We study the excitations that emerge upon doping the translationally invariant correlated insulating states in magic-angle twisted bilayer graphene at various integer filling factors $\nu$. We identify parameter regimes where these are excitations associated with skyrmion textures in the spin or pseudospin degrees of freedom, and explore both short-distance pairing effects and the formation of long-range ordered skyrmion crystals. We perform a comprehensive analysis of the pseudospin skyrmions that emerge upon doping insulators at even $\nu$, delineating the regime in parameter space where these are the lowest-energy charged excitations by means of self-consistent Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key ingredient behind a recent proposal of skyrmion superconductivity. Building upon this, we construct hopping models to extract the effective masses of paired skyrmions, and discuss our findings and their implications for skyrmion superconductivity in relation to experiments, focusing on the dome-shaped dependence of the transition temperature on the twist angle. We also investigate the properties of spin skyrmions about the quantized anomalous Hall insulator at $\nu =+3$. In both cases, we demonstrate the formation of robust spin or pseudospin skyrmion crystals upon doping to a finite density away from integer filling.

中文翻译：

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扭曲双层石墨烯中的 Skyrmions：稳定性、配对和结晶

我们研究了以各种整数填充因子在魔角扭曲双层石墨烯中掺杂平移不变相关绝缘态时出现的激发$\nu$. 我们确定参数方案，其中这些是与自旋或赝自旋自由度中的斯格明子纹理相关的激发，并探索短距离配对效应和长程有序斯格明子晶体的形成。我们对掺杂绝缘体上出现的赝自旋skyrmions进行了全面分析$\nu$，通过对相互作用的 Bistritzer-MacDonald 模型的自洽 Hartree-Fock 计算，描绘了参数空间中的状态，其中这些是最低能量的带电激发。我们明确地证明了纯电子介导的斯格明子配对，这是最近提出的斯格明子超导性背后的关键因素。在此基础上，我们构建了跳跃模型以提取配对斯格明子的有效质量，并讨论我们的发现及其对与实验相关的斯格明子超导性的影响，重点关注转变温度对扭曲角的圆顶形依赖性。我们还研究了关于量子化异常霍尔绝缘体的自旋skyrmions的性质$\nu =+3$. 在这两种情况下，我们都证明了在掺杂到远离整数填充的有限密度时形成了稳健的自旋或赝自旋斯格明子晶体。