  Recently it was reported experimentally that the monolayer graphene can be
doped to beyond the Van Hove singularity. We study theoretically the possible
superconductivity and the corresponding spin excitations of the monolayer
graphene in this doping region. A static spin-density-wave state is favorable
due to the nested Fermi surface as the Fermi level is doped to the Van Hove
singularity point. Superconductivity may be realized upon further doping. The
spin excitations in the superconducting state are studied theoretically based
on the random phase approximation. The overall features are qualitatively the
same with those in cuprate superconductors. Thus we have proposed an exciting
possibility, namely, the heavily overdoped monolayer graphene can become a
novel platform to study the unconventional superconductivity.
