Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of three electrons per moiré unit cell. The AQH effect arises in an insulating state with both valley and ferromagnetic order. We argue that weak doping of such a system leads to the formation of a novel topological spin texture, a “double-tetarton lattice.” The building block of this lattice, the “double-tetarton,” is a spin configuration which covers $1/4$ of the unit sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields are more conventional skyrmion lattices recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective nonlinear sigma model which includes the effects of long-ranged Coulomb interactions.

中文翻译：

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扭曲双层石墨烯中的Skyrmion和tetarton晶格

最近在扭曲的双层石墨烯上进行的实验表明，在每个摩尔单元晶胞中填充三个电子时，会出现异常量子霍尔（AQH）效应。AQH效应以谷和铁磁有序的绝缘状态出现。我们认为，这种系统的弱掺杂会导致形成新颖的拓扑自旋纹理，即“双Tetarton晶格”。这种格子的构造块“ double-tetarton”是一种旋转结构，覆盖了$\mathrm{1个}/4$单位球的两倍。与天蝎子晶格相反，这种磁性纹理的净磁化强度消失了。只有在较大的磁场下，才能恢复更常规的天体离子晶格。但是，即使对于大磁场，在铁磁AQH状态中添加一个电荷也会使数百个自旋翻转。我们的分析基于对有效非线性sigma模型的研究，其中包括远程库仑相互作用的影响。