We describe monocrystalline graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar electric field effect such that electrons and holes in concentrations up to 10(13) per square centimeter and with room-temperature mobilities of approximately 10,000 square centimeters per volt-second can be induced by applying gate voltage.

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

Research on graphene and other two-dimensional atomic crystals is intense and is likely to remain one of the leading topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. The first, already remarkably complex, such heterostructures (often referred to as 'van der Waals') have recently been fabricated and investigated, revealing unusual properties and new phenomena. Here we review this emerging research area and identify possible future directions. With steady improvement in fabrication techniques and using graphene's springboard, van der Waals heterostructures should develop into a large field of their own.

Permeation through nanometer pores is important in the design of materials for filtration and separation techniques and because of unusual fundamental behavior arising at the molecular scale. We found that submicrometer-thick membranes made from graphene oxide can be completely impermeable to liquids, vapors, and gases, including helium, but these membranes allow unimpeded permeation of water (H(2)O permeates through the membranes at least 10(10) times faster than He). We attribute these seemingly incompatible observations to a low-friction flow of a monolayer of water through two-dimensional capillaries formed by closely spaced graphene sheets. Diffusion of other molecules is blocked by reversible narrowing of the capillaries in low humidity and/or by their clogging with water.

Graphene-based materials can have well-defined nanometer pores and can exhibit low frictional water flow inside them, making their properties of interest for filtration and separation. We investigate permeation through micrometer-thick laminates prepared by means of vacuum filtration of graphene oxide suspensions. The laminates are vacuum-tight in the dry state but, if immersed in water, act as molecular sieves, blocking all solutes with hydrated radii larger than 4.5 angstroms. Smaller ions permeate through the membranes at rates thousands of times faster than what is expected for simple diffusion. We believe that this behavior is caused by a network of nanocapillaries that open up in the hydrated state and accept only species that fit in. The anomalously fast permeation is attributed to a capillary-like high pressure acting on ions inside graphene capillaries.

A stoichiometric derivative of graphene with a fluorine atom attached to each carbon is reported. Raman, optical, structural, micromechanical, and transport studies show that the material is qualitatively different from the known graphene-based nonstoichiometric derivatives. Fluorographene is a high-quality insulator (resistivity >10(12) Ω) with an optical gap of 3 eV. It inherits the mechanical strength of graphene, exhibiting a Young's modulus of 100 N m(-1) and sustaining strains of 15%. Fluorographene is inert and stable up to 400 °C even in air, similar to Teflon.

Graphene oxide membranes show exceptional molecular permeation properties, with a promise for many applications. However, their use in ion sieving and desalination technologies is limited by a permeation cutoff of 9 Å, which is larger than hydrated ion diameters for common salts. The cutoff is determined by the interlayer spacing d 13.5 Å, typical for graphene oxide laminates that swell in water. Achieving smaller d for the laminates immersed in water has proved to be a challenge. Here we describe how to control d by physical confinement and achieve accurate and tuneable ion sieving. Membranes with d from  9.8 Å to 6.4 Å are demonstrated, providing the sieve size smaller than typical ions' hydrated diameters. In this regime, ion permeation is found to be thermally activated with energy barriers of 10-100 kJ/mol depending on d. Importantly, permeation rates decrease exponentially with decreasing the sieve size but water transport is weakly affected (by a factor of <2). The latter is attributed to a low barrier for water molecules entry and large slip lengths inside graphene capillaries. Building on these findings, we demonstrate a simple scalable method to obtain graphene-based membranes with limited swelling, which exhibit 97% rejection for NaCl.Selectively permeable membranes with sub-nm pores attract strong interest due to analogies with biological membranes and potential applications in water filtration, molecular separation and desalination [1][2][3][4][5][6][7][8] . Nanopores with sizes comparable to, or smaller than, the diameter D of hydrated ions are predicted to show enhanced ion selectivity 7,9-12 because of dehydration required to pass through such atomic-scale sieves. Despite extensive research on ion dehydration effects 3,7,9-13 , experimental investigation of the ion sieving controlled by dehydration has been limited because of difficulties in fabricating uniform membranes with well-defined sub-nm pores. The realisation of membranes with dehydration-assisted selectivity would be a significant step forward. So far, research into novel membranes has mostly focused on improving the water flux rather than ion selectivity. On the other hand, modelling of practically relevant filtration processes shows that an increase in water permeation rates above the rates currently achieved (2-3 L/m 2 ×h×bar) would not contribute greatly to the overall efficiency of desalination 8,14,15 . Alternative approaches based on higher water-ion selectivity may open new possibilities for improving filtration technologies, as the performance of state-of-the-art membranes is currently limited by the solution-diffusion mechanism, in which water molecules dissolve in the membrane material and then diffuses across the membrane 8 . Recently, carbon nanomaterials including carbon nanotubes (CNT)

Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional (2D) electron systems and, ultimately, create materials with tailored electronic properties 1-8 . Previously, it proved difficult to realize superlattices with sufficiently short periodicity and weak disorder, and most of the observed features could be explained in terms of commensurate cyclotron orbits 1-4 . Evidence for the formation of superlattice minibands (so called Hofstadter's butterfly 9 ) has been limited to the observation of new low-field oscillations 5 and an internal structure within Landau levels 6-8 . Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moiré potential 10-12 leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points 13-22 appear as pronounced peaks in resistivity accompanied by reversal of the Hall effect. The latter indicates that the sign of the effective mass changes within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning 23 of the third generation of Dirac points that are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices open a venue to study the rich physics expected for incommensurable quantum systems 7-9,22-24 and illustrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostuctures 25 .Since the first observation of Weiss oscillations 1,2 , 2D electronic systems subjected to a periodic potential have been studied in great detail [3][4][5][6][7][8] . The advent of graphene has rapidly sparked interest in its superlattices, too [13][14][15][16][17][18][19][20][21][22] . The principal novelty in this case is the Dirac-like spectrum and the fact that charge carriers are not buried deep under the surface, allowing a relatively strong superlattice potential on a true nanometer scale. One promising avenue for making nanoscale graphene superlattices is the use of a potential induced by another crystal. For example, graphene placed on top of graphite or hexagonal boron nitride (hBN) exhibits a moiré pattern [10][11][12]26 , and graphene's tunneling density of states becomes strongly modified 12,26 indicating the formation of superlattice minibands. The spectral reconstruction occurs near the edges of superlattice's Brillouin zone (SBZ) that are characterized by wavevector G =4/ D and energy E S =v F G/2 (D is the superlattice period and v F graphene's Fermi velocity) 12,22 .To observe moiré minibands in transport properties, graphene has to be doped so that the Fermi energy reaches the reconstructed part of the spectrum. This imposes severe constraints on the misalignment angle  of graphene relatively to hBN. Indeed, D is given by  and the 1.8% difference between the two lattice constants ...