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.

van der Waals heterostructures constitute a new class of artificial materials formed by stacking atomically thin planar crystals. We demonstrated band structure engineering in a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally aligned hexagonal boron nitride substrate. The spatially varying interlayer atomic registry results in both a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. In our samples, this interplay between short- and long-wavelength effects resulted in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality. This picture is confirmed by our observation of fractional quantum Hall states at ± 5/3 filling and features associated with the Hofstadter butterfly at ultrahigh magnetic fields.

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A two-dimensional electronic system forms at the interface between the band insulators 1,2 LaAlO 3 and SrTiO 3 . Samples fabricated until now have been found to be either magnetic or superconducting, depending on growth conditions 3,4 . Combining high-resolution magnetic torque magnetometry and transport measurements, we report here magnetization measurements providing direct evidence of magnetic ordering of the two-dimensional electron liquid at the interface. The magnetic ordering exists from well below the superconducting transition to up to 200 K, and is characterized by an in-plane magnetic moment. Surprisingly, despite the presence of this magnetic ordering, the interface superconducts below 120 mK. This is unusual because conventional superconductivity rarely exists in magnetically ordered metals 5,6 . Our results suggest that there is either phase separation or coexistence between magnetic and superconducting states. The coexistence scenario would point to an unconventional superconducting phase as the ground state.Superconductivity and magnetic order are in general mutually exclusive phenomena. Nonetheless, the coexistence of magnetism and superconductivity has been suggested for finite-momentum pairing states 5,6 . Coexistence of magnetism and superconductivity has been reported in a few three-dimensional superconducting systems 7-9 , such as RuSr 2 GdCu 2 O 8 and UGe 2 . The question remains if such coexistence can occur in a two-dimensional electronic system. An intriguing candidate is the interface between the two band insulators LaAlO 3 (LAO) and SrTiO 3 (STO). At their ntype interface a conducting two-dimensional electron liquid is generated. Moreover, the LAO/STO interface was also reported to have a two-dimensional superconducting ground state 3 . For this system, magnetic ordering was suggested in ref. 4, the authors of which deduced the presence of magnetic scattering centres from the temperature dependence of the interface resistance R and a hysteresis of R during the sweep of magnetic field H . Different magnetotransport studies indicate an antiferromagnetic order 10 or a non-uniform field-induced magnetization and strong magnetic anisotropy 11 . Recently, it was found that, at both chemically treated STO bulk and LAO/STO interfaces, charges are electronically phase separated into regions containing a quasi-two-dimensional electron-gas phase, a ferromagnetic phase persisting above room temperature or a diamagnetic/paramagnetic phase 12 below 60 K. On the theoretical side, electronic-structure calculations yield complicated pictures for the magnetism at the interface layers [13][14][15][16] . Specifically, the calculations do not support magnetically ordered moments at the interface of an LAO/STO bilayer covered by Coexistence of magnetism and superconductivity has not been reported at the LAO/STO interfaces. The ground state was found to be controlled by growth conditions, carrier concentration 18 and external magnetic field 19 . These experimental observations based on transport properties ...

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