Hydrogen bond symmetrization by proton quantum motion and high Tc superconductivity in Sulfur hydrides at high pressure.

Atoms in a crystal are quantum particles differing substantial from classical particles. The vibrational energy associated to the quantum oscillations can strongly modify the static energy landscape, even changing the ground state derived from the Born-Oppenheimer energy surface (BOES) minimum. Here, making use of density-functional theory and of the Stochastic Self-consistent Harmonic Approximation, we show that the ground state of the high Tc superconductor hydrogen sulfide at 155 GPa is completely determined by quantum fluctuations. Indeed, despite the minimum of the BOES is obtained for a rhombohedral structure with covalently bonded H3S units and hydrogen bonds between them, quantum fluctuations favor a fully symmetric cubic structure in which the covalent and hydrogen bonds equalize. The quantum hydrogen-bond symmetrization and the large anharmonic effects are crucial to understand the pressure dependence of the observed extraordinary T$_c$=205 K at 155 GPa. We finally show how, the dependence of Tc as a function of pressure can be completely explained in the framework of a phonon mediated pairing mechanism in the presence of large anharmonic effects.