Hydrogen sulphide at high pressure: a strongly-anharmonic phonon-mediated superconductor

Abstract

We use first principles calculations to study structural, vibrational and superconducting properties of H${}_2$S at pressures $P\ge 200$ GPa. The inclusion of zero point energy leads to two different possible dissociations of H${}_2$S, namely 3H${}_2$S $\to$ 2H${}_3$S + S and 5H${}_2$S $\to$ 3H${}_3$S + HS${}_2$, where both H${}_3$S and HS${}_2$ are metallic. For H${}_3$S, we perform non-perturbative 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 HS 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.

5 pages + supplemental material

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