Nanometre-scale pores and capillaries have long been studied because of their importance in many natural phenomena and their use in numerous applications. A more recent development is the ability to fabricate artificial capillaries with nanometre dimensions, which has enabled new research on molecular transport and led to the emergence of nanofluidics. But surface roughness in particular makes it challenging to produce capillaries with precisely controlled dimensions at this spatial scale. Here we report the fabrication of narrow and smooth capillaries through van der Waals assembly, with atomically flat sheets at the top and bottom separated by spacers made of two-dimensional crystals with a precisely controlled number of layers. We use graphene and its multilayers as archetypal two-dimensional materials to demonstrate this technology, which produces structures that can be viewed as if individual atomic planes had been removed from a bulk crystal to leave behind flat voids of a height chosen with atomic-scale precision. Water transport through the channels, ranging in height from one to several dozen atomic planes, is characterized by unexpectedly fast flow (up to 1 metre per second) that we attribute to high capillary pressures (about 1,000 bar) and large slip lengths. For channels that accommodate only a few layers of water, the flow exhibits a marked enhancement that we associate with an increased structural order in nanoconfined water. Our work opens up an avenue to making capillaries and cavities with sizes tunable to ångström precision, and with permeation properties further controlled through a wide choice of atomically flat materials available for channel walls.

Many layered materials can be cleaved down to individual atomic planes, similar to graphene, but only a small minority of them are stable under ambient conditions. The rest react and decompose in air, which has severely hindered their investigation and potential applications. Here we introduce a remedial approach based on cleavage, transfer, alignment, and encapsulation of air-sensitive crystals, all inside a controlled inert atmosphere. To illustrate the technology, we choose two archetypal two-dimensional crystals that are of intense scientific interest but are unstable in air: black phosphorus and niobium diselenide. Our field-effect devices made from their monolayers are conductive and fully stable under ambient conditions, which is in contrast to the counterparts processed in air. NbSe2 remains superconducting down to the monolayer thickness. Starting with a trilayer, phosphorene devices reach sufficiently high mobilities to exhibit Landau quantization. The approach offers a venue to significantly expand the range of experimentally accessible two-dimensional crystals and their heterostructures.

Monolayers of molybdenum and tungsten dichalcogenides are direct bandgap semiconductors, which makes them promising for optoelectronic applications. In particular, van der Waals heterostructures consisting of monolayers of MoS2 sandwiched between atomically thin hexagonal boron nitride (hBN) and graphene electrodes allows one to obtain light emitting quantum wells (LEQWs) with low-temperature external quantum efficiency (EQE) of 1%. However, the EQE of MoS2- and MoSe2-based LEQWs shows behavior common for many other materials: it decreases fast from cryogenic conditions to room temperature, undermining their practical applications. Here we compare MoSe2 and WSe2 LEQWs. We show that the EQE of WSe2 devices grows with temperature, with room temperature EQE reaching 5%, which is 250× more than the previous best performance of MoS2 and MoSe2 quantum wells in ambient conditions. We attribute such different temperature dependences to the inverted sign of spin-orbit splitting of conduction band states in tungsten and molybdenum dichalcogenides, which makes the lowest-energy exciton in WSe2 dark.

Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting micron-scale ballistic transport. Can other atomically flat crystals be used as substrates for making quality graphene heterostructures? Here we report on our search for alternative substrates. The devices fabricated by encapsulating graphene with molybdenum or tungsten disulphides and hBN are found to exhibit consistently high carrier mobilities of about 60,000 cm$^{2}$V$^{-1}$s$^{-1}$. In contrast, encapsulation with atomically flat layered oxides such as mica, bismuth strontium calcium copper oxide and vanadium pentoxide results in exceptionally low quality of graphene devices with mobilities of ~ 1,000 cm$^{2}$ V$^{-1}$s$^{-1}$. We attribute the difference mainly to self-cleansing that takes place at interfaces between graphene, hBN and transition metal dichalcogenides. Surface contamination assembles into large pockets allowing the rest of the interface to become atomically clean. The cleansing process does not occur for graphene on atomically flat oxide substrates.

Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting micron-scale ballistic transport. Can other atomically flat crystals be used as substrates for making quality graphene heterostructures? Here we report on our search for alternative substrates. The devices fabricated by encapsulating graphene with molybdenum or tungsten disulphides and hBN are found to exhibit consistently high carrier mobilities of about 60,000 cm$^{2}$V$^{-1}$s$^{-1}$. In contrast, encapsulation with atomically flat layered oxides such as mica, bismuth strontium calcium copper oxide and vanadium pentoxide results in exceptionally low quality of graphene devices with mobilities of ~ 1,000 cm$^{2}$ V$^{-1}$s$^{-1}$. We attribute the difference mainly to self-cleansing that takes place at interfaces between graphene, hBN and transition metal dichalcogenides. Surface contamination assembles into large pockets allowing the rest of the interface to become atomically clean. The cleansing process does not occur for graphene on atomically flat oxide substrates.

Capacitance measurements provide a powerful means of probing the density of states. The technique has proved particularly successful in studying 2D electron systems, revealing a number of interesting many-body effects. Here, we use large-area high-quality graphene capacitors to study behavior of the density of states in this material in zero and high magnetic fields. Clear renormalization of the linear spectrum due to electron-electron interactions is observed in zero field. Quantizing fields lead to splitting of the spin- and valley-degenerate Landau levels into quartets separated by interaction-enhanced energy gaps. These many-body states exhibit negative compressibility but the compressibility returns to positive in ultrahigh B. The reentrant behavior is attributed to a competition between field-enhanced interactions and nascent fractional states.

We have performed magneto-transport experiments in monolayer, bilayer, trilayer and four layered graphene, at temperatures between 2 and 190 K and magnetic fields up to 28 T. In particular, in monolayer graphene we studied the quantum Hall effect and the metal-insulator transition. On the other hand, in bilayer graphene we observed quantum Hall plateaus at filling factor v = 4, 8,12,16,20, ... and the v = 6 plateau in trilayer graphene, studying their temperature dependence. We have also studied the symmetry properties which are related with different contact configurations describing the method used to study inhomogeneus samples. Finally, four layered graphene we did not found quantum Hall plateaus, but we observed and investigated an ambipolar conduction effect.

Nature Physics 7, 701–704 (2011); published online 24 July 2011; corrected after print 21 December 2011. In the version of this Letter originally published, the prefactor in equation (2) should have been -8/π2Nf. This error has been corrected in the HTML and PDF versions of the Letter.

: There was a steady increase in average flake size in the years following the initial isolation of monolayer grapheme in 2004, but even by 2008, flakes rarely exceeded 1000 sq microns. As part of the research for this grant, carefully analyzed the factors that affect flake size, including: graphite source (natural, HOPG, Kish), type of adhesive tape, number of cleaves, substrate material and roughness, substrate cleaning (sonication, piranha etch, oxygen plasma, etc.) and temperature. They found that the number of graphite cleaves and the substrate cleaning procedures were the most common factors that limited flake size. By cleaving only 5-10 times (typical number of cleaves in previous procedures was 20) and cleaning with oxygen plasma, we were able to routinely prepare flakes 100, 000 sq microns and occasionally 1 sq mm. With flakes more than 100 microns in diameter, a wider range of experiments became possible. Optical scanning measurements over large regions, ellipsometry, infra-red-spectroscopy and capacitance devices have yielded interesting results. Occasionally when preparing large flakes, air can get trapped between the substrate and the grapheme, forming bubbles. The shape of these bubbles can be controlled with a gate voltage, potentially allowing for grapheme-based adaptive focus lenses.

Using infrared spectroscopy, we investigate bottom gated ABA-stacked trilayer graphene subject to an additional environment-induced p-type doping. We find that the Slonczewski-Weiss-McClure tight-binding model and the Kubo formula reproduce the gate voltage-modulated reflectivity spectra very accurately. This allows us to determine the charge densities and the potentials of the π-band electrons on all graphene layers separately and to extract the interlayer permittivity due to higher energy bands.

We present ellipsometric spectra of a graphene flake placed on a surface of oxidized silicon wafer. Our measurements demonstrate that spectroscopic ellipsometry can be successfully used to count the number of graphene layers in a flake. We also show that visible transparency of any two-dimensional system with a symmetric electronic spectrum is governed by the fine structure constant and derive an expression for the absorption coefficient of such a system.

We describe the identification of single- and few- layer boron nitride. Its optical contrast is much smaller than that of graphene but even monolayers are discernable by optimizing viewing conditions. Raman spectroscopy can be used to confirm BN monolayers. They exhibit an upshift in the fundamental Raman mode by up to 4 cm-1. The number of layers in thicker crystals can be counted by exploiting an integer-step increase in the Raman intensity and optical contrast.

Raised above the substrate and elastically deformed areas of graphene in the form of bubbles are found on different substrates. They come in a variety of shapes, including those which allow strong modification of the electronic properties of graphene. We show that the shape of the bubble can be controlled by an external electric field. This effect can be used to make graphene-based adaptive focus lenses.

Graphene is one of the most interesting materials synthesized in the last years which two-dimensional nature along with the fascinating electronic properties attracts the great attention from the scientific community. Graphene has an unique electronic properties such as the linear dispersion law leading to zero effective mass for electrons and holes. It already applied as solar cell [1], liquid crystal device [2], molecular sensor [3] and nano-sized transistor prototype [4].

Devices made from graphene encapsulated in hexagonal boron-nitride exhibit pronounced negative bend resistance and an anomalous Hall effect, which are a direct consequence of room-temperature ballistic transport at a micrometer scale for a wide range of carrier concentrations. The encapsulation makes graphene practically insusceptible to the ambient atmosphere and, simultaneously, allows the use of boron nitride as an ultrathin top gate dielectric.

We have performed magneto-transport experiments in trilayer graphene, at temperatures between 2 and 190K and magnetic fields up to 22T. Here we report the integer quantum Hall effect in trilayer graphene, showing the quantum Hall plateau at ν=6 and studying its temperature dependence. The symmetry properties of the resistance in the quantum Hall regime and at low magnetic fields are also investigated. The measurements obey the reciprocity relation, and reveal new symmetries that relate the resistances measured with different contact configurations.

We report capacitors in which a finite electronic compressibility of graphene dominates the electrostatics, resulting in pronounced changes in capacitance as a function of magnetic field and carrier concentration. The capacitance measurements have allowed us to accurately map the density of states D, and compare it against theoretical predictions. Landau oscillations in D are robust and zero Landau level (LL) can easily be seen at room temperature in moderate fields. The broadening of LLs is strongly affected by charge inhomogeneity that leads to zero LL being broader than other levels.

In this letter, we show how high-resolution scanning tunneling microscopy (STM) imaging can be used to reveal that certain edges of micromechanically exfoliated single layer graphene crystals on silicon oxide follow either zigzag or armchair orientation. Using the cleavage technique, graphene flakes are obtained that very often show terminating edges seemingly following the crystallographic directions of the underlying honeycomb lattice. Performing atomic resolution STM-imaging on such flakes, we were able to directly prove this assumption. Raman imaging carried out on the same flakes further validated our findings.

We demonstrate the application of graphene as a support for imaging individual biological molecules in transmission electron microscope (TEM). A simple procedure to produce free-standing graphene membranes has been designed. Such membranes are extremely robust and can support practically any submicrometer object. Tobacco mosaic virus has been deposited on graphene samples and observed in a TEM. High contrast has been achieved even though no staining has been applied.