Ab initio investigation on the experimental observation of metallic hydrogen

The optical spectra of hydrogen at $\sim 500$ GPa were studied theoretically using a combination of ab initio methods. Among the four most competitive structures, i.e., C2/c-24, Cmca-12, Cmca-4, and I41/amd, only the atomic phase I41/amd can provide satisfactory interpretations of the recent experimental observation, and the electron-phonon interactions (EPIs) play a crucial role. Anharmonic effects (AHEs) due to lattice vibration are nonnegligible but not sufficient to account for the experimentally observed temperature dependence of the reflectance. The drop of the reflectance at 2 eV is not caused by diamond's band gap reducing or interband plasmon, but very likely by defect absorptions in diamond. These results provide theoretical support for the recent experimental realization of metallic hydrogen. The strong EPIs and the nonnegligible AHEs also emphasize the necessity for quantum treatment of both the electrons and the nuclei in future studies.

Figure 1

Static-nuclei optical spectra of I41/amd at 495 GPa. (a) the reflectance $R_{xx}$=$R_{yy}$ (red solid line) and $R_{zz}$ (blue dashed line); (b) the real parts, $\text{Re}{\varepsilon }_{xx}=\text{Re}{\varepsilon }_{yy}$ (magenta solid line) and $\text{Re}{\varepsilon }_{zz}$ (magenta dashed line), and imaginary parts, $\text{Im}{\varepsilon }_{xx}=\text{Im}{\varepsilon }_{yy}$ (thick orange solid line) and $\text{Im}{\varepsilon }_{zz}$ (thick orange dashed line), of the dielectric functions as well as loss functions $\text{–Im}{\varepsilon }_{xx}^{-1}=\text{–Im}{\varepsilon }_{yy}^{-1}$ (olive dash-dotted line) and $\text{–Im}{\varepsilon }_{zz}^{-1}$ (olive dotted line). $\text{Im}\varepsilon =\text{Im}{\varepsilon }_{\text{inter}}$ for $\omega >0$. The inset in (a) shows the reflectance in visible and IR ranges. The inset in (b) shows the interband plasmon, where the loss function is multiplied by 100 and the vertical dotted line labels the plasmon frequency (6.3 eV).

Figure 2

The optical spectra of I41/amd with EPIs using WL-HA at 495 GPa and 5 K. (a) the reflectance $R_{xx}$= $R_{yy}$ (red solid line) and $R_{zz}$ (blue dashed line); (b) the real parts, $\text{Re}{\varepsilon }_{xx}=\text{Re}{\varepsilon }_{yy}$ (magenta solid line) and $\text{Re}{\varepsilon }_{zz}$ (magenta dashed line), and imaginary parts, $\text{Im}{\varepsilon }_{xx}=\text{Im}{\varepsilon }_{yy}$ (thick orange solid line) and $\text{Im}{\varepsilon }_{zz}$ (thick orange dashed line), of the dielectric functions as well as loss functions $\text{–Im}{\varepsilon }_{xx}^{-1}=\text{–Im}{\varepsilon }_{yy}^{-1}$ (olive dash-dotted line) and $\text{–Im}{\varepsilon }_{zz}^{-1}$ (olive dotted line). $\text{Im}\varepsilon =\text{Im}{\varepsilon }_{\text{intra}}+\text{Im}{\varepsilon }_{\text{inter}}$. The inset in (a) shows the reflectance in visible and IR ranges. The upper inset in (b) shows the interband plasmon, where the loss function is multiplied by 100 and the vertical dotted line labels the plasmon frequency (6.1 eV). The bottom inset in (b) shows the dielectric functions in visible and IR ranges.

Figure 3

Effective bandstructure of I41/amd at 495 GPa. (a) and (c) without EPIs; (b) and (d) with EPIs at 5 K using WL-HA. The white arrows in (c) and (d) highlight that those intraband and interband transitions forbidden in the static-nuclei case are allowed when including EPIs. “Intra” means intraband transitions. “Indirect inter” means indirect interband transitions and labels additional states appearing near N in (d). The color scale bar corresponds to the spectra weight when unfolding the supercell's band structure to the primitive Brillouin zone.

Figure 4

(a) Comparisons between DS's experiment at 5 K (black lower-triangle dashed line) and 83 K (gray upper-triangle dashed line) with the pressure being 495 GPa and the WL-HA diamond/hydrogen interface reflectance of four structures at 495 GPa and 5 K, i.e., C2/c-24 (blue short-dashed line), Cmca-12 (green dash-dotted line), Cmca-4 (purple dashed line) and I41/amd (red solid line). (b) The influences of nuclear AHEs on the reflectance of I41/amd at 495 GPa by comparing the results of WL-HA at 5 K using 72-atom (orange dash-dotted line) and 864-atom (thick red solid line) unit cells to the ones of WL-PIMD at 50 K (blue dashed line) and 83 K (green solid line) using 72-atom unit cells. The inset of (b) shows the imaginary parts $\left(\text{Im}\varepsilon =\text{Im}{\varepsilon }_{\text{intra}}+\text{Im}{\varepsilon }_{\text{inter}}\right)$ of the dielectric funtions within a 72-atom unit cell by using WL-HA (orange dash-dotted line) in 5 K and WL-PIMD in 50 K (blue dashed line) and 83 K (green solid line). The diamond's refractive index is 2.41 for the calculations of diamond/hydrogen interface reflectance in (a) and (b).

Figure 5

(a) Comparisons between calculated tetragonal diamond's Raman spectrum using DFPT (red dotted line) and DS's experiment (black solid line) at 495 GPa. Band structures of the tetragonal diamond using DFT-LDA (black solid line) and $G_0{W}_0$@LDA (red dashed line) at 495 GPa. The top of valence bands is set as zero energy.

Figure 6

(a) Comparisons between DS's experiment at 5 K (black lower-triangle dashed line) and 83 K (gray upper-triangle dashed line) with the pressure being 495 GPa and the corrected WL-HA diamond/hydrogen interface reflectance of I41/amd at 495 GPa and 5 K. A, B, Ci, and Cii are diamond samples. The former three are not annealed while Cii is annealed at $1600{}^{\circ }\mathrm{C}$. The diamond's refractive index is 2.41 for the calculations of diamond/hydrogen interface reflectance. (b) Room-temperature optical absorption spectra for the four diamond samples A, B, Ci, and Cii (taken from Khan's paper [104]).