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We study the Hubbard model on the honeycomb lattice with nearest-neighborhopping ($t>0$) and next-nearest-neighbor one ($t'<0$). When $t'<-t/6$, thesingle-particle spectrum is featured by the continuously distributed Van-Hovesaddle points at the band bottom, where the density of states diverges inpower-law. We investigate possible unconventional superconductivity in suchsystem with Fermi level close to the band bottom by employing both random phaseapproximation and determinant quantum Monte-Carlo approaches. Our study revealsa possible triplet $p+ip$ superconductivity in this system with appropriateinteractions. Our results might provide a possible route to look for tripletsuperconductivity with relatively-high transition temperature in a low-filledgraphene and other similar systems.

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