We reveal that electron-phonon systems described by the Holstein model on abipartite lattice exhibit, away from half filling, a supersolid (SS) phasecharacterized by coexisting charge order (CO) and superconductivity (SC), andan accompanying quantum critical point (QCP). The SS, demonstrated by thedynamical mean-field theory with a quantum Monte Carlo impurity solver, emergesin the intermediate-coupling regime, where the peak of the Tc dome is locatedand the metal-insulator crossover occurs. On the other hand, in the weak- andstrong-coupling regimes the CO-SC boundary is of first order with nointervening SS phases. The QCP is associated with the continuous transitionfrom SS to SC and characterized by a reentrant behavior of the SS around it. Wefurther show that the SS-SC transition is hallmarked by diverging chargefluctuations and a kink (peak) in the superfluid density.
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