Density Waves and Cooper Pairing on the Honeycomb Lattice

Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density-wave order. Away from half-filling, f-wave triplet-pairing and d + id singlet-pairing instabilities are found to emerge out of density-wave regimes.