Effect of quantum anharmonicity on the superconductivity of I4¯3m CH4−H3S at high pressures: A first-principles study

Making use of first-principles calculations, we analyze the effect of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of $I\overline{4}3m {\mathrm{CH}}_{4}\text{\ensuremath{-}}{\mathrm{H}}_{3}\mathrm{S}$, one of the lowest enthalpy structures in the C-S-H system, in the 150--300 GPa pressure range within the stochastic self-consistent harmonic approximation. We predict a correction to the crystal structure, which is formed by an ${\mathrm{H}}_{3}\mathrm{S}$ lattice and ${\mathrm{CH}}_{4}$ molecules, the phonon spectra, and the pressure-dependent superconducting critical temperatures, which have been estimated in previous calculations without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for the lattice dynamics. Our results show that quantum ionic fluctuations have an impact on the distance between H atoms and S atoms in the ${\mathrm{H}}_{3}\mathrm{S}$ host lattice, pushing it towards more symmetric bonds, while the methane molecules are barely affected. According to our anharmonic phonon spectra, this structure is dynamically stable above 150 GPa, which is 30 GPa lower than the pressure at which the harmonic approximation predicts the emergence of an instability. As a consequence of the strong anharmonic enhancement of the phonon frequencies, the electron-phonon coupling constant is suppressed by 46% at 200 GPa, and even more at lower pressures. As a result, the superconducting critical temperature is overestimated by around 50 K at 200 GPa, such that it falls below 150 K in the whole pressure range studied. Our results underline that ternary hydrides are subject to strong anharmonic effects on their structural, vibrational, and superconducting properties.