Lu Xiaobo, Lian Biao, Chaudhary Gaurav, Piot Benjamin A, Romagnoli Giulio, Watanabe Kenji, Taniguchi Takashi, Poggio Martino, MacDonald Allan H, Bernevig B Andrei, Efetov Dmitri K
Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona 08860, Spain;
Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544.
Proc Natl Acad Sci U S A. 2021 Jul 27;118(30). doi: 10.1073/pnas.2100006118.
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 θ ∼ 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 θ ∼ 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.
二维范德华异质结构中的莫尔超晶格为设计电子能带特性提供了一种有效方法。近期在扭曲双层石墨烯（tBLG）中发现的奇异量子相及其相互作用，使这个莫尔体系成为最著名的凝聚态物质平台之一。到目前为止，对tBLG的研究主要集中在第一个魔角θ ∼ 1.1°处最低的两个平坦莫尔能带，高阶莫尔能带和魔角在很大程度上尚未得到探索。在此，我们报告在接近第二个魔角θ ∼ 0.5°的tBLG中观察到多个高度隔离的平坦莫尔能带，若不考虑电子-电子相互作用，这一现象无法得到解释。通过高磁场磁输运测量，我们进一步揭示了一个能量上无界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跨越了所有平凡能带间隙。相连的霍夫施塔特蝴蝶有力地证明了多个莫尔能带具有非平凡的拓扑结构。总体而言，我们的工作为理解tBLG中的量子相以及多个拓扑能带的分形霍夫施塔特谱提供了一个视角。
