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 materials1. 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 nitride2,3,4,5. 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 theoretically6, 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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We acknowledge discussions with L. Levitov, P. Lee, S. Todadri, B. I. Halperin, S. Carr, Z. Alpichshev, J. Y. Khoo and N. Staley. This work was primarily supported by the National Science Foundation (NSF; DMR-1405221) and the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4541 for device fabrication, transport measurements and data analysis (Y.C., J.Y.L., J.D.S.-Y. and P.J.H.), with additional support from the NSS Program, Singapore (J.Y.L.). Capacitance work by R.C.A., A.D. and S.L.T. and theory work by S.F. was supported by the STC Center for Integrated Quantum Materials, NSF grant number DMR-1231319. Data analysis by V.F. was supported by AFOSR grant number FA9550-16-1-0382. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan and JSPS KAKENHI grant numbers JP15K21722 and JP25106006. This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities supported by the NSF (DMR-0819762) and of Harvard’s Center for Nanoscale Systems, supported by the NSF (ECS-0335765). E.K. acknowledges support by ARO MURI award W911NF-14-0247. R.C.A. acknowledges support by the Gordon and Betty Moore Foundation under grant number GBMF2931.