Beyond fractional quantum Hall Unlike most electronic topological phenomena, the fractional quantum Hall effect requires correlations among electrons. Spanton et al. describe a class of related but even more unusual states, the fractional Chern insulators (see the Perspective by Repellin and Regnault). They observed these states in samples of bilayer graphene, where one of the graphene layers was misaligned by a small angle with respect to an adjoining layer of hexagonal boron nitride. The misalignment created a superlattice potential and topologically nontrivial bands, which had a fractional filling, thanks to strong electronic interactions. The findings expand the class of correlated topological states, which have been predicted to harbor exotic excitations. Science, this issue p. 62; see also p. 31 Capacitance measurements on bilayer graphene together with calculations reveal a class of correlated topological states. Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices C=−1, ±2, and ±3. Some of these phases, in C=−1 and C=2 bands, are characterized by fractional Hall conductance—that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.

中文翻译：

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范德华异质结构中分数陈绝缘体的观察

超越分数量子霍尔与大多数电子拓扑现象不同，分数量子霍尔效应需要电子之间的相关性。斯潘顿等人。描述一类相关但更不寻常的状态，分数陈绝缘体（参见 Repellin 和 Regnault 的观点）。他们在双层石墨烯样品中观察到这些状态，其中石墨烯层之一相对于相邻的六方氮化硼层错位了一个小角度。由于强电子相互作用，未对准产生了超晶格势和拓扑上非平凡的带，这些带具有部分填充。这些发现扩展了相关拓扑状态的类别，这些拓扑状态已被预测为具有奇异的激发。科学，这个问题 p。62; 另见第。31 双层石墨烯的电容测量以及计算揭示了一类相关的拓扑状态。拓扑有序相的特征在于长程量子纠缠和分数统计，而不是对称破坏。首先在分数填充的连续朗道能级中观察到，拓扑序被提议更普遍地出现在拓扑非平凡陈带的分数填充中。在这里，我们报告了对由磁场和双层石墨烯-六方氮化硼异质结构中的超晶格势的相互作用产生的 Harper-Hofstadter 带的部分填充的有隙状态的观察。我们在陈指数 C=-1、±2 和 ±3 的谱带部分填充处观察到相位。其中一些相位，在 C=-1 和 C=2 波段，