Functional renormalization group and variational Monte Carlo studies of   the electronic instabilities in graphene near 1/4 doping
  We study the electronic instabilities of near 1/4 electron doped graphene using the functional renormalization group (FRG) and variational Monte-Carlo method. A modified FRG implementation is utilized to improve the treatment of the von Hove singularity. At 1/4 doping the system is a chiral spin density wave state exhibiting the anomalous quantized Hall effect, or equivalently a Chern 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 1/4 electron or hole doped graphene is a fertile playground for the search of Chern insulators and superconductors. 
Wan-Sheng Wang, Yuan-Yuan Xiang, Qiang-Hua Wang, Fa Wang, Fan Yang and   Dung-Hai Lee
cond-mat.supr-con cond-mat.str-el