Spectral characterization of magic angles in twisted bilayer graphene
Spectral characterization of magic angles in twisted bilayer graphene
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DOI：
10.1103/physrevb.103.165113
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发表时间：
2020-10
影响因子：
3.7
通讯作者：
Simon Becker;M. Embree;Jens Wittsten;M. Zworski
中科院分区：
文献类型：
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作者：
Simon Becker;M. Embree;Jens Wittsten;M. Zworski
实验观察发现，当以特定的“魔角”扭转时，扭曲双层石墨烯（TBG）会呈现出近乎平坦的能带。在这篇快报中，我们报告了关于扭曲双层石墨烯连续统模型及其电子能带结构的新成果。我们表明，在AA耦合可忽略的近似下，“魔角”（存在完全平坦能带时的扭转角）由一个非厄米算符的本征值给出，并且当角度\(\theta\)趋于\(0\)时，所有能带都开始以指数速度快速压缩。特别地，随着相互作用势的变化，“魔角”的动态变化涉及非物理的复本征值。利用我们新的光谱表征，我们证明了反“魔角”的等距缩放对于连续统模型中隧穿势的选择而言是特殊的，且不受对称性保护。虽然我们还表明，只要粒子 - 空穴对称性得以保持，零能态的保护在连续统模型中依然成立，但我们观察到平坦能带的存在和指数压缩是手性模型的特殊性质。
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.