Intrinsic triplet p$+$ip topological superconductivity in low filled graphene

Inspired by the continuously distributed Van-Hove saddle points at the band bottom, we studied the low filled Hubbard-model on the Honeycomb-lattice with negative next-nearest-neighbor hopping integrals, which represents the graphene system. Within different parameter regimes, our combined weak coupling random phase approximation and strong coupling determinant quantum Monte-Carlo approaches consistently reveal the triplet p$+$ip topological superconductivity in the ground state of the system. Further more, when a weak Kane-Mele spin-orbit coupling is included, the time-reversal invariant Z2 weak topological superconductivity will be realized in the system. Our unbiased numerical results provide basis to realize the intrinsic exotic topological superconductivity in the graphene and similar systems.