Journal Article•
Electronic Confinement and Coherence in Patterned Epitaxial Graphene
TL;DR: The transport properties, which are closely related to those of carbon nanotubes, are dominated by the single epitaxial graphene layer at the silicon carbide interface and reveal the Dirac nature of the charge carriers.
Abstract: Ultrathin epitaxial graphite was grown on single-crystal silicon carbide by vacuum graphitization. The material can be patterned using standard nanolithography methods. The transport properties, which are closely related to those of carbon nanotubes, are dominated by the single epitaxial graphene layer at the silicon carbide interface and reveal the Dirac nature of the charge carriers. Patterned structures show quantum confinement of electrons and phase coherence lengths beyond 1 micrometer at 4 kelvin, with mobilities exceeding 2.5 square meters per volt-second. All-graphene electronically coherent devices and device architectures are envisaged.
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TL;DR: Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.
Abstract: Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.
35,293 citations
Cites background from "Electronic Confinement and Coherenc..."
...Only lately, few-layer graphene obtained on SiC was characterized with respect to its electronic properties, revealing high-mobility charge carrier...
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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 or result from "Electronic Confinement and Coherenc..."
...Epitaxially grown multilayers exhibit SdH oscillations with a Berry phase shift of π (Berger et al., 2006), which is the same as the phase shift for Dirac fermions...
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...Epi-taxially grown multilayers exhibit SdH os illations witha Berry phase shift of π (Berger et al., 2006), whi his the same as the phase shift for Dira fermions ob-served in a single layer as well as for some subbandspresent in multilayer graphene (see further) and graphite(Luk'yan huk and…...
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...…grown this way is heavily doped due to the harge transfer from the substrate to the graphene layer(with the hemi al potential well above the Dira point)and therefore all samples have strong metalli hara -ter with large ele troni mobilities (Berger et al., 2006;de Heer et al., 2007)....
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...Moreover, graphene grown this way is heavily doped due to the charge transfer from the substrate to the graphene layer (with the chemical potential well above the Dirac point) and therefore all samples have strong metallic character with large electronic mobilities (Berger et al., 2006; de Heer et al., 2007)....
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TL;DR: It is shown that graphene grows in a self-limiting way on copper films as large-area sheets (one square centimeter) from methane through a chemical vapor deposition process, and graphene film transfer processes to arbitrary substrates showed electron mobilities as high as 4050 square centimeters per volt per second at room temperature.
Abstract: Graphene has been attracting great interest because of its distinctive band structure and physical properties. Today, graphene is limited to small sizes because it is produced mostly by exfoliating graphite. We grew large-area graphene films of the order of centimeters on copper substrates by chemical vapor deposition using methane. The films are predominantly single-layer graphene, with a small percentage (less than 5%) of the area having few layers, and are continuous across copper surface steps and grain boundaries. The low solubility of carbon in copper appears to help make this growth process self-limiting. We also developed graphene film transfer processes to arbitrary substrates, and dual-gated field-effect transistors fabricated on silicon/silicon dioxide substrates showed electron mobilities as high as 4050 square centimeters per volt per second at room temperature.
10,663 citations
TL;DR: The direct synthesis of large-scale graphene films using chemical vapour deposition on thin nickel layers is reported, and two different methods of patterning the films and transferring them to arbitrary substrates are presented, implying that the quality of graphene grown by chemical vapours is as high as mechanically cleaved graphene.
Abstract: Problems associated with large-scale pattern growth of graphene constitute one of the main obstacles to using this material in device applications. Recently, macroscopic-scale graphene films were prepared by two-dimensional assembly of graphene sheets chemically derived from graphite crystals and graphene oxides. However, the sheet resistance of these films was found to be much larger than theoretically expected values. Here we report the direct synthesis of large-scale graphene films using chemical vapour deposition on thin nickel layers, and present two different methods of patterning the films and transferring them to arbitrary substrates. The transferred graphene films show very low sheet resistance of approximately 280 Omega per square, with approximately 80 per cent optical transparency. At low temperatures, the monolayers transferred to silicon dioxide substrates show electron mobility greater than 3,700 cm(2) V(-1) s(-1) and exhibit the half-integer quantum Hall effect, implying that the quality of graphene grown by chemical vapour deposition is as high as mechanically cleaved graphene. Employing the outstanding mechanical properties of graphene, we also demonstrate the macroscopic use of these highly conducting and transparent electrodes in flexible, stretchable, foldable electronics.
10,033 citations
TL;DR: An improved method for the preparation of graphene oxide (GO) is described, finding that excluding the NaNO(3), increasing the amount of KMnO(4), and performing the reaction in a 9:1 mixture of H(2)SO(4)/H(3)PO(4) improves the efficiency of the oxidation process.
Abstract: An improved method for the preparation of graphene oxide (GO) is described. Currently, Hummers’ method (KMnO4, NaNO3, H2SO4) is the most common method used for preparing graphene oxide. We have found that excluding the NaNO3, increasing the amount of KMnO4, and performing the reaction in a 9:1 mixture of H2SO4/H3PO4 improves the efficiency of the oxidation process. This improved method provides a greater amount of hydrophilic oxidized graphene material as compared to Hummers’ method or Hummers’ method with additional KMnO4. Moreover, even though the GO produced by our method is more oxidized than that prepared by Hummers’ method, when both are reduced in the same chamber with hydrazine, chemically converted graphene (CCG) produced from this new method is equivalent in its electrical conductivity. In contrast to Hummers’ method, the new method does not generate toxic gas and the temperature is easily controlled. This improved synthesis of GO may be important for large-scale production of GO as well as the ...
9,812 citations
Cites methods from "Electronic Confinement and Coherenc..."
...Few- and single-layer transferable graphene nanosheets were first obtained by mechanical exfoliation (“Scotch-tape” method) of bulk graphite(2) and by epitaxial chemical vapor deposition.(3) Although those routes might be preferred for precise device assembly, they can be less effective for large-scale manufacturing....
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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
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
Journal Article•
TL;DR: An experimental investigation of magneto-transport in a high-mobility single layer of graphene observes an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene.
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 neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted 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 structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures 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.
10,112 citations
TL;DR: In this paper, the structure of the electronic energy bands and Brillouin zones for graphite was developed using the "tight binding" approximation, and it was found that graphite is a semi-conductor with zero activation energy, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled.
Abstract: The structure of the electronic energy bands and Brillouin zones for graphite is developed using the "tight binding" approximation. Graphite is found to be a semi-conductor with zero activation energy, i.e., there are no free electrons at zero temperature, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled. The electrical conductivity is treated with assumptions about the mean free path. It is found to be about 100 times as great parallel to as across crystal planes. A large and anisotropic diamagnetic susceptibility is predicted for the conduction electrons; this is greatest for fields across the layers. The volume optical absorption is accounted for.
4,395 citations
TL;DR: It is found that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges, when the system size is on a nanometer scale.
Abstract: Finite graphite systems having a zigzag edge exhibit a special edge state. The corresponding energy bands are almost flat at the Fermi level and thereby give a sharp peak in the density of states. The charge density in the edge state is strongly localized on the zigzag edge sites. No such localized state appears in graphite systems having an armchair edge. By utilizing the graphene ribbon model, we discuss the effect of the system size and edge shape on the special edge state. By varying the width of the graphene ribbons, we find that the nanometer size effect is crucial for determining the relative importance of the edge state. We also have extended the graphene ribbon to have edges of a general shape, which is defined as a mixture of zigzag and armchair sites. Examining the relative importance of the edge state for graphene ribbons with general edges, we find that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges. We demonstrate that such an edge shape with three or four zigzag sites per sequence is sufficient to show an edge state, when the system size is on a nanometer scale. The special characteristics of the edge state play a large role in determining the density of states near the Fermi level for graphite networks on a nanometer scale.
3,834 citations