High-temperature superconductivity in atomic metallic hydrogen

Superconductivity in the recently proposed ground-state structures of atomic metallic hydrogen is calculated over the pressure range 500 GPa to $3.5$ TPa. Near molecular dissociation, the electron-phonon coupling $\lambda$ and renormalized Coulomb repulsion are similar to the molecular phase. A nearly continuous increase in the critical temperature $T_c$ with pressure is thus predicted in this range, to $\sim 356$ K near 500 GPa. As the atomic phase stabilizes with increasing pressure, $\lambda$ increases, causing $T_c$ to approach 481 K near 700 GPa. At the first atomic-atomic structural phase transformation near 1–$1.5$ TPa, a discontinuous jump in $\lambda$ occurs, causing $T_c$ to increase up to 764 K.

Figure 1

Ground-state structures of atomic metallic hydrogen. Left: Conventional unit cell of $I{4}_1/amd$ at 700 GPa. Right: $2\times 2\times 1$ supercell of $R$-$3m$ at 2 TPa. $a$ and $c$ parameters are shown in the figure, as discussed in the text. Fictitious bonds have been drawn for clarity.

Figure 2

Phonon densities of states of $I{4}_1/amd$ (dashed red line) and $R$-$3m$ (solid blue line) at $1.5$ TPa. The results have been normalized by the number of atoms per primitive unit-cell. Negative values indicate imaginary frequencies (and thus instabilities, as discussed in the text).

Figure 3

Gibbs free energies versus temperature of for $I{4}_1/amd$ (dashed red line) and $R$-$3m$ (solid blue line) at $1.5$ TPa.

Figure 4

Temperature prefactors $\langle \omega \rangle /k_{\mathrm{B}}$ (solid blue line) and ${\omega }_{\ln }/k_{\mathrm{B}}$ (dashed red line) as a function of pressure in atomic metallic hydrogen.

Figure 5

Electron-phonon-induced interaction $\lambda$ as a function of pressure in atomic metallic hydrogen.

Figure 6

Electron-phonon spectral functions ${\alpha }^{2}F\left(\omega \right)$ for $I{4}_1/amd$ at 500 and 700 GPa.

Figure 7

Phonon dispersion curves for $I{4}_1/amd$ at 700 GPa. The numbers 5 and 6 denote the highest-frequency phonon modes at $\Gamma$.

Figure 8

Phonon linewidths for $I{4}_1/amd$ at 700 GPa. The numbers 5 and 6 denote the linewidths corresponding to coupling to the highest-frequency phonon modes at $\Gamma$.

Figure 9

Electron-phonon spectral functions ${\alpha }^{2}F\left(\omega \right)$ for $I{4}_1/amd$ (dashed red line) and $R$-$3m$ (solid blue line) at $1.5$ TPa.

Figure 10

Phonon dispersion curves for $R$-$3m$ at $1.5$ TPa. Negative values correspond to imaginary frequencies and indicate instabilities, as discussed in the text. The lowest-frequency (and unstable) mode is denoted using the number 1.

Figure 11

Phonon linewidths for $R$-$3m$ at $1.5$ TPa. The linewidth corresponding to coupling to the unstable phonon mode is denoted using the number 1.

Figure 12

Electron-phonon spectral functions ${\alpha }^{2}F\left(\omega \right)$ for $R$-$3m$ at 2 and 3 TPa.

Figure 13

Superconducting critical temperatures $T_c$ of atomic metallic hydrogen calculated using Eqs. (2) and (3). The estimated value of $T_c$ for the high-pressure molecular phase Cmca (Refs.20, 21, 22) is shown as x.