By comparing with recently available experimental data from several groups, we critically discuss the manifestation of continuum many body interaction effects in twisted bilayer graphene (tBLG) with small twist angles and low carrier densities, which arise naturally within the Dirac cone approximation for the non-interacting band structure. We provide two specific examples of such continuum many body theories: one involving electron-phonon interaction and one involving electron-electron interaction. In both cases, the experimental findings are only partially quantitatively consistent with rather clear-cut leading-order theoretical predictions based on well-established continuum many body theories. We provide a critical discussion, based mainly on the currently available tBLG experimental data, on possible future directions for understanding many body renormalization involving electron-phonon and electron-electron interactions in the system. One definitive conclusion based on the comparison between theory and experiment is that the leading order 1-loop perturbative renormalization group theory completely fails to account for the electron-electron interaction effects in the strong-coupling limit of flatband moire tBLG system near the magic twist angle even at low doping where the Dirac cone approximation should apply. By contrast, approximate nonperturbative theoretical results based on Borel-Pade resummation or $1/N$ expansion seems to work well compared with experiments, indicating rather small interaction corrections to Fermi velocity or carrier effective mass. For electron-phonon interactions, however, the leading-order continuum theory works well except when van Hove singularities in the density of states come into play.

中文翻译：

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扭曲双层石墨烯中的电子-声子和电子-电子相互作用效应

通过与几组最近可用的实验数据进行比较，我们批判性地讨论了具有小扭转角和低载流子密度的扭曲双层石墨烯（tBLG）中连续多体相互作用效应的表现，这些效应在狄拉克锥近似内自然出现相互作用的能带结构。我们提供了这种连续多体理论的两个具体例子：一个涉及电子 - 声子相互作用，一个涉及电子 - 电子相互作用。在这两种情况下，实验结果仅在部分定量上与基于完善的连续体多体理论的相当明确的超前序理论预测一致。我们提供了一个批判性的讨论，主要基于当前可用的 tBLG 实验数据，关于理解系统中涉及电子-声子和电子-电子相互作用的许多体重整化可能的未来方向。基于理论与实验比较的一个明确结论是，领先的阶一环微扰重整化群理论完全不能解释平带莫尔 tBLG 系统在魔术扭曲角附近的强耦合极限中的电子-电子相互作用效应。即使在应该应用狄拉克锥近似的低掺杂情况下。相比之下，与实验相比，基于 Borel-Pade 求和或 $1/N$ 扩展的近似非微扰理论结果似乎效果很好，表明对费米速度或载流子有效质量的相互作用修正相当小。然而，对于电子-声子相互作用，