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-T$_c$ conventional superconductivity in the phase diagram of the binary Li-S system, using 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 interstitial charge localization observed in other alkali-metal compounds. Of all predicted phases, only an fcc phase of Li$_3$S, metastable before 640 GPa, exhibits a sizable T$_c$, in contrast to what is observed in sulfur and phosphorus hydrides, where several stoichiometries lead to high T$_c$. We attribute this difference to 2$s$-2$p$ hybridization and avoided core overlap, and predict similar behavior for other alkali-metal compounds. [1] C. Kokail, C. Heil and L. Boeri, Phys. Rev. B 94, 060502 (R) (2016)