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

Graphene is a wonder material with many superlatives to its name. It is the thinnest known material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have zero effective mass, and can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a benchtop experiment. This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

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Graphene: Status and Prospects

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.

Large-scale pattern growth of graphene films for stretchable transparent electrodes

Nanoelectromechanical systems were fabricated from single- and multilayer graphene sheets by mechanically exfoliating thin sheets from graphite over trenches in silicon oxide. Vibrations with fundamental resonant frequencies in the megahertz range are actuated either optically or electrically and detected optically by interferometry. We demonstrate room-temperature charge sensitivities down to 8 × 10 –4 electrons per root hertz. The thinnest resonator consists of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nanoelectromechanical systems.

https://science.sciencemag.org/content/sci/315/5811/490.full.pdf

Electromechanical Resonators from Graphene Sheets

Using an atomic force microscope, we measured effective spring constants of stacks of graphene sheets (less than 5) suspended over photolithographically defined trenches in silicon dioxide. Measurements were made on layered graphene sheets of thicknesses between 2 and 8nm, with measured spring constants scaling as expected with the dimensions of the suspended section, ranging from 1to5N∕m. When our data are fitted to a model for doubly clamped beams under tension, we extract a Young’s modulus of 0.5TPa, compared to 1TPa for bulk graphite along the basal plane, and tensions on the order of 10−7N.

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Mechanical properties of suspended graphene sheets

We investigate the design, fabrication, and experimental characterization of high quality factor photonic crystal nanobeam cavities in silicon. Using a five-hole tapered one-dimensional photonic crystal mirror and precise control of the cavity length, we designed cavities with theoretical quality factors as high as 1.4×107. By detecting the cross-polarized resonantly scattered light from a normally incident laser beam, we measure a quality factor of nearly 7.5×105. The effect of cavity size on mode frequency and quality factor was simulated and then verified experimentally.

High quality factor photonic crystal nanobeam cavities

We present dynamically reconfigurable photonic crystal nanobeam cavities, operating at ~1550 nm, that can be continuously and reversibly tuned over a 9.5 nm wavelength range. The devices are formed by two coupled nanobeam cavities, and the tuning is achieved by varying the lateral gap between the nanobeams. An electrostatic force, obtained by applying bias voltages directly to the nanobeams, is used to control the spacing between the nanobeams, which in turn results in tuning of the cavity resonance. The observed tuning trends were confirmed through simulations that modeled the electrostatic actuation as well as the optical resonances in our reconfigurable geometries.

Programmable photonic crystal nanobeam cavities

Nanoscale optomechanical systems offer a route to using optical forces for a range of devices based on photonic structures. Deotare et al. present a reconfigurable optical filter based on coupled silicon photonic crystal nanobeam cavities that can overcome thermo-optic effects at high frequencies.

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Ian W. Frank

Papers

Electromechanical Resonators from Graphene Sheets

Mechanical properties of suspended graphene sheets

High quality factor photonic crystal nanobeam cavities

Programmable photonic crystal nanobeam cavities

All optical reconfiguration of optomechanical filters