If we stack up two layers of graphene while changing their respective orientation by some twisting angle, we end up with a strikingly different system when compared to single-layer graphene. For a very specific value of this twist angle, known as magic angle, twisted bilayer graphene displays a unique phase diagram that cannot be found in other systems. Recently, high-harmonic generation spectroscopy has been successfully applied to elucidate the electronic properties of quantum materials. The purpose of the present work is to exploit the nonlinear optical response of magic-angle twisted bilayer graphene to unveil its electronic properties. We show that the band structure of magic-angle twisted bilayer graphene is imprinted onto its high-harmonic spectrum. Specifically, we observe a drastic decrease of harmonic signal as we approach the magic angle. Our results show that high-harmonic generation can be used as a spectroscopy tool for measuring the twist angle and also the electronic properties of twisted bilayer graphene, paving the way for an all-optical characterization of moiré materials.

中文翻译：

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扭曲的高次谐波产生：魔角扭曲双层石墨烯的全光学表征

如果我们堆叠两层石墨烯，同时通过一些扭转角度改变它们各自的方向，那么与单层石墨烯相比，我们最终会得到一个截然不同的系统。对于这个扭曲角的非常具体的值（称为魔角），扭曲双层石墨烯显示出在其他系统中找不到的独特相图。最近，高次谐波产生光谱已成功应用于阐明量子材料的电子特性。目前工作的目的是利用魔角扭曲双层石墨烯的非线性光学响应来揭示其电子特性。我们表明，魔角扭曲双层石墨烯的能带结构被印在其高次谐波谱上。具体来说，当我们接近魔角时，我们观察到谐波信号急剧减少。我们的结果表明，高次谐波产生可以用作测量扭转双层石墨烯扭转角和电子特性的光谱工具，为莫尔材料的全光学表征铺平道路。