Search for high-Tc conventional superconductivity at megabar pressures in the lithium-sulfur system

Motivated by the recent report of superconductivity above 200 K in ultra-dense hydrogen sulfide, we search for high-\tc\ conventional superconductivity in the phase diagram of the binary Li-S system, using {\em ab-initio} methods for crystal structure prediction and linear response calculations for the electron-phonon coupling. We find that at pressures higher than 20 GPa, several new compositions, besides the known Li$_2$S, are stabilized; many exhibit electride-like {\em interstitial} charge localization observed in other alkali metal compounds. Of all predicted phases, only Li$_3$S at P > 640 GPa displays a sizable \tc, in contrast to what is observed in sulfur and phosphorus hydrides, where several stoichiometries lead to high \tc. We attribute this difference to 2$s$-2$p$ hybridization and avoided core overlap, and predict similar behavior for other alkali metal compounds.