Presented are new, earth-abundant lithium superionic conductors, Li3Y(PS4)2 and Li5PS4Cl2, that emerged from a comprehensive screening of the Li—P—S and Li-M-P—S chemical spaces. Both candidates are derived from the relatively unexplored quaternary silver thiophosphates. One key enabler of this discovery is the development of a first-of-its-kind high-throughput first principles screening approach that can exclude candidates unlikely to satisfy the stringent Li+ conductivity requirements using a minimum of computational resources. Both candidates are predicted to be synthesizable, and are electronically insulating. Systems and methods according to present principles enable new, all-solid-state rechargeable lithium-ion batteries.