标题： 扭曲双层石墨烯中魔角的光谱表征 显示英文标题

标题： Spectral characterization of magic angles in twisted bilayer graphene

摘要： 扭曲双层石墨烯（TBG）已被实验观察到，当扭转发生在某些魔角时，会表现出几乎平坦的能带。 在本信中，我们报告了关于扭曲双层石墨烯连续模型及其电子能带结构的新结果。 在我们显示，在AA耦合消失的近似下，魔角（存在完全平坦能带的角度）是非厄米算子的本征值，并且所有能带在角度$\theta$趋近于$0$时开始以指数速度压缩。 特别是，当相互作用势变化时，魔角的动力学涉及非物理的复数本征值。 使用我们的新谱特性，我们表明逆魔角的等距标度对于连续模型中的隧穿势的选择是特殊的，并不被对称性所保护。 虽然我们还表明，只要保持电荷-空穴对称性，零能态的保护在连续模型中仍然成立，但我们观察到平坦能带和指数压缩是手征模型的特殊性质。 显示英文摘要

摘要： Twisted bilayer graphene (TBG) has been experimentally observed to exhibit almost flat bands when the twisting occurs at certain magic angles. In this letter, we report new results on the continuum model of twisted bilayer graphene and its electronic band structure. Under we show that in the approximation of vanishing AA-coupling, the magic angles (at which there exist entirely flat bands) are given as the eigenvalues of a non-hermitian operator, and that all bands start squeezing exponentially fast as the angle $\theta$ tends to $0$. In particular, as the interaction potential changes, the dynamics of magic angles involves the non-physical complex eigenvalues. Using our new spectral characterization, we show that the equidistant scaling of inverse magic angles, is special for the choice of tunnelling potentials in the continuum model, and is not protected by symmetries. While we also show that the protection of zero-energy states holds in the continuum model as long as particle-hole symmetry is preserved, we observe that the existence of flat bands and the exponential squeezing are special properties of the chiral model.