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We analyze the microscopic origin and the physical properties of thesuperconducting phase recently observed in MoS$_2$. We show how the combinationof the valley structure of the conduction band, the density dependence of thescreening of the long range Coulomb interactions, the short range electronicrepulsion, and the relative weakness of the electron-phonon interactions, makespossible the existence of a phase where the superconducting order parameter hasopposite signs in different valleys, resembling the superconductivity found inthe pnictides and cuprates.

Interactions and superconductivity in heavily doped MoS2