposed LaH10 to be thermodynamically stable against decomposition above 150 GPa. A sodalite type-structure with space group $Fm$-$3m$ and T{}_{\text{c}}$$\sim280 K was suggested above $\sim$220 GPa (see Fig. 1), and a distorted version of it below with space group $C2/m$ and a rhombohedral La sublattice [19, 20]. By laser heating a lanthanum sample in a hydrogen-rich atmosphere within a diamond anvil cell (DAC), a lanthanum superhydride was synthesized right after [20]. Based on the unit cell volume obtained by x-ray diffraction, the hydrogen to lanthanum ratio was estimated to be between 9 and 12. An fcc arrangement of the La atoms was determined above $\sim$160 GPa, and a rhombohedral lattice below with $R$-$3m$ space group for the La sublattice. Due to the small x-ray cross section of hydrogen, experimentally it is not possible to resolve directly the H sublattice. Early this year, evidences of a superconducting transition at 260 K and 188 GPa were reported in a lanthanum superhydride [2]. These findings were confirmed and put in solid grounds few months later by an independent group that measured a T${}_{\text{c}}$ of 250 K from 137 to 218 GPa in a structure with fcc arrangement of the La atoms and suggested a LaH10 stoichiometry [3].

Even if it is tempting to assign the record superconductivity to the $Fm$-$3m$ phase predicted previously [2, 3], there is a clear problem: the $Fm$-$3m$ structure is predicted to be dynamically unstable in the whole pressure range where a 250 K T${}_{\text{c}}$ was observed. This implies that this phase is not a minimum of the Born-Oppenheimer energy surface. Consequently, no T${}_{\text{c}}$ has been estimated for this phase in the experimental pressure range. Considering that quantum proton fluctuations symmetrize hydrogen bonds in the high-pressure X phase of ice [21] and in H3S [22, 23], this contradiction may signal a problem of the classical treatment of the atomic vibrations in the calculations. We show here how quantum atomic fluctuations completely reshape the energy landscape making the $Fm$-$3m$ phase the true ground state and the responsible for the observed superconducting critical temperature.

We start by calculating with DFT the lowest enthalpy structures of LaH10 as a function of pressure with state-of-the-art crystal structure prediction methods [24, 25]. The contribution associated with atomic fluctuations is not included, so that the energy just corresponds to the Born-Oppenheimer energy $V(\mathbf{R})$, where $\mathbf{R}$ represents the position of atoms treated classically as simple points. As shown in Figure 1, different distorted phases of LaH10 are thermodynamically more stable than the $Fm$-$3m$ phase. Above $\sim$250 GPa all phases merge to the $Fm$-$3m$ symmetric phase. These results are in agreement with previous calculations [19], even if we identify other possible distorted structures with lower enthalpy such as the $R$-$3m$, $C2$ and $P1$ (not shown) phases. These phases not only imply a distortion of the H atoms, also show a La sublattice without an fcc arrangement, and thus should be detectable by x-ray. The fact that many structures are predicted underlines that the classical $V(\mathbf{R})$ energy surface is of a multifunnel structure tractable to many different saddle and local minima, as sketched in Figure 1.

This picture completely changes when including the energy of quantum atomic fluctuations, the zero-point energy (ZPE). We calculate the ZPE within the stochastic self-consistent harmonic approximation (SSCHA) [26, 27, 28]. The SSCHA is a variational method that calculates the $E(\bm{\mathcal{R}})$ energy of the system including atomic quantum fluctuations as a function of the centroid positions $\bm{\mathcal{R}}$, which determine the center of the ionic wave functions. The calculations are performed without approximating the $V(\mathbf{R})$ potential, keeping all its anharmonic terms. We perform a minimization of $E(\bm{\mathcal{R}})$ and determine the centroid positions at its minimum. By calculating the stress tensor from $E(\bm{\mathcal{R}})$ [28], we relax the lattice parameters seeking for structures with isotropic stress conditions considering quantum effects. We start the quantum relaxation for both $R$-$3m$ and $C2$ phases with the lattice that yields a classical isotropic pressure of 150 GPa and vanishing classical forces, i.e., calculated from $V(\mathbf{R})$. All quantum relaxations quickly evolve into the $Fm$-$3m$ phase. This suggests that the quantum $E(\bm{\mathcal{R}})$ energy landscape is much simpler than the classical $V(\mathbf{R})$ as sketched in Figure 1. And that the sodalite symmetric $Fm$-$3m$ phase is the ground state for LaH10 in all the pressure range of interest. Quantum effects are colossal: reshaping the energy landscape and stabilizing structures by more than 60 meV per LaH10.

Our results further confirm that the structure of LaH10 responsible for the 250 K superconductivity is $Fm$-$3m$. This is completely consistent with the fcc arrangement of La atoms found experimentally [3]. However, Geballe et al. [20] observed a rhombohedral distortion below $\sim$160 GPa, with an $R$-$3m$ space group for the La sublattice and a rhombohedral angle of approximately 61.3°($c/a\sim 2.38$ in the hexagonal representation). Our calculations show that this distortion is compatible with slight anisotropic stress conditions in the DAC. Indeed, performing a SSCHA minimization for our $R$-$3m$ phase but keeping the rhombohedral angle fixed at 62.3°(the value that yields an isotropic pressure of 150 GPa at the classical level) the quantum stress tensor shows a 6% anisotropy between the diagonal direction and the perpendicular plane. This suggests that anisotropic conditions inside the DAC can produce the $R$-$3m$ phase, while other experimental stress conditions could favor other crystal phases.

The $Fm$-$3m$ phonon spectra calculated in the harmonic approximation from the Hessian of $V(\mathbf{R})$ show clear phonon instabilities in a broad region of the Brillouin zone (see Figure 2). These instabilities appear below $\sim$230 GPa. This is consistent with the fact that below this pressure many possible atomic distortions lower the enthalpy of this phase. On the contrary, as shown in Figure 2, when calculating the phonons from the Hessian of $E(\bm{\mathcal{R}})$ [27], which effectively captures the full anharmonicity of $V(\mathbf{R})$, no instability is observed. This confirms again that the $Fm$-$3m$ phase is a minimum in the quantum-energy landscape in the whole pressure range where a 250 K T${}_{\text{c}}$ was observed. While the $Fm$-$3m$ phase of LaH10 remains a minimum of $E(\bm{\mathcal{R}})$ as low as $\sim$ 129 GPa, the case of LaD10 shows instabilities at 126 GPa, implying that at this pressure the $Fm$-$3m$ phase of LaD10 distorts to a new phase (as suggested by Drozdov et al. [3]). Below this pressure we also predict that LaH10 composition is not longer thermodynamically stable and low-hydrogen compositions are likely to occur.

Flagrantly, the breakdown of the classical harmonic approximation for phonons makes impossible the estimation of T${}_{\text{c}}$ below $\sim$250 GPa in the $Fm$-$3m$ phase and questions all previous calculations [19, 29]. Indeed, the anharmonic phonon renormalization remains huge also at 264 GPa (see Figure 2). On the contrary, with anharmonic phonons derived from the Hessian of $E(\bm{\mathcal{R}})$ we can readily calculate the electron-phonon interaction and the superconducting T${}_{\text{c}}$ in the experimental range of pressure (120–210 GPa). The superconducting critical temperature is estimated fully ab initio –without any empirical parameter– by solving Migdal-Éliashberg (ME) equations and applying SuperConducting DFT (SCDFT). As shown in Figure 3, the numerical solutions of ME equations with anisotropic energy gap are almost on top of the experimental values. SCDFT values systematically show a slightly lower T${}_{\text{c}}$. Our reported values of T${}_{\text{c}}$ evidence the phonon-driven mechanism of superconductivity and confirm LaH10 in its $Fm$-$3m$ structure as responsible for the highest-T${}_{\text{c}}$ up to date reported. Our calculations for LaD10 in the $Fm$-$3m$ phase are also in agreement with the experimental point reported. Despite the large anharmonic effects at play, the isotope coefficient $\alpha=-\left[\ln{\mathrm{T_{\text{c}}(LaD_{10})}}-\ln{\mathrm{T_{\text{c}}(LaH_{10})}}\right]/\ln 2$ is close to 0.5 (0.43 around 160 GPa), the expected value in BCS theory, and it is in agreement with the experimentally reported $\alpha=0.46$.

We finally check T${}_{\text{c}}$ for the subtle rhombohedral distortion that could be induced by anisotropic stress conditions of pressure. Fixing the rhombohedral angle at 62.3° the obtained T${}_{\text{c}}$ for the $R$-$3m$ phase at 160 GPa is a 9% lower than for the $Fm$-$3m$. Thus, the observed weak pressure dependence of T${}_{\text{c}}$ is consistent with the absence of a rhombohedral distortion, as suggested by the x-ray data [3]. However, as argued above, undesired anisotropic stress conditions in the DAC can induce phase transitions. We thus believe that other experimental T${}_{\text{c}}$ measurements with lower values but around 200 K correspond to distorted structures induced by anisotropic conditions of pressure. In fact, we can safely rule out that compositions such as LaH11, proposed to yield a high critical temperature [3], is responsible for any sizable T${}_{\text{c}}$ (see Extended Data).

In summary, this work demonstrates how quantum effects are of capital importance in determining the ground state structures of superconducting hydrides, challenging all current predictions and evidencing flaws in standard theoretical methods. It also illustrates that quantum fluctuations are indispensable to sustain crystals with huge $\lambda$’s ($\lambda$ reaches a record value of 3.6 at 129 GPa for LaH10) that be otherwise destabilized by the colossal electron-phonon interaction to distorted (low symmetry) structures reducing the electronic density of states at the Fermi level (see Extended Data) [7]. This is relevant since large $\lambda$ is required to guarantee high-T${}_{\text{c}}$ [5, 6], not simply light atomic masses.