Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling

Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using truncated unity functional renormalization group approach. We consider an extended Hubbard model on including on-site nearest-neighbor Coulomb repulsions, ferromagnetic exchange pair hopping interactions. By varying strength coupling repulsion as free parameters, present rich ground-state phase diagrams which contain spin-triplet $f$-wave spin-singlet chiral $d$-wave phases, commensurate incommensurate spin- charge-density-wave phase. In absence for small value repulsion, four-sublattice spin-density-wave is generated right around filling, while superconductivity emerges slightly away from it. Surprisingly, strongly suppressed weak our calculations. argue that this suppression might be one reasons why proposed graphene has not yet been observed experimentally.