Graphene devices on standard SiO(2) substrates are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. Although suspending the graphene above the substrate leads to a substantial improvement in device quality, this geometry imposes severe limitations on device architecture and functionality. There is a growing need, therefore, to identify dielectrics that allow a substrate-supported geometry while retaining the quality achieved with a suspended sample. Hexagonal boron nitride (h-BN) is an appealing substrate, because it has an atomically smooth surface that is relatively free of dangling bonds and charge traps. It also has a lattice constant similar to that of graphite, and has large optical phonon modes and a large electrical bandgap. Here we report the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal h-BN substrates, by using a mechanical transfer process. Graphene devices on h-BN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO(2). These devices also show reduced roughness, intrinsic doping and chemical reactivity. The ability to assemble crystalline layered materials in a controlled way permits the fabrication of graphene devices on other promising dielectrics and allows for the realization of more complex graphene heterostructures.

Heterostructures based on layering of two-dimensional (2D) materials such as graphene and hexagonal boron nitride represent a new class of electronic devices. Realizing this potential, however, depends critically on the ability to make high-quality electrical contact. Here, we report a contact geometry in which we metalize only the 1D edge of a 2D graphene layer. In addition to outperforming conventional surface contacts, the edge-contact geometry allows a complete separation of the layer assembly and contact metallization processes. In graphene heterostructures, this enables high electronic performance, including low-temperature ballistic transport over distances longer than 15 micrometers, and room-temperature mobility comparable to the theoretical phonon-scattering limit. The edge-contact geometry provides new design possibilities for multilayered structures of complimentary 2D materials.

Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. When subject to both a magnetic field and a periodic electrostatic potential, two-dimensional systems of electrons exhibit a self-similar recursive energy spectrum. Known as Hofstadter's butterfly, this complex spectrum results from an interplay between the characteristic lengths associated with the two quantizing fields, and is one of the first quantum fractals discovered in physics. In the decades since its prediction, experimental attempts to study this effect have been limited by difficulties in reconciling the two length scales. Typical atomic lattices (with periodicities of less than one nanometre) require unfeasibly large magnetic fields to reach the commensurability condition, and in artificially engineered structures (with periodicities greater than about 100 nanometres) the corresponding fields are too small to overcome disorder completely. Here we demonstrate that moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic modulation with ideal length scales of the order of ten nanometres, enabling unprecedented experimental access to the fractal spectrum. We confirm that quantum Hall features associated with the fractal gaps are described by two integer topological quantum numbers, and report evidence of their recursive structure. Observation of a Hofstadter spectrum in bilayer graphene means that it is possible to investigate emergent behaviour within a fractal energy landscape in a system with tunable internal degrees of freedom.

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Graphene-based photodetectors have attracted strong interest for their exceptional physical properties, which include an ultrafast response 1-3 across a broad spectrum 4 , a strong electronelectron interaction 5 and photocarrier multiplication [6][7][8] . However, the weak optical absorption of graphene 2,3 limits its photoresponsivity. To address this, graphene has been integrated into nanocavities 9 , microcavities 10 and plasmon resonators 11,12 , but these approaches restrict photodetection to narrow bands. Hybrid graphene-quantum dot architectures can greatly improve responsivity 13 , but at the cost of response speed. Here, we demonstrate a waveguide-integrated graphene photodetector that simultaneously exhibits high responsivity, high speed and broad spectral bandwidth. Using a metal-doped graphene junction coupled evanescently to the waveguide, the detector achieves a photoresponsivity exceeding 0.1 A W 21 together with a nearly uniform response between 1,450 and 1,590 nm. Under zero-bias operation, we demonstrate response rates exceeding 20 GHz and an instrumentation-limited 12 Gbit s 21 optical data link.Graphene demonstrates ultrafast carrier dynamics for both electrons and holes, and it has been shown that a weak internal electric field allows high-speed and efficient photocarrier separation 2,3,14 . Moreover, graphene's two-dimensional nature appears to enable the generation of multiple electron-hole pairs for every highenergy photon excitation 6-8 . This carrier multiplication process is equivalent to inherent gain in graphene photodetection, which exists even without external bias, unlike traditional avalanche detection 15 . Despite these attractive features, the low optical absorption in graphene results in low photoresponsivity in vertical-incidence photodetector designs.Recently it has been revealed that coupling graphene to a bus waveguide can enhance light absorption over a broadband spectrum 16,17 . Here, we show that, by integrating a graphene photodetector onto a silicon-on-insulator (SOI) bus waveguide, it is possible to greatly enhance graphene absorption and the corresponding photodetection efficiency without sacrificing the high speed and broad spectral bandwidth. In our device, presented in Fig. 1a, a silicon waveguide is backfilled with SiO 2 and then planarized to provide a smooth surface for the deposition of graphene. A thin SiO 2 layer ( 10 nm) deposited on the planarized chip electrically isolates the graphene layer from the underlying silicon structures. The optical waveguide mode couples to the graphene layer through the evanescent field, leading to optical absorption and the generation of photocarriers. Two metal electrodes located on opposite sides of the waveguide collect the photocurrent. One of these electrodes is positioned 100 nm from the edge of the waveguide to create a lateral metal-doped junction that overlaps with the waveguide mode. The junction is close enough to the waveguide to efficiently separate the photoexcited electron-hole pairs at zero bias, but the meta...