标题： 扭曲双层石墨烯中的RKKY二次和双二次自旋-自旋相互作用 显示英文标题

标题： RKKY quadratic and biquadratic spin-spin interactions in twisted bilayer graphene

摘要： 我们研究了魔角之外扭曲双层石墨烯中两个磁性杂质之间的RKKY二次和双二次自旋-自旋相互作用的竞争。 我们应用了Bistritzer-MacDonald模型，该模型描述了两层石墨烯以一个小角度彼此扭转的情况。 通过将模型简化为具有修正费米速度的狄拉克型模型，我们利用自由能的微扰理论推导出了RKKY二次和双二次自旋相互作用的表达式。 双二次相互作用被更大的相互作用常数幂次抑制，并且随着杂质之间距离的增加比二次相互作用更快地减小。 然而，由于杂质分离距离、化学势、扭转角和温度的振荡周期不同，有可能精细调节系统进入主导双二次相互作用的模式。 这种精细调节模式的存在可能为观察非传统自旋有序提供一个有希望的机会。 显示英文摘要

摘要： We study the competition between the RKKY quadratic and biquadratic spin-spin interactions of two magnetic impurities in twisted bilayer graphene away from the magic angle. We apply the Bistritzer-MacDonald model of two graphene layers twisted with respect to each other by a small angle. By reducing the model to the Dirac-type one with modified Fermi velocity, we derive expressions for the RKKY quadratic and biquadratic spin interactions using perturbation theory for the free energy. The biquadratic interaction is suppressed by a larger power of the interaction constant and decreases faster with a the distance between impurities comparing to the quadratic one. Nevertheless, due to the different period of oscillations with impurity separation distance, chemical potential, twist angle and temperature, it is possible to fine-tune the system to the regime of dominating biquadratic interaction. The existence of such fine-tuned regime might provide a promising opportunity to observe non-conventional spin ordering.