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.

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The electronic properties of graphene

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

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Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

There is intense interest in graphene in fields such as physics, chemistry, and materials science, among others. Interest in graphene's exceptional physical properties, chemical tunability, and potential for applications has generated thousands of publications and an accelerating pace of research, making review of such research timely. Here is an overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.

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Graphene and Graphene Oxide: Synthesis, Properties, and Applications

Ultrahigh electron mobility in suspended graphene

We investigate the tight-binding approximation for the dispersion of the $\ensuremath{\pi}$ and ${\ensuremath{\pi}}^{*}$ electronic bands in graphene and carbon nanotubes. The nearest-neighbor tight-binding approximation with a fixed ${\ensuremath{\gamma}}_{0}$ applies only to a very limited range of wave vectors. We derive an analytic expression for the tight-binding dispersion including up to third-nearest neighbors. Interaction with more distant neighbors qualitatively improves the tight-binding picture, as we show for graphene and three selected carbon nanotubes.

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Tight-binding description of graphene

Preface. 1 Introduction. 2 Structure and Symmetry. 2.1 Structure of Carbon Nanotubes. 2.2 Experiments. 2.3 Symmetry of Single-walled Carbon Nanotubes. 2.3.1 Symmetry Operations. 2.3.2 Symmetry-based Quantum Numbers. 2.3.3 Irreducible representations. 2.3.4 Projection Operators. 2.3.5 Phonon Symmetries in Carbon Nanotubes. 2.4 Summary. 3 Electronic Properties of Carbon Nanotubes. 3.1 Graphene. 3.1.1 Tight-binding Description of Graphene. 3.2 Zone-folding Approximation. 3.3 Electronic Density of States. 3.3.1 Experimental Verifications of the DOS. 3.4 Beyond Zone Folding - Curvature Effects. 3.4.1 Secondary Gaps in Metallic Nanotubes. 3.4.2 Rehybridization of the sigma and pi States. 3.5 Nanotube Bundles. 3.5.1 Low-energy Properties. 3.5.2 Visible Energy Range. 3.6 Summary. 4 Optical P roperties. 4.1 Absorption and Emission. 4.1.1 Selection Rules and Depolarization. 4.2 Spectra of Isolated Tubes. 4.3 Photoluminescence Excitation - (n1, n2) Assignment. 4.4 4-A-diameter Nanotubes. 4.5 Bundles of Nanotubes. 4.6 Excited-state Carrier Dynamics. 4.7 Summary. 5 Electronic Transport. 5.1 Room-temperature Conductance of Nanotubes. 5.2 Electron Scattering. 5.3 Coulomb Blockade. 5.4 Luttinger Liquid. 5.5 Summary. 6 Elastic Properties. 6.1 Continuum Model of Isolated Nanotubes. 6.1.1 Ab-initio, Tight-binding, and Force-constants Calculations. 6.2 Pressure Dependence of the Phonon Frequencies. 6.3 Micro-mechanical Manipulations. 6.4 Summary. 7 Raman Scattering. 7.1 Raman Basics and Selection Rules. 7.2 Tensor Invariants. 7.2.1 Polarized Measurements. 7.3 Raman Measurements at Large Phonon q. 7.4 Double Resonant Raman Scattering. 7.5 Summary. 8 Vibrational Properties. 8.1 Introduction. 8.2 Radial Breathing Mode. 8.2.1 The RBM in Isolated and Bundled Nanotubes. 8.2.2 Double-walled Nanotubes. 8.3 The Defect-induced D Mode. 8.3.1 The D Mode in Graphite. 8.3.2 The D Mode in Carbon Nanotubes. 8.4 Symmetry of the Raman Modes. 8.5 High-energy Vibrations. 8.5.1 Raman and Infrared Spectroscopy. 8.5.2 Metallic Nanotubes. 8.5.3 Single- and Double-resonance Interpretation. 8.6 Summary. 8.7 What we Can Learn from the Raman Spectra of Single-walled Carbon Nanotubes. Appendix A: Character and Correlation Tables of Graphene. Appendix B: Raman Intensities in Unoriented Systems. Appendix C: Fundamental Constants. Bibliography. Index.

Carbon Nanotubes: Basic Concepts and Physical Properties

We present scanning tunneling microscopy (STM) images of single-layer graphene crystals examined under ultrahigh vacuum conditions. The samples, with lateral dimensions on the micrometer scale, were prepared on a silicon dioxide surface by direct exfoliation of crystalline graphite. The single-layer films were identified by using Raman spectroscopy. Topographic images of single-layer samples display the honeycomb structure expected for the full hexagonal symmetry of an isolated graphene monolayer. The absence of observable defects in the STM images is indicative of the high quality of these films. Crystals composed of a few layers of graphene also were examined. They exhibited dramatically different STM topography, displaying the reduced threefold symmetry characteristic of the surface of bulk graphite.

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High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface

We report the chemical reaction of single-layer graphene with hydrogen atoms, generated in situ by electron-induced dissociation of hydrogen silsesquioxane (HSQ). Hydrogenation, forming sp3 C−H functionality on the basal plane of graphene, proceeds at a higher rate for single than for double layers, demonstrating the enhanced chemical reactivity of single sheet graphene. The net H atom sticking probability on single layers at 300 K is at least 0.03, which exceeds that of double layers by at least a factor of 15. Chemisorbed hydrogen atoms, which give rise to a prominent Raman D band, can be detached by thermal annealing at 100∼200 °C. The resulting dehydrogenated graphene is “activated” when photothermally heated it reversibly binds ambient oxygen, leading to hole doping of the graphene. This functionalization of graphene can be exploited to manipulate electronic and charge transport properties of graphene devices.

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Reversible basal plane hydrogenation of graphene.

Excitonic effects in the linear and nonlinear optical properties of single-walled carbon nanotubes are manifested by photoluminescence excitation experiments and ab initio calculations. One- and two-photon spectra showed a series of exciton states; their energy splitting is the fingerprint of excitonic interactions in carbon nanotubes. By ab initio calculations we determine the energies, wave functions, and symmetries of the excitonic states. Combining experiment and theory we find binding energies of $0.3\char21{}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for nanotubes with diameters between 6.8 and $9.0\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$.

Janina Maultzsch

Papers

Tight-binding description of graphene

Carbon Nanotubes: Basic Concepts and Physical Properties

High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface

Reversible basal plane hydrogenation of graphene.

Exciton binding energies in carbon nanotubes from two-photon photoluminescence