The discovery of superconducting and insulating states in magic-angle twisted bilayer graphene (MATBG)1,2 has ignited considerable interest in understanding the nature of electronic interactions in this chemically pristine material. The transport properties of MATBG as a function of doping are similar to those of high-transition-temperature copper oxides and other unconventional superconductors1–3, which suggests that MATBG may be a highly interacting system. However, to our knowledge, there is no direct experimental evidence of strong many-body correlations in MATBG. Here we present high-resolution spectroscopic measurements, obtained using a scanning tunnelling microscope, that provide such evidence as a function of carrier density. MATBG displays unusual spectroscopic characteristics that can be attributed to electron–electron interactions over a wide range of doping levels, including those at which superconductivity emerges in this system. We show that our measurements cannot be explained with a mean-field approach for modelling electron–electron interactions in MATBG. The breakdown of a mean-field approach when applied to other correlated superconductors, such as copper oxides, has long inspired the study of the highly correlated Hubbard model3. We show that a phenomenological extended-Hubbard-model cluster calculation, which is motivated by the nearly localized nature of the relevant electronic states of MATBG, produces spectroscopic features that are similar to those that we observed experimentally. Our findings demonstrate the critical role of many-body correlations in understanding the properties of MATBG. Scanning tunnelling spectroscopy and extended-Hubbard-model cluster calculations reveal that magic-angle twisted bilayer graphene is a strongly correlated electron system, similar to other unconventional superconductors.

中文翻译：

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魔角扭曲双层石墨烯中多体相关性的光谱特征

魔角扭曲双层石墨烯 (MATBG)1,2 中超导和绝缘状态的发现激发了人们对了解这种化学原始材料中电子相互作用性质的极大兴趣。作为掺杂函数的 MATBG 的传输特性类似于高转变温度氧化铜和其他非常规超导体的传输特性 1-3，这表明 MATBG 可能是一个高度相互作用的系统。然而，据我们所知，在 MATBG 中没有强多体相关性的直接实验证据。在这里，我们展示了使用扫描隧道显微镜获得的高分辨率光谱测量，这些测量提供了作为载流子密度函数的证据。MATBG 显示出不寻常的光谱特性，这可归因于各种掺杂水平上的电子 - 电子相互作用，包括在该系统中出现超导性的那些。我们表明，我们的测量不能用平均场方法来解释 MATBG 中的电子 - 电子相互作用。当应用于其他相关超导体（例如氧化铜）时，平均场方法的分解长期以来激发了对高度相关的哈伯德模型的研究。我们表明，由 MATBG 相关电子状态的近乎局部性质所激发的现象学扩展哈伯德模型集群计算产生的光谱特征与我们通过实验观察到的特征相似。我们的研究结果证明了多体相关性在理解 MATBG 特性中的关键作用。扫描隧道光谱和扩展哈伯德模型簇计算表明，魔角扭曲双层石墨烯是一种强相关电子系统，类似于其他非常规超导体。