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

Raman spectroscopy of graphene and graphite: Disorder, electron phonon coupling, doping and nonadiabatic effects

We investigate Raman spectra of graphite oxide and functionalized graphene sheets with epoxy and hydroxyl groups and Stone−Wales and 5−8−5 defects by first-principles calculations to interpret our experimental results. Only the alternating pattern of single−double carbon bonds within the sp2 carbon ribbons provides a satisfactory explanation for the experimentally observed blue shift of the G band of the Raman spectra relative to graphite. To obtain these single−double bonds, it is necessary to have sp3 carbons on the edges of a zigzag carbon ribbon.

Raman Spectra of Graphite Oxide and Functionalized Graphene Sheets

Molybdenum disulfide (MoS2) of single- and few-layer thickness was exfoliated on SiO2/Si substrate and characterized by Raman spectroscopy. The number of S−Mo−S layers of the samples was independently determined by contact-mode atomic force microscopy. Two Raman modes, E12g and A1g, exhibited sensitive thickness dependence, with the frequency of the former decreasing and that of the latter increasing with thickness. The results provide a convenient and reliable means for determining layer thickness with atomic-level precision. The opposite direction of the frequency shifts, which cannot be explained solely by van der Waals interlayer coupling, is attributed to Coulombic interactions and possible stacking-induced changes of the intralayer bonding. This work exemplifies the evolution of structural parameters in layered materials in changing from the three-dimensional to the two-dimensional regime.

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Anomalous lattice vibrations of single- and few-layer MoS2.

Every few years, a new material with unique properties emerges and fascinates the scientific community, typical recent examples being high-temperature superconductors and carbon nanotubes. Graphene is the latest sensation with unusual properties, such as half-integer quantum Hall effect and ballistic electron transport. This two-dimensional material which is the parent of all graphitic carbon forms is strictly expected to comprise a single layer, but there is considerable interest in investigating two-layer and few-layer graphenes as well. Synthesis and characterization of graphenes pose challenges, but there has been considerable progress in the last year or so. Herein, we present the status of graphene research which includes aspects related to synthesis, characterization, structure, and properties.

Graphene: The New Two-Dimensional Nanomaterial

We present Raman spectroscopy measurements on single- and few-layer graphene flakes. By using a scanning confocal approach, we collect spectral data with spatial resolution, which allows us to directly compare Raman images with scanning force micrographs. Single-layer graphene can be distinguished from double- and few-layer by the width of the D' line: the single peak for single-layer graphene splits into different peaks for the double-layer. These findings are explained using the double-resonant Raman model based on ab initio calculations of the electronic structure and of the phonon dispersion. We investigate the D line intensity and find no defects within the flake. A finite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry.

Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene

We report on the fabrication and characterization of bulk micromachined pressure sensors based on individual single-walled carbon nanotubes (SWNTs) as the active electromechanical transducer elements. The electromechanical sensor device consists of an individual electrically connected SWNT adsorbed on top of a 100-nm-thick atomic layer deposited (ALD) circular alumina (Al2O3) membrane with a radius in the range of 50−100 μm. A white light interferometer (WLI) was used to measure the deflection of the membrane due to differential pressure, and the mechanical properties of the device were characterized by bulge testing. Finally, we performed the first electromechanical measurements on strained metallic SWNTs adhering to a membrane and found a piezoresistive gauge factor of approximately 210 for metallic SWNTs.

Fabrication of Single-Walled Carbon-Nanotube-Based Pressure Sensors

We present a nano-electromechanical system based on an individual single-walled carbon nanotube (SWNT) demonstrating their potential use for future displacement sensing at the nanoscale. The fabrication and characterization of the proposed nanoscaled transducer, consisting of a suspended metal cantilever mounted on top of the center of a suspended SWNT, is presented and discussed. The displacement of the nanoscale cantilever is detected via the electromechanically induced change in conductance of the strained SWNT. A relative differential resistance sensitivity (for a metallic SWNT) of up to 27.5%/nm was measured and a piezoresistive gauge factor of a SWNT of up to 2900 was extracted.

Nano-electromechanical displacement sensing based on single-walled carbon nanotubes.

Sensors are key components in an overwhelming wealth of systems for industrial and consumer applications. Further system miniaturization will demand for continuous down-scaling of sensor functions in such systems most likely towards nanoscale. Then new sensor device concepts will emerge to improve performance, e.g. sensitivity, or to utilize unique functional properties of nanoscale structures. This paper presents concepts and demonstrators of nano electromechanical sensors based on carbon nanotubes (CNTs). First, different transducer concepts based on the unique electrical, mechanical and electromechanical properties of single-walled carbon nanotubes (SWNTs) are addressed and discussed. Second, fabrication techniques and methods for the integration of SWNTs in micro or nanosystems are presented. Finally, demonstrators of suspended SWNT-based cantilever structures and a membrane-based nanotube pressure sensor are introduced and evaluated. Electromechanical measurements on these test devices prove SWNTs as exceptional piezoresistive electromechanical transducers with gauge factors far above the values of state-of-the-art strain gauges.

Nano electromechanical sensors based on carbon nanotubes

Understanding the influence of vibrational motion of the atoms on electronic transitions in molecules constitutes a cornerstone of quantum physics, as epitomized by the Franck–Condon principle1, 2 of spectroscopy. Recent advances in building molecular-electronics devices3 and nanoelectromechanical systems4 open a new arena for studying the interaction between mechanical and electronic degrees of freedom in transport at the single-molecule level. The tunnelling of electrons through molecules or suspended quantum dots5, 6 has been shown to excite vibrational modes, or vibrons6, 7, 8, 9. Beyond this effect, theory predicts that strong electron–vibron coupling strongly suppresses the current flow at low biases, a collective behaviour known as Franck–Condon blockade10, 11. Here, we show measurements on quantum dots formed in suspended single-wall carbon nanotubes revealing a remarkably large electron–vibron coupling that, owing to the high quality and unprecedented tunability of our samples, allow a quantitative analysis of vibron-mediated electronic transport in the regime of strong electron–vibron coupling. This enables us to unambiguously demonstrate the Franck–Condon blockade in a suspended nanostructure. The large observed electron–vibron coupling could ultimately be a key ingredient for the detection of quantized mechanical motion12, 13. It also emphasizes the unique potential for nanoelectromechanical device applications based on suspended graphene sheets and carbon nanotubes.

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Christofer Hierold

Papers

Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene

Fabrication of Single-Walled Carbon-Nanotube-Based Pressure Sensors

Nano-electromechanical displacement sensing based on single-walled carbon nanotubes.

Nano electromechanical sensors based on carbon nanotubes

Franck–Condon blockade in suspended carbon nanotube quantum dots