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See detailDielectric screening of the Kohn anomaly of graphene on hexagonal boron nitride
Forster, F.; Molina-Sanchez, Alejandro UL; Engels, S. et al

in Physical Review. B, Condensed Matter and Materials Physics (2013), 88

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See detailVariations in the work function of doped single- and few-layer graphene assessed by Kelvin probe force microscopy and density functional theory
Ziegler, D.; Gava, P.; Guettinger, J. et al

in Physical Review. B, Condensed Matter and Materials Physics (2011), 83(23),

We present Kelvin probe force microscopy measurements of single-and few-layer graphene resting on SiO2 substrates. We compare the layer thickness dependency of the measured surface potential with ab ... [more ▼]

We present Kelvin probe force microscopy measurements of single-and few-layer graphene resting on SiO2 substrates. We compare the layer thickness dependency of the measured surface potential with ab initio density functional theory calculations of the work function for substrate-doped graphene. The ab initio calculations show that the work function of single-and bilayer graphene is mainly given by a variation of the Fermi energy with respect to the Dirac point energy as a function of doping, and that electrostatic interlayer screening only becomes relevant for thicker multilayer graphene. From the Raman G-line shift and the comparison of the Kelvin probe data with the ab initio calculations, we independently find an interlayer screening length in the order of four to five layers. Furthermore, we describe in-plane variations of the work function, which can be attributed to partial screening of charge impurities in the substrate, and result in a nonuniform charge density in single-layer graphene. [less ▲]

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See detailRaman imaging of doping domains in graphene on SiO(2)
Stampfer, C.; Molitor, F.; Graf, D. et al

in Applied Physics Letters (2007), 91(24),

We present spatially resolved Raman images of the G and 2D lines of single-layer graphene flakes. The spatial fluctuations of G and 2D lines are correlated and are thus shown to be affiliated with local ... [more ▼]

We present spatially resolved Raman images of the G and 2D lines of single-layer graphene flakes. The spatial fluctuations of G and 2D lines are correlated and are thus shown to be affiliated with local doping domains. We investigate the position of the 2D line-the most significant Raman peak to identify single-layer graphene-as a function of charging up to vertical bar n vertical bar approximate to 4x10(12) cm(-2). Contrary to the G line which exhibits a strong and symmetric stiffening with respect to electron and hole doping, the 2D line shows a weak and slightly asymmetric stiffening for low doping. Additionally, the linewidth of the 2D line is, in contrast to the G line, doping independent making this quantity a reliable measure for identifying single-layer graphene. (C) 2007 American Institute of Physics. [less ▲]

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See detailSpatially resolved raman spectroscopy of single- and few-layer graphene
Graf, D.; Molitor, F.; Ensslin, K. et al

in Nano Letters (2007), 7(2), 238-242

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 ... [more ▼]

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. [less ▲]

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See detailRaman imaging of graphene
Graf, D.; Molitor, F.; Ensslin, K. et al

in Solid State Communications (2007), 143(1-2), 44-46

A Raman spectrum of a solid contains information about its vibrational and electronic properties. Collecting spectral data with spatial resolution and encoding it in a 2D plot generates images with ... [more ▼]

A Raman spectrum of a solid contains information about its vibrational and electronic properties. Collecting spectral data with spatial resolution and encoding it in a 2D plot generates images with information complementary to optical and scanning force imaging. In the case of few-layer graphene the frequency of the G line and especially the width of the D ' line turn out to be sensitive to single layers. The thickness of the few-layer graphene flake is reflected in the intensity of the G line and in the reduced intensity of the dominant peak of the underlying silicon oxide. (c) 2007 Elsevier Ltd. All rights reserved. [less ▲]

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See detailRaman mapping of a single-layer to double-layer graphene transition
Graf, D.; Molitor, F.; Ensslin, K. et al

in European Physical Journal. Special Topics (2007), 148

We report on confocal Raman spectroscopy on a few-layer graphene flake. Adjacent single- and double-layer graphene sections allow mapping the transition in vibrational and electronic properties to a ... [more ▼]

We report on confocal Raman spectroscopy on a few-layer graphene flake. Adjacent single- and double-layer graphene sections allow mapping the transition in vibrational and electronic properties to a second stacked graphene sheet and with it a weak interlayer coupling. Most prominently the width of the D' peak doubles upon going from a single to a double layer, which can be explained within the double-resonant Raman model. The intensities of the G and G' lines decrease at the crossover to a single layer. Contrary to the G' line the G peak position shifts to higher wave numbers, however, not uniformly over the entire section: its frequency fluctuates spatially. The Raman map of the D line intensity shows a non-zero contribution at the boundaries of the flake and the individual sections, which can be attributed either to defects and disorder or to the breakdown of translational symmetry, whereas within the flake no D line signal is detected. [less ▲]

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See detailPseudopath semiclassical approximation to transport through open quantum billiards: Dyson equation for diffractive scattering
Stampfer, C.; Rotter, S.; Burgdorfer, J. et al

in Physical Review. E. (2005), 72(3),

We present a semiclassical theory for transport through open billiards of arbitrary convex shape that includes diffractively scattered paths at the lead openings. Starting from a Dyson equation for the ... [more ▼]

We present a semiclassical theory for transport through open billiards of arbitrary convex shape that includes diffractively scattered paths at the lead openings. Starting from a Dyson equation for the semiclassical Green's function we develop a diagrammatic expansion that allows a systematic summation over classical and pseudopaths, the latter consisting of classical paths joined by diffractive scatterings ("kinks"). This renders the inclusion of an exponentially proliferating number of pseudopath combinations numerically tractable for both regular and chaotic billiards. For a circular billiard and the Bunimovich stadium the path sum leads to a good agreement with the quantum path length power spectrum up to long path length. Furthermore, we find excellent numerical agreement with experimental studies of quantum scattering in microwave billiards where pseudopaths provide a significant contribution. [less ▲]

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See detailSemiclassical theory for transmission through open billiards: Convergence towards quantum transport
Wirtz, Ludger UL; Stampfer, C.; Rotter, S. et al

in Physical Review. E. (2003), 67(1),

We present a semiclassical theory for transmission through open quantum billiards which converges towards quantum transport. The transmission amplitude can be expressed as a sum over all classical paths ... [more ▼]

We present a semiclassical theory for transmission through open quantum billiards which converges towards quantum transport. The transmission amplitude can be expressed as a sum over all classical paths and pseudopaths which consist of classical path segments joined by "kinks," i.e., diffractive scattering at lead mouths. For a rectangular billiard we show numerically that the sum over all such paths with a given number of kinks K converges to the quantum transmission amplitude as K-->infinity. Unitarity of the semiclassical theory is restored as K approaches infinity. Moreover, we find excellent agreement with the quantum path-length power spectrum up to very long path length. [less ▲]

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