Spin bond order driven by extended repulsive interactions in doped graphene

We use the truncated-unity functional renormalization group (TUFRG) to study many-body instabilities of correlated electrons in graphene doped near the van Hove singularity (VHS). The system is described by an extended Hubbard model including several Coulomb repulsions between neighboring sites. With the repulsion parameters, which turn out to be suitable for low-energy consideration of graphene, we find a spin-bond-order phase in the vicinity of the VHS. This phase gives way to a spin-density-wave phase when involving a weak additional screening. The ground-state phase diagram is presented in the space of the doping level and the screening parameter. We describe in detail both of these spin-ordered states by using recently developed TUFRG + mean-field (MF) scheme, i.e. a combined approach of TUFRG and MF theory. The collinear states are energetically preferable in both cases of the spin bond order and the spin-density wave. But if the third-nearest-neighbor hopping is absent, these spin orders become chiral. The band structures of two collinear spin-ordered states are presented, revealing the metallic behavior of the system.