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

中文翻译：

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具有增强交换耦合的重掺杂蜂窝晶格上的竞争电子订单

受最近在扭曲双层石墨烯中发现相关绝缘和超导行为的启发，我们使用截断的统一功能重整化群方法重新研究了石墨烯在范霍夫奇点附近掺杂的蜂窝晶格。我们考虑蜂窝晶格上的扩展哈伯德模型，包括现场和最近邻库仑排斥，以及最近邻铁磁交换和对跳跃相互作用。通过改变最近邻交换耦合和库仑排斥作为自由参数的强度，我们提出了丰富的基态相图，其中包含自旋三重态$F$-波和自旋单线态手性 $d$波超导相、相称和不相称的自旋波和电荷密度波相以及铁磁相。在没有交换耦合和最近邻排斥的小值的情况下，四亚晶格自旋密度波相位就在范霍夫填充周围产生，而手征$d$波超导性在远离它的地方出现。令人惊讶的是，手性$d$在我们的计算中，-波超导性受到弱最近邻交换耦合的强烈抑制。我们认为这种抑制可能是尚未通过实验观察到为掺杂石墨烯提出的手性超导性的原因之一。