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We study the electronic instabilities of near 1/4 electron doped grapheneusing the functional renormalization group (FRG) and variational Monte-Carlomethod. A modified FRG implementation is utilized to improve the treatment ofthe von Hove singularity. At 1/4 doping the system is a chiral spin densitywave state exhibiting the anomalous quantized Hall effect, or equivalently aChern insulator. When the doping deviates from 1/4, the $d_{x^2-y^2}+i d_{xy}$Cooper pairing becomes the leading instability. Our results suggest near 1/4electron or hole doped graphene is a fertile playground for the search of Cherninsulators and superconductors.

Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping