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Possible Triplet $p+ip$ Superconductivity in Graphene at Low Filling

We study the Hubbard model on the honeycomb lattice with nearest-neighbor hopping ($t>0$) and next-nearest-neighbor one ($t'<0$). When $t'<-t/6$, the single-particle spectrum is featured by the continuously distributed Van-Hove saddle points at the band bottom, where the density of states diverges in power-law. We investigate possible unconventional superconductivity in such system with Fermi level close to the band bottom by employing both random phase approximation and determinant quantum Monte-Carlo approaches. Our study reveals a possible triplet $p+ip$ superconductivity in this system with appropriate interactions. Our results might provide a possible route to look for triplet superconductivity with relatively-high transition temperature in a low-filled graphene and other similar systems.