On the roughness of single- and bi-layer graphene membranes
TL;DR: In this paper, a detailed transmission electron microscopy and electron diffraction study of the thinnest possible membrane, a single layer of carbon atoms suspended in vacuum and attached only at its edges, is presented.
About: This article is published in Solid State Communications.The article was published on 2007-07-01 and is currently open access. It has received 575 citations till now. The article focuses on the topics: Membrane & Graphene.
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TL;DR: In this paper, the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations, are discussed.
Abstract: This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.
20,824 citations
Cites background from "On the roughness of single- and bi-..."
...…are many and an varyfrom ordinary e e ts ommonly found in semi ondu -tors, su h as ionized impurities in the Si substrate, to adatoms and various mole ules adsorbed in the graphenesurfa e, to more unusual defe ts su h as ripples asso i-ated with the soft stru ture of graphene (Meyer et al.,2007a)....
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...In fact, static rippling of graphene flakes suspended on scaffolds have been observed for single layer as well as bilayers (Meyer et al., 2007)....
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...Adapted from(Meyer et al., 2007a)....
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...can also be obtained as a suspended membrane, that is, without a substrate, being supported only by a scaffold or bridging micron-scale gaps (Bunch et al., 2007; Meyer et al., 2007)....
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...In fa t, stati ripplingof graphene akes suspended on s a olds have been ob-served for single layer as well as bilayers (Meyer et al.,2007a,b)....
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6,213 citations
TL;DR: Graphene dispersions with concentrations up to approximately 0.01 mg ml(-1), produced by dispersion and exfoliation of graphite in organic solvents such as N-methyl-pyrrolidone are demonstrated.
Abstract: Fully exploiting the properties of graphene will require a method for the mass production of this remarkable material. Two main routes are possible: large-scale growth or large-scale exfoliation. Here, we demonstrate graphene dispersions with concentrations up to approximately 0.01 mg ml(-1), produced by dispersion and exfoliation of graphite in organic solvents such as N-methyl-pyrrolidone. This is possible because the energy required to exfoliate graphene is balanced by the solvent-graphene interaction for solvents whose surface energies match that of graphene. We confirm the presence of individual graphene sheets by Raman spectroscopy, transmission electron microscopy and electron diffraction. Our method results in a monolayer yield of approximately 1 wt%, which could potentially be improved to 7-12 wt% with further processing. The absence of defects or oxides is confirmed by X-ray photoelectron, infrared and Raman spectroscopies. We are able to produce semi-transparent conducting films and conducting composites. Solution processing of graphene opens up a range of potential large-area applications, from device and sensor fabrication to liquid-phase chemistry.
5,600 citations
TL;DR: This work illustrates the concept of graphene as a robust atomic-scale scaffold on the basis of which new two-dimensional crystals with designed electronic and other properties can be created by attaching other atoms and molecules.
Abstract: Although graphite is known as one of the most chemically inert materials, we have found that graphene, a single atomic plane of graphite, can react with atomic hydrogen, which transforms this highly conductive zero-overlap semimetal into an insulator. Transmission electron microscopy reveals that the obtained graphene derivative (graphane) is crystalline and retains the hexagonal lattice, but its period becomes markedly shorter than that of graphene. The reaction with hydrogen is reversible, so that the original metallic state, the lattice spacing, and even the quantum Hall effect can be restored by annealing. Our work illustrates the concept of graphene as a robust atomic-scale scaffold on the basis of which new two-dimensional crystals with designed electronic and other properties can be created by attaching other atoms and molecules.
3,735 citations
TL;DR: Graphene has emerged as a subject of enormous scientific interest due to its exceptional electron transport, mechanical properties, and high surface area, and when incorporated appropriately, these atomically thin carbon sheets can significantly improve physical properties of host polymers at extremely small loading.
Abstract: Graphene has emerged as a subject of enormous scientific interest due to its exceptional electron transport, mechanical properties, and high surface area. When incorporated appropriately, these atomically thin carbon sheets can significantly improve physical properties of host polymers at extremely small loading. We first review production routes to exfoliated graphite with an emphasis on top-down strategies starting from graphite oxide, including advantages and disadvantages of each method. Then solvent- and melt-based strategies to disperse chemically or thermally reduced graphene oxide in polymers are discussed. Analytical techniques for characterizing particle dimensions, surface characteristics, and dispersion in matrix polymers are also introduced. We summarize electrical, thermal, mechanical, and gas barrier properties of the graphene/polymer nanocomposites. We conclude this review listing current challenges associated with processing and scalability of graphene composites and future perspectives f...
2,979 citations
References
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TL;DR: Monocrystalline graphitic 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.
Abstract: 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 ∼10,000 square centimeters per volt-second can be induced by applying gate voltage.
55,532 citations
"On the roughness of single- and bi-..." refers background or methods in this paper
...membranes do not remain flat but show a roughness that appears to be intrinsic to graphene membranes. To make graphene membranes, we started with the established procedure of micromechanical cleavage [1, 2, 3, 4] and obtained graphene crystallites on top of a silicon substrate with a 300nm silicon dioxide layer. Potential mono-layer sheets were identified by optical microscopy or scanning electron microscopy,...
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...roughness is presented for two-layer membranes where we used the variation of diffracted intensities with the local orientation of the membrane. The recent discovery of graphene in a quasi-free state [1, 2] has sparked considerable interest in the science and applications of this new material with its remarkable electronic properties. Graphene monolayers on semiconductor substrates can be patterned and ...
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TL;DR: This study reports 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 and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.
Abstract: 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 Schrodinger 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.
18,958 citations
"On the roughness of single- and bi-..." refers background in this paper
...Graphene monolayers on semiconductor substrates can be patterned and contacted by conventional lithographic techniques, and the resulting devices provide access to the rich physics of quantum electrodynamics in a solid state physics experiment [3,4]....
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TL;DR: This work shows that graphene's electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers, and allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.
Abstract: Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers The D peak second order changes in shape, width, and position for an increasing number of layers, reflecting the change in the electron bands via a double resonant Raman process The G peak slightly down-shifts This allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area
13,474 citations
TL;DR: In this paper, an experimental investigation of magneto-transport in a high-mobility single layer of Graphene is presented, where an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene is observed.
Abstract: When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality1,2. Indeed, a distinctive half-integer quantum Hall effect has been predicted3,4,5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure6,7. Recent advances in micromechanical extraction and fabrication techniques for graphite structures8,9,10,11,12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
11,122 citations
TL;DR: By using micromechanical cleavage, a variety of 2D crystals including single layers of boron nitride, graphite, several dichalcogenides, and complex oxides are prepared and studied.
Abstract: We report free-standing atomic crystals that are strictly 2D and can be viewed as individual atomic planes pulled out of bulk crystals or as unrolled single-wall nanotubes. By using micromechanical cleavage, we have prepared and studied a variety of 2D crystals including single layers of boron nitride, graphite, several dichalcogenides, and complex oxides. These atomically thin sheets (essentially gigantic 2D molecules unprotected from the immediate environment) are stable under ambient conditions, exhibit high crystal quality, and are continuous on a macroscopic scale.
10,586 citations
"On the roughness of single- and bi-..." refers background in this paper
...The recent discovery of graphene in a quasi-free state [1,2] has sparked considerable interest in the science and applications of this new material with its remarkable electronic properties....
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