Motivated by the possibility of superconductivity in doped graphene sheets, we investigate superconducting order in the extended Hubbard model on the two-dimensional graphene lattice using the variational cluster approximation (VCA) and the cellular dynamical mean-field theory (CDMFT) with an exact diagonalization solver at zero temperature. The nearest-neighbor interaction is treated using a mean-field decoupling between clusters. We compare different pairing symmetries, singlet and triplet, based on short-range pairing. VCA simulations show that the real (nonchiral), triplet $p$-wave symmetry is favored for small $V$, small onsite interaction $U$, or large doping, whereas the chiral combination $p+ip$ is favored for larger values of $V$, stronger onsite interaction $U$, or smaller doping. CDMFT simulations confirm the stability of the $p+ip$ solution, even at half-filling. Singlet superconductivity (extended $s$ wave or $d$ wave) is either absent or subdominant.

• Received 28 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.085121