High-Pressure Hydrogen Sulfide from First Principles: A Strongly Anharmonic Phonon-Mediated Superconductor

We use first-principles calculations to study structural, vibrational, and superconducting properties of ${\mathrm{H}}_2\mathrm{S}$ at pressures $P\ge 200\mathrm{GPa}$. The inclusion of zero-point energy leads to two different possible dissociations of ${\mathrm{H}}_2\mathrm{S}$, namely $3{\mathrm{H}}_2\mathrm{S}\to 2{\mathrm{H}}_3\mathrm{S}+\mathrm{S}$ and $5{\mathrm{H}}_2\mathrm{S}\to 3{\mathrm{H}}_3\mathrm{S}+{\mathrm{HS}}_2$, where both ${\mathrm{H}}_3\mathrm{S}$ and ${\mathrm{HS}}_2$ are metallic. For ${\mathrm{H}}_3\mathrm{S}$, we perform nonperturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction ($\lambda \approx 2.64$ at 200 GPa) and $T_c$. Anharmonicity hardens H─S bond-stretching modes and softens H─S bond-bending modes. As a result, the electron-phonon coupling is suppressed by 30% ($\lambda \approx 1.84$ at 200 GPa). Moreover, while at the harmonic level $T_c$ decreases with increasing pressure, the inclusion of anharmonicity leads to a $T_c$ that is almost independent of pressure. High-pressure hydrogen sulfide is a strongly anharmonic superconductor.

Figure 1

Results of structure searching at 200 and 250 GPa. Convex hulls are shown as continuous lines, with and without the inclusion of zero-point energy (ZPE).

Figure 2

Phonon dispersion, phonon density of states projected onto selected atoms and directions, and the Eliashberg function of ${\mathrm{H}}_3\mathrm{S}$ in the harmonic approximation (top) and with the inclusion of anharmonic effects (bottom) for ${\mathrm{H}}_3\mathrm{S}$ at 200 GPa. ${\mathrm{H}}_{\perp }$ and ${\mathrm{H}}_{\parallel }$ label displacements of an H atom in the directions perpendicular or parallel to a H─S bond. The magnitude of the phonon linewidth is indicated by the size of the red error bars.