We use a first-principles based self-consistent momentum-resolved density fluctuation (MRDF) model to compute the combined effects of electron-electron and electron-phonon interactions to describe the superconducting dome in the correlated ${\mathrm{MoS}}_2$ thin flake and ${\mathrm{TiSe}}_2$. We find that without including the electron-electron interaction, the electron-phonon coupling and the superconducting transition temperature ($T_c$) are overestimated in both these materials. However, once the full angular and dynamical fluctuations of the spin and charge density induced quasiparticle self-energy effects are included, the electron-phonon coupling and $T_c$ are reduced to the experimental value. With doping, both electronic correlation and electron-phonon coupling grows, and above some doping value, the former becomes so large that it starts to reduce the quasiparticle-phonon coupling constant and $T_c$, creating a superconducting dome, in agreement with experiments.

• Received 5 August 2014
• Revised 9 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.094510