A van der Waals heterostructure is a type of metamaterial that consists of vertically stacked two-dimensional building blocks held together by the van der Waals forces between the layers. This design means that the properties of van der Waals heterostructures can be engineered precisely, even more so than those of two-dimensional materials. One such property is the ‘twist’ angle between different layers in the heterostructure. This angle has a crucial role in the electronic properties of van der Waals heterostructures, but does not have a direct analogue in other types of heterostructure, such as semiconductors grown using molecular beam epitaxy. For small twist angles, the moiré pattern that is produced by the lattice misorientation between the two-dimensional layers creates long-range modulation of the stacking order. So far, studies of the effects of the twist angle in van der Waals heterostructures have concentrated mostly on heterostructures consisting of monolayer graphene on top of hexagonal boron nitride, which exhibit relatively weak interlayer interaction owing to the large bandgap in hexagonal boron nitride. Here we study a heterostructure consisting of bilayer graphene, in which the two graphene layers are twisted relative to each other by a certain angle. We show experimentally that, as predicted theoretically, when this angle is close to the ‘magic’ angle the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling. These flat bands exhibit insulating states at half-filling, which are not expected in the absence of correlations between electrons. We show that these correlated states at half-filling are consistent with Mott-like insulator states, which can arise from electrons being localized in the superlattice that is induced by the moiré pattern. These properties of magic-angle-twisted bilayer graphene heterostructures suggest that these materials could be used to study other exotic many-body quantum phases in two dimensions in the absence of a magnetic field. The accessibility of the flat bands through electrical tunability and the bandwidth tunability through the twist angle could pave the way towards more exotic correlated systems, such as unconventional superconductors and quantum spin liquids.

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魔角石墨烯超晶格中半填充的相关绝缘体行为

范德华异质结构是一种超材料，由垂直堆叠的二维构建块组成，通过层间的范德华力保持在一起。这种设计意味着可以精确地设计范德华异质结构的特性，甚至比二维材料的特性还要精确。一种这样的特性是异质结构中不同层之间的“扭曲”角。这个角度在范德华异质结构的电子特性中起着至关重要的作用，但在其他类型的异质结构中没有直接的类似物，例如使用分子束外延生长的半导体。对于小扭曲角，由二维层之间的晶格错位产生的莫尔图案会产生堆叠顺序的长程调制。迄今为止，对范德华异质结构中扭曲角影响的研究主要集中在由六方氮化硼顶部的单层石墨烯组成的异质结构上，由于六方氮化硼的带隙较大，其层间相互作用相对较弱。在这里，我们研究了一种由双层石墨烯组成的异质结构，其中两个石墨烯层以一定的角度相对于彼此扭曲。我们通过实验表明，正如理论上预测的那样，当这个角度接近“魔角”时，由于强层间耦合，零费米能量附近的电子能带结构变得平坦。这些平带在半填充时表现出绝缘状态，这在电子之间缺乏相关性的情况下是无法预料的。我们表明，半填充时的这些相关状态与莫特类绝缘体状态一致，这可能是由于电子位于由莫尔图案引起的超晶格中引起的。魔角扭曲双层石墨烯异质结构的这些特性表明，这些材料可用于在没有磁场的情况下研究其他二维多体量子相。通过电可调性获得平坦带和通过扭曲角获得带宽可调性可以为更奇特的相关系统铺平道路，例如非常规超导体和量子自旋液体。魔角扭曲双层石墨烯异质结构的这些特性表明，这些材料可用于在没有磁场的情况下研究其他二维多体量子相。通过电可调性获得平坦带和通过扭曲角获得带宽可调性可以为更奇特的相关系统铺平道路，例如非常规超导体和量子自旋液体。魔角扭曲双层石墨烯异质结构的这些特性表明，这些材料可用于在没有磁场的情况下研究其他二维多体量子相。通过电可调性获得平坦带和通过扭曲角获得带宽可调性可以为更奇特的相关系统铺平道路，例如非常规超导体和量子自旋液体。