The correlated insulator (CI) states and the recently discovered density wave (DW) states in magic-angle twisted bilayer graphene (TBG) have stimulated intense research interest. However, to date, the nature of these “featureless” correlated states with zero Chern numbers are still elusive and lack a characteristic experimental signature. Thus, an experimental probe to identify the characters of these featureless CI and DW states is urgently needed. In this Letter, we theoretically study the correlated insulators and density wave states at different integer and fractional fillings of the flat bands in magic-angle TBG based on extended unrestricted Hartree-Fock calculations including the Coulomb screening effects from the remote bands. We further investigate the nonlinear optical response of the various correlated states and find that the nonlinear optical conductivities can be used to identify the nature of these CI and DW states at most of the fillings. Therefore, we propose that a nonlinear optical response can serve as a promising experimental probe for unveiling the nature of the CI and DW states observed in magic-angle TBG.

中文翻译：

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魔角扭曲双层石墨烯中的相关绝缘体、密度波态及其非线性光学响应

魔角扭曲双层石墨烯 (TBG) 中的相关绝缘体 (CI) 态和最近发现的密度波 (DW) 态激发了强烈的研究兴趣。然而，迄今为止，这些陈数为零的“无特征”相关状态的性质仍然难以捉摸，并且缺乏特征性的实验特征。因此，迫切需要一种实验探针来识别这些无特征的 CI 和 DW 状态的特征。在这封信中，我们基于扩展的无限制 Hartree-Fock 计算，包括来自远程带的库仑屏蔽效应，从理论上研究了魔角 TBG 中平坦带的不同整数和分数填充的相关绝缘体和密度波状态。我们进一步研究了各种相关状态的非线性光学响应，发现非线性光学电导率可用于识别大多数填充物的这些 CI 和 DW 状态的性质。因此，我们提出非线性光学响应可以作为一种有前途的实验探针，用于揭示在魔角 TBG 中观察到的 CI 和 DW 状态的性质。