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首页> 外文期刊>Physical review, B >Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions
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Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions

机译：扭曲双层石墨烯的乐队结构：紧急对称，相称近似值和卫生障碍物

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摘要

A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (e.g., theta similar to 1.05 degrees). In this regime, correlated insulating states and superconductivity have been experimentally observed. A microscopic description of these phenomena requires an understanding of universal aspects of the band structure, which we discuss here. First, we point out the importance of emergent symmetries, such as valley conservation, which are excellent symmetries in the limit of small twist angles and dictate qualitative features of the band structure. These have sometimes been overlooked when discussing commensurate approximants to the band structure, which we also review here, and solidify their connection with the continuum theory which incorporates all emergent symmetries. Finally, we discuss obstructions to writing tight-binding models of just the isolated bands, and in particular a symmetry-based diagnostic of these obstructions, as well as relations to band topology and strategies for resolving the obstruction. Especially, we construct a four-band model where the two lower isolated bands realize all identified Wannier obstructions of the single-valley nearly flat bands of twisted bilayer graphene.
机译：双层石墨烯的频带结构在小扭转角度的一个显着特征是隔离带附近的中立频带的外观，其带宽可以在某些魔角（例如，类似于1.05度的θ。在该制度中，已经通过实验观察相关的绝缘状态和超导性。这些现象的微观描述需要了解我们在这里讨论的乐队结构的普遍方面。首先，我们指出了紧急对称的重要性，例如山谷保护，这在小扭曲角度的极限下是出色的对称性，并决定带结构的定性特征。当讨论与乐队结构的相应近似值讨论时，这些人有时被忽略了，我们在此审查，并巩固了与纳入所有紧急对称的连续性理论的关系。最后，我们讨论了障碍物，以写入孤立的频段的紧密绑定模型，特别是对这些障碍物的基于对称的诊断，以及与解决障碍物的带拓扑和策略的关系。特别是，我们构造了一个四带模型，其中两个下隔离带意识到单个谷的所有识别的WANNIER障碍物的扭曲双层石墨烯的单谷几乎是平坦的带。

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