The interplay of superconductivity with charge density wave (CDW) in metallic transition-metal dichalcogenides has been widely debated, and viable strategies manipulating these quantum states in the two-dimensional (2D) limit remain unclear. Using the ab initio anisotropic Migdal-Eliashberg theory, we successfully explain the superconductivity observed in monolayer $1H\text{−}{\mathrm{TaS}}_2$ by simultaneously determining its precise CDW structure and treating the marked modification of electron-phonon interaction and critical temperature $T_{\mathrm{c}}$ by spin-orbit coupling effects. With this paradigm, we further show that electron doping weakens the CDW order leading to increased $T_{\mathrm{c}}$ up to 11 K, along with a single-gap to two-gap superconductivity transition due to the suppression of the CDW gap. By contrast, a low hole doping barely affects the CDW but still yields a significantly enhanced superconducting order, implying their good coexistence. Combined with the synergistic behavior of CDW and superconductivity, which cooperate upon ${\mathrm{TaS}}_2$ thickness reduction causing an unusual rise of $T_{\mathrm{c}}$, our results unravel diversified interactions between the two collective orders in ultrathin ${\mathrm{TaS}}_2$, being competition, coexistence or cooperation depending on external stimuli, which provide key clues for controlling correlated states in devices based on 2D CDW superconductors.

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• Charge density waves
• Electron-phonon coupling
• First-principles calculations
• Multiband superconductivity
• Monolayer films
• Superconductors
• Transition metal dichalcogenides
• Density functional theory
• Eliashberg theory