论文标题
扭曲双层石墨烯中魔法角度的光谱表征
Spectral characterization of magic angles in twisted bilayer graphene
论文作者
论文摘要
扭曲的双层石墨烯（TBG）已在实验上观察到在某些魔法角度发生时几乎表现出几乎平坦的带。在这封信中，我们报告了有关扭曲双层石墨烯及其电子带结构的连续模型的新结果。在我们表明，在消失的AA耦合的近似中，魔术角（在其中存在完全平坦的频带）被作为非热门操作员的特征值，并且所有乐队都开始快速地挤压$θ$的角度，倾向于$ 0 $。特别是，随着相互作用势的变化，魔法角度的动力学涉及非物理复合体特征值。使用我们的新光谱表征，我们表明，反向魔法角的等距尺度对于连续模型中选择隧道电位的选择是特殊的，并且不受对称性的保护。虽然我们还表明，只要保留了颗粒 - 孔对称性，对零能状态的保护就存在于连续模型中，但我们观察到，平坦带和指数挤压的存在是手性模型的特殊特性。
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 $θ$ 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.
