Superconducting states of pure and doped graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states; s wave and an exotic p + ip that is possible because of the special structure of the honeycomb lattice. At half filling, the p + ip phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.