  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 MoS2 thin flake and TiSe2. We find that without including the
electron-electron interaction, the electron-phonon coupling and the
superconducting transition temperature (Tc) 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 Tc 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 Tc, creating a superconducting
dome, in agreement with experiments.
