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.

Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point [1,2]. However, accessing the physics of the low density region at the Dirac point has been difficult because of the presence of disorder which leaves the graphene with local microscopic electron and hole puddles [3][4][5], resulting in a finite density of carriers even at the charge neutrality point. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult [6,7].Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance [8]. In this letter, we use scanning tunneling microscopy to show that graphene conforms to hBN, as evidenced by the presence of Moiré patterns in the topographic images. However, contrary to recent predictions [9,10], this conformation does not lead to a sizable band gap due to the misalignment of the lattices. Moreover, local spectroscopy measurements demonstrate that the electron-hole charge fluctuations are reduced by two orders of magnitude as compared to those on silicon oxide. This leads to charge fluctuations which are as small as in suspended graphene [6], opening up Dirac point physics to more diverse experiments than are possible on freestanding devices.

The Schrödinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of bandgaps near points of the reciprocal lattice known as Brillouin zone boundaries 1 . However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a bandgap and instead new Dirac points appear in the electronic structure of the material 2,3 . Graphene on hexagonal boron nitride exhibits a rotation-dependent moiré pattern 4,5 . Here, we show experimentally and theoretically that this moiré pattern acts as a weak periodic potential and thereby leads to the emergence of a new set of Dirac points at an energy determined by its wavelength. The new massless Dirac fermions generated at these superlattice Dirac points are characterized by a significantly reduced Fermi velocity. Furthermore, the local density of states near these Dirac cones exhibits hexagonal modulation due to the influence of the periodic potential.Owing to its hexagonal lattice structure with a diatomic unit cell, graphene has low-energy electronic properties that are governed by the massless Dirac equation 6 . This has a number of consequences, among them Klein tunnelling [7][8][9][10] , which prevents electrostatic confinement of charge carriers and inhibits the fabrication of standard semiconductor devices. This has motivated a number of recent theoretical investigations of graphene in periodic potentials 2,3,[11][12][13][14][15] , which explored ways of controlling the propagation of charge carriers by means of various superlattice potentials. On the analytical side, one-dimensional potentials render particle propagation anisotropic 2,3,11,14 and generate new Dirac points, where the electron and hole bands meet, at energies ±hv F |G|/2 given by the reciprocal superlattice vectors G (refs 2,3), where v F is the Fermi velocity. Numerical approaches have extended several of these results to the case of two-dimensional potentials 2,3,14,15 . Unlike for Schrödinger fermions, the periodic potentials generally induce new Dirac points but do not open bandgaps in graphene, owing to the chiral nature of the Dirac fermions.Recent scanning tunnelling microscope (STM) topography experiments have reported well-developed moiré patterns in graphene on crystalline substrates, which suggests that the latter generate effective periodic potentials 4,5,16,17 . Of particular interest is hexagonal boron nitride (hBN), because it is an insulator which only couples weakly to graphene. Furthermore, graphene on hBN exhibits the highest mobility ever reported for graphene on any substrate 18 , and has strongly suppressed charge inhomogeneities 4,5 . Hexagonal boron nitride is a layered material whose planes have the same atomic structure as graphene, with a 1.8% longer lattice constant. The influence of the weak graphene-substrate interlayer coupling on the electronic transport and spectroscopic properties of graphene is not well understood. In particular, there ...

The chemical functionalization of graphene enables control over electronic properties and sensor recognition sites. However, its study is confounded by an unusually strong influence of the underlying substrate. In this paper, we show a stark difference in the rate of electron transfer chemistry with aryl diazonium salts on monolayer graphene supported on a broad range of substrates. Reactions proceed rapidly when graphene is on SiO 2 and Al 2 O 3 (sapphire), but negligibly on alkyl-terminated and hexagonal boron nitride (hBN) surfaces. The effect is contrary to expectations based on doping levels and can instead be described using a reactivity model accounting for substrate-induced electron-hole puddles in graphene. Raman spectroscopic mapping is used to characterize the effect of the substrates on graphene. Reactivity imprint lithography (RIL) is demonstrated as a technique for spatially patterning chemicalgroups on graphene by patterning the underlying substrate, and is applied to the covalent tethering of proteins on graphene.

, many of which can only be realized by confining graphene into nanoribbons and other nanostructures. For example, ballistic room-temperature transistors 3-5 and carbon-based spintronic devices 6-10 are two tantalizing possibilities which could one day be realized in a graphene nanodevice. First though, a reliable method must be found to controllably produce graphene nanostructures with specific sizes, geometries, and defined crystallographic edges. Theoretical predictions indicate that a graphene nanoribbon with zig-zag edges can behave as a half-metal 6, 7 which, paired with graphene's long spin relaxation time 11 , could be used to produced spin-valves and other spintronic devices. In addition, nanosized geometric structures such as triangles with zig-zag edges are predicted to have a net nonzero spin 8,9,12, 13 , furthering the potential use of graphene as a canvas for spintronic circuits. For field effect transistor applications, quantum confinement induces a band gap in the normally gapless graphene 10,14,15 , but the potential performance of the device depends strongly on the edge structure as well 4,16,17 . . Indeed, previous studies of catalytic gasification of carbon found that catalytic metal nanoparticles would sometimes etch graphite along crystallographic directions, creating both armchair and zigzag edges [27][28][29][30][31] .

Twisted bilayer graphene (TBLG) is one of the simplest van der Waals heterostructures, yet it yields a complex electronic system with intricate interplay between moiré physics and interlayer hybridization effects. We report on electronic transport measurements of high mobility small angle TBLG devices showing clear evidence for insulating states at the superlattice band edges, with thermal activation gaps several times larger than theoretically predicted. Moreover, Shubnikov-de Haas oscillations and tight binding calculations reveal that the band structure consists of two intersecting Fermi contours whose crossing points are effectively unhybridized. We attribute this to exponentially suppressed interlayer hopping amplitudes for momentum transfers larger than the moiré wave vector.

Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires, and graphene. Recently, a new paradigm has emerged with the advent of symmetry-protected surface states on the boundary of topological insulators, enabling the creation of electronic systems with novel properties. For example, time reversal symmetry (TRS) endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, locking the orientation of their spin relative to their momentum 1,2 . Weakly breaking this symmetry generates a gap on the surface, 3 resulting in charge carriers with finite effective mass and exotic spin textures 4 . Analogous manipulations of the one-dimensional boundary states of a two-dimensional topological insulator are also possible, but have yet to be observed in the leading candidate materials 5,6 . Here, we demonstrate experimentally that charge neutral monolayer graphene displays a new type of quantum spin Hall (QSH) effect 7,8 , previously thought to exist only in time reversal invariant topological insulators 5,9-11 , when it is subjected to a very large magnetic field angled with respect to the graphene plane. Unlike in the TRS case 5,9,10 , the QSH presented here is protected by a spin-rotation symmetry that emerges as electron spins in a half-filled Landau level are polarized by the large in-plane magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability [12][13][14] , which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic (CAF) state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with tunable band gap and associated spin-texture 15 .In the integer quantum Hall effect, the topology of the bulk Landau level (LL) energy bands 16 requires the existence of gapless edge states at any interface with the vacuum. The metrological precision of the Hall quantization can be traced to the inability of these edge states to backscatter due to the physical separation of modes with opposite momentum by the insulating sample bulk 17 . In contrast, counterpropagating boundary states in a symmetry-protected topological (SPT) insulator coexist spatially but are prevented from backscattering by a symmetry of the experimental system 1,2 . The local symmetry that protects transport in SPT surface states is unlikely to be as robust as the inherently nonlocal physical separation that protects the quantum Hall effect. However, it enables the creation of new electronic systems in which momentum and some quantum number such as spin are coupled, potentially leading to devices with new functionality. Most experimentally realized SPT phases are based on TRS, with counterpropagating states protected from intermixing by the Kram...