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Black metal hydrogen above 360 GPa driven by proton quantum fluctuations


Hydrogen metallization under stable conditions is a substantial step towards the realization of the first room-temperature superconductor. Recent low-temperature experiments1,2,3 report different metallization pressures, ranging from 360 GPa to 490 GPa. In this work, we simulate the structural properties and vibrational Raman, infrared and optical spectra of hydrogen phase III, accounting for proton quantum effects. We demonstrate that nuclear quantum fluctuations downshift the vibron frequencies by 25%, introduce a broad lineshape into the Raman spectra and reduce the optical gap by 3 eV. We show that hydrogen metallization occurs at 380 GPa in phase III due to band overlap, in good agreement with transport data2. Our simulations predict that this state is a black metal—transparent in the infrared—so the shiny metal observed at 490 GPa (ref. 1) is not phase III. We predict that the conductivity onset and optical gap will substantially increase if hydrogen is replaced by deuterium, underlining that metallization is driven by quantum fluctuations and is thus isotope-dependent. We show how hydrogen acquires conductivity and brightness at different pressures, explaining the apparent contradictions in existing experimental scenarios1,2,3.

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Fig. 1: Sketch of the physical properties of low-temperature hydrogen.
Fig. 2: Crystal structure with and without quantum effects of hydrogen phase III.
Fig. 3: Vibrational spectra at 0 K.
Fig. 4: Optical properties of phase III of hydrogen.

Data availability

Data for the structures reported in this paper are provided in Extended Data Fig. 1. Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The source code used to implement the SSCHA will be released with a GPLv3 licence and will be made available. The source code to compute the dielectric function in equation (7) is a custom version of Quantum ESPRESSO and is available from GitLab:


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L.M. acknowledges a CINECA award under the ISCRA initiative for the availability of high-performance computing resources and support. This work was performed using HPC resources from Idris and The Grand Challenge Jean Zay. I.E. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 802533).

Author information




The project was conceived by all authors. L.M. performed the analytical and numerical calculations and prepared the figures with input from all authors. All authors contributed to the redaction of the manuscript.

Corresponding author

Correspondence to Francesco Mauri.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Giulia Galli and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Phase III quantum structure.

Average nuclear positions of phase III (C2/c symmetry group) after the relaxation with quantum effects, both on the cell and the atoms within the BLYP functional. All the Wyckoff positions are 8f. Only symmetry nonequivalent atoms in crystal coordinates are given. The lattice parameters are given in Angstrom and angles in degrees. The structures are in the conventional monoclinic cell. The data in the primitive cell of Fig. 1 in the main text are obtained as 4a2 = A2 + B2, c = C and gamma= arctan(A/B).

Extended Data Fig. 2 X-ray comparison.

Structural data of phase III compared with the X-Ray diffraction experiments computed by9. The discrepancies on the c/a ratio is probably due to the different temperature between the simulation (0 K) and the experiment (room temperature). The c and a parameters, as well as the unit cell volume, have been resized to account for the fact that X-ray diffraction does not distinguish the single atoms in the molecule, and thus identifies a different cell periodicity. a’=a / sqrt(3), c’ = c/2 and V’ = V / 6.

Extended Data Fig. 3 DOS.

Comparison of the electronic density of states with different simulation boxes (compared with the classical nuclei). The use of a small simulation cell (like the one of 96 atoms), leads to a strong underestimation of the metallic transition, as it introduces metallic states inside the gap. These simulations have been performed using the BLYP functional, thus the overall gap differs from the one of TB09 reported in the main text.

Extended Data Fig. 4 Optical gap.

Comparison of the optical properties with two different simulation cells, containing 96 and 432 atoms respectively. Also, in this case, the optical gap is completely missed by using a small simulation cell. This effect is due to the combination of the overestimation of the Drude peak in the small cell that results from the higher DOS close on the Fermi level (see Extended Data Fig. 3) and a subsequent increment of the plasma frequency and the reflectivity at low energy that kills the absorption profile. Moreover, the optical gap is also strongly affected by optical transitions involving phonons with q points not commensurate with the cell of 96 atoms. These simulations are performed using the BLYP functional using the structures at 355 GPa.

Extended Data Fig. 5 Band structure.

Comparison of the band structure at 260 GPa for the average centroid position with different DFT exchange-correlation functionals. TB09 is the functional we used for computing optical properties in the main text. Since the structure is very close to a hexagonal cell, we adopt the typical k-path along high symmetry lines for hexagonal crystals. Both HSE06 and TB09 go beyond DFT, employing, respectively, hybrid and meta-GGA functionals. HSE06 is a general-purpose functional that provide very good electronic bands, at a much high computational cost required by the calculation of the exact exchange. On the other side, TB09 is aimed only to compute electronic properties, present a lot of limitations on isolated atoms, but it has a computational cost comparable to that one of BLYP (allowing calculation with more atoms in the cell). The precision of TB09 and HSE06 in the band structure calculation is comparable. By assuming a similar accuracy of TB09 and HSE06, we can estimate an error of 0.4 eV in the bandgap of each functional on static configurations.

Extended Data Fig. 6 Scissor corrected optical gap.

The direct gap with quantum fluctuations estimated with the BLYP functional plus a constant scissor correction, to match the value of the HSE06 results. As clearly shown, the difference with the results reported by using TB09 (main text, figure 3 panel d) provides an estimation of the error on the bandgap due to the exchange-correlation functional of about 0.3 eV. This is a bit lower than what we obtained by comparing TB09 and HSE06 on a static snapshot in Extended Data Fig. 5. This probably indicates that the choice of the DFT functional for the bandgap is less sensitive in the ionic displaced configurations than in the static ones.

Extended Data Fig. 7 Complex conductivity.

Imaginary part of the conductivity at the simulated pressures. Combining these data with the real part if the conductivity reported in Figure 4 of the main text, it is possible to compute the dielectric function and the all the optical properties (reflectivity and transmittance). These data are computed with quantum nuclei using the TB09 functional.

Extended Data Fig. 8 Stochastic error on the optical gap.

Comparison between reflectivity and transmittance obtained with different configurations extracted by the nuclear density matrix with 432 atoms. The stochastic error for each configuration on the gap is about 0.1 eV.

Extended Data Fig. 9 LO-TO splitting in the IR vibron.

The IR vibron at 355 GPa computed as the absorbance and the imaginary part of the ionic green function only. The IR vibron linewidth cannot be explained by anharmonicity alone, but requires properly accounting for the absorbance induced by the negative dielectric function between the TO mode (the pole of the susceptibility) and the LO one (induced by the effective charges).

Extended Data Fig. 10 Raman anharmonic broadening.

Comparison between the Raman spectrum at 360 GPa computed with quantum nuclei (anharmonic) and experimental data. The simulated spectrum has been shifted to match the vibron energy of experiments to compare the lineshape.

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Monacelli, L., Errea, I., Calandra, M. et al. Black metal hydrogen above 360 GPa driven by proton quantum fluctuations. Nat. Phys. 17, 63–67 (2021).

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