Understanding the origin of superconducting dome in electron-doped MoS$_2$ monolayer

We investigate the superconducting properties of molybdenum disulphide (MoS$_2$) monolayer across a broad doping range, successfully recreating the so far unresolved superconducting dome. Our first-principles findings reveal several dynamically stable phases across the doping-dependent phase diagram. We observe a doping-induced increase in the superconducting transition temperature $T_c$, followed by a reduction in $T_c$ due to the formation of charge density waves (CDWs), polaronic distortions, and structural transition from the H to the 1T$'$ phase. Our work reconciles various experimental observations of CDWs in MoS$_2$ with its doping-dependent superconducting dome structure, which occurs due to the $1\times 1$ H to $2\times 2$ CDW phase transition.