First-principles demonstration of superconductivity at 280 K in hydrogen sulfide with low phosphorus substitution

Recently, BCS superconductivity at 203 K has been observed in a highly compressed hydrogen sulfide. We use first-principles calculations to systematically examine the effects of partially substituting chalcogen atoms on the superconductivity of hydrogen chalcogenides under high pressures. We find detailed trends of how the critical temperature changes upon increasing the V-, VI- or VII-substitution rate. These trends highlight the key roles played by low atomic mass and metallized covalent bonds. In particular, a possible record high critical temperature of 280 K is predicted in stable ${\mathrm{H}}_3{\mathrm{S}}_{0.925}{\mathrm{P}}_{0.075}$ with the $Im\overline{3}m$ structure under 250 GPa.

Figure 1

$Im\overline{3}m$ structure of ${\mathrm{H}}_3\mathrm{S}$ and phonon spectra with a phonon linewidth of VI-substitution systems at 200 GPa. (a) The $Im\overline{3}m$ structure of hydrogen chalcogenides. (b)–(e) Phonon spectra and phonon linewidths of four representative VI-substitution systems: (b) ${\mathrm{H}}_3\mathrm{S}$, (c) ${\mathrm{H}}_3\mathrm{Se}$, (d) ${\mathrm{H}}_3{\mathrm{S}}_{0.4}{\mathrm{O}}_{0.6}$, and (e) ${\mathrm{H}}_3{\mathrm{S}}_{0.7}{\mathrm{Te}}_{0.3}$. The magnitude of the phonon linewidth is indicated by the size of the red error bar, and the magnitude for ${\mathrm{H}}_3{\mathrm{S}}_{0.4}{\mathrm{O}}_{0.6}$ is plotted with twice the real values.

Figure 2

Electron-phonon coupling and critical temperature at 200 GPa of hydrogen chalcogenides with chemical substitutions. Upper panels: the integral function ${\lambda }^{\prime }\left(\omega \right)$. Lower panels: the electron-phonon coupling constant $\lambda$ (blue lines) and the critical temperature $T_c$ (red lines) vs the substitution concentration $x$. The left, middle, and right panels show the results for the case of VI-, V-, and VII-substitutions, respectively.

Figure 3

Phonon spectra with a phonon linewidth of V- and VII-substitution systems at 200 GPa. (a) ${\mathrm{H}}_3{\mathrm{S}}_{0.9}{\mathrm{P}}_{0.1}$, (b) ${\mathrm{H}}_3{\mathrm{S}}_{0.8}{\mathrm{P}}_{0.2}$, and (c) ${\mathrm{H}}_3{\mathrm{S}}_{0.8}{\mathrm{Cl}}_{0.2}$. The magnitude of the phonon linewidths in ${\mathrm{H}}_3{\mathrm{S}}_{0.9}{\mathrm{P}}_{0.1} \left({\mathrm{H}}_3{\mathrm{S}}_{0.8}{\mathrm{Cl}}_{0.2}\right)$ is too large (small) and thus plotted with half of (twice) the real values.

Figure 4

The effect of pressure in ${\mathrm{H}}_3{\mathrm{S}}_{1-x}{\mathrm{P}}_x$. (a) and (b) The phonon spectra and ${\lambda }^{\prime }\left(\omega \right)$ of ${\mathrm{H}}_3{\mathrm{S}}_{0.925}{\mathrm{P}}_{0.075}$ and ${\mathrm{H}}_3{\mathrm{S}}_{0.9}{\mathrm{P}}_{0.1}$ at 250 GPa. The magnitude of the phonon linewidth is plotted with half of the real values. The solid (dashed) lines plot ${\lambda }^{\prime }\left(\omega \right)$ at 250 (200) GPa. (c) $T_c$ of ${\mathrm{H}}_3{\mathrm{S}}_{0.925}{\mathrm{P}}_{0.075}$ (red solid line) and ${\mathrm{H}}_3{\mathrm{S}}_{0.9}{\mathrm{P}}_{0.1}$ (black dashed line) vs pressure. The error bars indicate the value range of $T_c$ with ${\mu }^{*}=0.1$–$0.15$.

Figure 5

Electronic band structures of VI-substitution systems at 200 GPa. (a) ${\mathrm{H}}_3\mathrm{Se}$, (b) ${\mathrm{H}}_3{\mathrm{S}}_{0.4}{\mathrm{O}}_{0.6}$, and (c) ${\mathrm{H}}_3{\mathrm{S}}_{0.7}{\mathrm{Te}}_{0.3}$. For comparison, the red dashed lines show the band structure of ${\mathrm{H}}_3\mathrm{S}$. The Fermi energies are set to be zero.

Figure 6

Electronic band structures of V-substitution and VII-substitution systems at 200 GPa. (a) ${\mathrm{H}}_3{\mathrm{S}}_{0.8}{\mathrm{P}}_{0.2}$, (b) ${\mathrm{H}}_3{\mathrm{Se}}_{0.8}{\mathrm{As}}_{0.2}$, (c) ${\mathrm{H}}_3{\mathrm{S}}_{0.8}{\mathrm{Cl}}_{0.2}$, and (d) ${\mathrm{H}}_3{\mathrm{Se}}_{0.8}{\mathrm{Br}}_{0.2}$. For comparison, the red dashed lines show the band structure of ${\mathrm{H}}_3\mathrm{S}$ in (a) and (c) and that of ${\mathrm{H}}_3\mathrm{Se}$ in (b) and (d). The Fermi energies are set to be zero.

Figure 7

Phonon spectra and linewidths of V-substitution and VII-substitution systems at 200 GPa. (a) ${\mathrm{H}}_3{\mathrm{Se}}_{0.85}{\mathrm{As}}_{0.15}$, (b) ${\mathrm{H}}_3{\mathrm{Se}}_{0.8}{\mathrm{As}}_{0.2}$, and (c) ${\mathrm{H}}_3{\mathrm{Se}}_{0.8}{\mathrm{Br}}_{0.2}$. The magnitude of the phonon linewidths in ${\mathrm{H}}_3{\mathrm{Se}}_{0.8}{\mathrm{Br}}_{0.2}$ is too small and thus plotted with twice of the real values.

Figure 8

Phonon spectrum and phonon linewidths of ${\text{H}}_3{\text{S}}_{0.96}{\text{Si}}_{0.04}$ at 250 GPa. The magnitude of the phonon linewidths is too large and thus plotted with half of the real values.

Figure 9

Comparison between the results obtained by the supercell method and by the VCA. (a) Electron DOS and (b) phonon DOS in ${\text{H}}_3{\text{S}}_{0.875}{\text{P}}_{0.125}$ at 200 GPa. Note that in ${\mathrm{H}}_3\mathrm{S}$, the position of the DOS peak is lower than the Fermi level.

Figure 10

The electronic DOS and the electron-phonon coupling $\lambda$ in ${\text{H}}_3{\text{S}}_{1-x}{\text{P}}_x$. (a) DOS and $\lambda$ vs the substitution concentration. (b) Linear relationship between $\lambda$ and DOS.