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

Ultrahigh electron mobility in suspended graphene

Graphene devices on standard SiO(2) substrates are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. Although suspending the graphene above the substrate leads to a substantial improvement in device quality, this geometry imposes severe limitations on device architecture and functionality. There is a growing need, therefore, to identify dielectrics that allow a substrate-supported geometry while retaining the quality achieved with a suspended sample. Hexagonal boron nitride (h-BN) is an appealing substrate, because it has an atomically smooth surface that is relatively free of dangling bonds and charge traps. It also has a lattice constant similar to that of graphite, and has large optical phonon modes and a large electrical bandgap. Here we report the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal h-BN substrates, by using a mechanical transfer process. Graphene devices on h-BN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO(2). These devices also show reduced roughness, intrinsic doping and chemical reactivity. The ability to assemble crystalline layered materials in a controlled way permits the fabrication of graphene devices on other promising dielectrics and allows for the realization of more complex graphene heterostructures.

Boron nitride substrates for high-quality graphene electronics

Graphene-Like Two-Dimensional Materials

Graphene, a two-dimensional monolayer of sp2-bonded carbon atoms, has been attracting great interest due to its unique transport properties. One of the promising applications of graphene is as a transparent conductive electrode owing to its high optical transmittance and conductivity. In this paper, we report on an improved transfer process of large-area graphene grown on Cu foils by chemical vapor deposition. The transferred graphene films have high electrical conductivity and high optical transmittance that make them suitable for transparent conductive electrode applications. The improved transfer processes will also be of great value for the fabrication of electronic devices such as field effect transistor and bilayer pseudospin field effect transistor devices.

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Transfer of large-area graphene films for high-performance transparent conductive electrodes

The electronic structure of graphene causes its charge carriers to behave like relativistic particles. For a perfect graphene sheet free from impurities and disorder, the Fermi energy lies at the so-called ‘Dirac point’, where the density of electronic states vanishes. But in the inevitable presence of disorder, theory predicts that equally probable regions of electron-rich and hole-rich puddles will arise. These puddles could explain graphene’s anomalous non-zero minimal conductivity at zero average carrier density. Here, we use a scanning single-electron transistor to map the local density of states and the carrier density landscape in the vicinity of the neutrality point. Our results confirm the existence of electron–hole puddles, and rule out extrinsic substrate effects as explanations for their emergence and topology. Moreover, we find that, unlike non-relativistic particles the density of states can be quantitatively accounted for by considering non-interacting electrons and holes.

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Observation of electron–hole puddles in graphene using a scanning single-electron transistor

The intrinsic doping level of graphene prepared by mechanical exfoliation and standard lithography procedures on thermally oxidized silicon varies significantly and seems to depend strongly on processing details and the substrate morphology. Moreover, transport properties of such graphene devices suffer from hysteretic behavior under ambient conditions. The hysteresis presumably originates from dipolar adsorbates on the substrate or graphene surface. Here, we demonstrate that it is possible to reliably obtain low intrinsic doping levels and to strongly suppress hysteretic behavior even in ambient air by depositing graphene on top of a thin, hydrophobic self-assembled layer of hexamethyldisilazane (HMDS). The HMDS serves as a reproducible template that prevents the adsorption of dipolar substances. It may also screen the influence of substrate deficiencies.

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Graphene on a Hydrophobic Substrate: Doping Reduction and Hysteresis Suppression under Ambient Conditions

In this paper, we describe a graphene p-n junction created by chemical doping. We find that chemical doping does not reduce mobility in contrast to top-gating. The preparation technique has been developed from systematic studies about influences on the initial doping of freshly prepared graphene. We investigated the removal of adsorbates by vacuum treatment, annealing, and compensation doping using NH(3). Hysteretic behavior is observed in the electric field effect due to dipolar adsorbates like water and NH(3). Finally we demonstrate spatially selective doping of graphene using patterned PMMA. Four-terminal transport measurements of the p-n devices reveal edge channel mixing in the quantum hall regime. Quantized resistances of h/e(2), h/3e(2) and h/15e(2) can be observed as expected from theory.

Four-terminal magneto-transport in graphene p-n junctions created by spatially selective doping.

We report about investigations of time-dependent structural modifications in single-crystal graphene due to laser irradiation even at moderate power levels of 1 mW in a diffraction-limited spot. The modifications have been characterized by in situ scanning confocal Raman spectroscopy, atomic force height microscopy, and transport studies. The time evolution of the Raman spectrum reveals two different effects: on a short-time scale, dopants, initially present on the flake, are removed. The longer time scale behavior points to a laser induced gradual local decomposition of single-crystal graphene into a network of interconnected nanocrystallites with a characteristic length scale of approximately 10 nm due to bond breaking. The broken bonds offer additional docking sites for adsorbates as confirmed in transport and AFM height studies. These controlled structural modifications may for instance be valuable for enhancing the local reactivity, trimming graphene based gas sensors and generating spatially varying doping patterns.

Laser-induced disassembly of a graphene single crystal into a nanocrystalline network

The effect of disorder in conventional two-dimensional electron systems is usually described in terms of individual electrons interacting with an underlying disorder potential. Scanning single-electron transistor measurements of graphene in a strong magnetic field indicate that in this system, coulombic interactions between electrons must also be taken into account.

http://yacoby.physics.harvard.edu/Publications/The%20nature%20of%20localization%20in%20graphene%20under%20quanum%20Hall%20conditions_2009.pdf

Timm Lohmann

Papers

Observation of electron–hole puddles in graphene using a scanning single-electron transistor

Graphene on a Hydrophobic Substrate: Doping Reduction and Hysteresis Suppression under Ambient Conditions

Four-terminal magneto-transport in graphene p-n junctions created by spatially selective doping.

Laser-induced disassembly of a graphene single crystal into a nanocrystalline network

The nature of localization in graphene under quantum Hall conditions