Twisted Van der Waals systems offer the unprecedented possibility to tune different states of correlated quantum matter with external noninvasive electrostatic doping. The nature of the superconducting order presents a recurring open question in this context. In this work, we assess quantitatively the case of spin-fluctuation-mediated pairing for $\mathrm{\Gamma }$-valley twisted transition metal dichalcogenide homobilayers. We calculate self-consistently and dynamically the doping-dependent superconducting transition temperature $T_{\mathrm{c}}$ revealing a superconducting dome with a maximal $T_{\mathrm{c}}\approx 0.1–1\mathrm{K}$ depending on twist angle. We compare our results with conventional phonon-mediated superconductivity, and we identify clear fingerprints in the doping dependence of $T_{\mathrm{c}}$, which enable experiments to distinguish between different pairing mechanisms.

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• Magnetic order
• Pairing mechanisms
• Superconducting phase transition
• Superconductivity
• Honeycomb lattice
• Strongly correlated systems
• Transition metal dichalcogenides
• Approximation methods for many-body systems
• Holstein model
• Hubbard model
• Wannier function methods