Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle
Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle
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DOI：
10.1073/pnas.2100006118
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发表时间：
2020-06
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通讯作者：
Xiaobo Lu;Biao Lian;G. Chaudhary;B. Piot;G. Romagnoli;Kenji Watanabe;T. Taniguchi;M. Poggio;A. Macdonald;B. Bernevig;D. Efetov
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作者：
Xiaobo Lu;Biao Lian;G. Chaudhary;B. Piot;G. Romagnoli;Kenji Watanabe;T. Taniguchi;M. Poggio;A. Macdonald;B. Bernevig;D. Efetov
意义 在高质量扭曲双层石墨烯中观察到多个平带，接近理论预测的第二魔角。这些隔离良好的平坦莫尔条纹具有非平凡的拓扑结构，连接的多频带霍夫施塔特蝴蝶光谱证明了这一点。这项工作为理解扭曲双层石墨烯中的涌现量子相（即强相关性和能带拓扑）和多个拓扑能带的分形霍夫施塔特谱提供了一个视角。二维范德华异质结构中的莫尔超晶格提供了一种设计电子能带特性的有效方法。最近发现的奇异量子相及其在扭曲双层石墨烯 (tBLG) 中的相互作用使该莫尔系统成为最著名的凝聚态物质平台之一。到目前为止，tBLG 的研究主要集中在第一魔角 θm1 ∼ 1.1° 处的最低两个平坦莫尔带，而高阶莫尔带和魔角基本上未被探索。在这里，我们报告了在 tBLG 中接近第二魔角 θm2 ∼ 0.5° 时观察到的多个隔离良好的平坦莫尔带，如果不考虑电子-电子相互作用，就无法解释这一点。通过高磁场磁输运测量，我们进一步揭示了能量上无束缚的霍夫施塔特蝴蝶谱，其中连续扩展的量子化朗道能级间隙穿过所有平凡的带隙。相连的霍夫施塔特蝴蝶有力地证明了多个莫尔带的拓扑结构。总的来说，我们的工作为理解 tBLG 中的量子相和多个拓扑带的分形 Hofstadter 谱提供了一个视角。
Significance Multiple flat bands in high-quality twisted bilayer graphene close to the theoretically predicted second magic angle are observed. These well-isolated flat moiré bands host a nontrivial topology which is evidenced by a connecting multiband Hofstadter butterfly spectrum. This work provides a perspective for understanding the emergent quantum phases (i.e., strong correlation and band topology) in twisted bilayer graphene and the fractal Hofstadter spectra of multiple topological bands. Moiré superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moiré system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moiré bands at the first magic angle θm1 ∼ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moiré bands in tBLG close to the second magic angle θm2 ∼ 0.5°, which cannot be explained without considering electron–election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.