A solid-state electrolyte for a multilayer solid-state electrochemical cell is described herein. The electrolyte comprises a lithium electrolyte salt and nanofibers of a cubic phase lithium lanthanum zirconium oxide (c-LLZO), and a polymer interspersed with the nanofibers and electrolyte salt. Electrochemical cells comprising the solid-state electrolyte, and solid-state cathodes comprising the nanofibers of c-LLZO are also described herein.