54 research outputs found
Asymptotics of an optimal compliance-location problem
We consider the problem of placing n small balls of given radius in a certain
domain subject to a force f in order to minimize the compliance of the
configuration. Then we let n tend to infinity and look at the asymptotics of
the minimization problem, after properly scaling the functionals involved, and
to the limit distribution of the centres of the balls. This problem is both
linked to optimal location and shape optimization problems.Comment: 20 pages with 2 figures; final accepted version (minor changes, some
extra details on the positivity assumption on
Electronic structure of epitaxial graphene layers on SiC: effect of the substrate
Recent transport measurements on thin graphite films grown on SiC show large
coherence lengths and anomalous integer quantum Hall effects expected for
isolated graphene sheets. This is the case eventhough the layer-substrate
epitaxy of these films implies a strong interface bond that should induce
perturbations in the graphene electronic structure. Our DFT calculations
confirm this strong substrate-graphite bond in the first adsorbed carbon layer
that prevents any graphitic electronic properties for this layer. However, the
graphitic nature of the film is recovered by the second and third absorbed
layers. This effect is seen in both the (0001)and 4H SiC
surfaces. We also present evidence of a charge transfer that depends on the
interface geometry. It causes the graphene to be doped and gives rise to a gap
opening at the Dirac point after 3 carbon layers are deposited in agreement
with recent ARPES experiments (T.Ohta et al, Science {\bf 313} (2006) 951)
Quantum Transport in Chemically-modified Two-Dimensional Graphene: From Minimal Conductivity to Anderson Localization
An efficient computational methodology is used to explore charge transport
properties in chemically-modified (and randomly disordered) graphene-based
materials. The Hamiltonians of various complex forms of graphene are
constructed using tight-binding models enriched by first-principles
calculations. These atomistic models are further implemented into a real-space
order-N Kubo-Greenwood approach, giving access to the main transport length
scales (mean free paths, localization lengths) as a function of defect density
and charge carrier energy. An extensive investigation is performed for epoxide
impurities with specific discussions on both the existence of a minimum
semi-classical conductivity and a crossover between weak to strong localization
regime. The 2D generalization of the Thouless relationship linking transport
length scales is here illustrated based on a realistic disorder model.Comment: 14 pages, 18 figures, submitte
Electronic structure and the minimum conductance of a graphene layer on SiO2 from density-functional methods.
The effect of the SiO substrate on a graphene film is investigated using
realistic but computationally convenient energy-optimized models of the
substrate supporting a layer of graphene. The electronic bands are calculated
using density-functional methods for several model substrates. This provides an
estimate of the substrate-charge effects on the behaviour of the bands near
, as well as a variation of the equilibrium distance of the graphene
sheet. A model of a wavy graphene layer is examined as a possible candidate for
understanding the nature of the minimally conducting states in graphene.Comment: 6 pages, 5 figure
Symmetry Breaking in Few Layer Graphene Films
Recently, it was demonstrated that the quasiparticle dynamics, the
layer-dependent charge and potential, and the c-axis screening coefficient
could be extracted from measurements of the spectral function of few layer
graphene films grown epitaxially on SiC using angle-resolved photoemission
spectroscopy (ARPES). In this article we review these findings, and present
detailed methodology for extracting such parameters from ARPES. We also present
detailed arguments against the possibility of an energy gap at the Dirac
crossing ED.Comment: 23 pages, 13 figures, Conference Proceedings of DPG Meeting Mar 2007
Regensburg Submitted to New Journal of Physic
Angle-resolved photoemission spectra of graphene from first-principles calculations
Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental
technique for directly probing electron dynamics in solids. The energy vs.
momentum dispersion relations and the associated spectral broadenings measured
by ARPES provide a wealth of information on quantum many-body interaction
effects. In particular, ARPES allows studies of the Coulomb interaction among
electrons (electron-electron interactions) and the interaction between
electrons and lattice vibrations (electron-phonon interactions). Here, we
report ab initio simulations of the ARPES spectra of graphene including both
electron-electron and electron-phonon interactions on the same footing. Our
calculations reproduce some of the key experimental observations related to
many-body effects, including the indication of a mismatch between the upper and
lower halves of the Dirac cone
Correlating Raman Spectral Signatures with Carrier Mobility in Epitaxial Graphene: A Guide to Achieving High Mobility on the Wafer Scale
We report a direct correlation between carrier mobility and Raman topography
of epitaxial graphene (EG) grown on silicon carbide (SiC). We show the Hall
mobility of material on the Si-face of SiC [SiC(0001)] is not only highly
dependent on thickness uniformity but also on monolayer strain uniformity. Only
when both thickness and strain are uniform over a significant fraction (> 40%)
of the device active area does the mobility exceed 1000 cm2/V-s. Additionally,
we achieve high mobility epitaxial graphene (18,100 cm2/V-s at room
temperature) on the C-face of SiC [SiC(000-1)] and show that carrier mobility
depends strongly on the graphene layer stacking. These findings provide a means
to rapidly estimate carrier mobility and provide a guide to achieve very high
mobility in epitaxial graphene. Our results suggest that ultra-high mobilities
(>50,000 cm2/V-s) are achievable via the controlled formation of uniform,
rotationally faulted epitaxial graphene.Comment: 13 pages including supplimental material. Submitted to Nature
Materials 2/23/200
Micro-Raman and micro-transmission imaging of epitaxial graphene grown on the Si and C faces of 6H-SiC
Micro-Raman and micro-transmission imaging experiments have been done on epitaxial graphene grown on the C- and Si-faces of on-axis 6H-SiC substrates. On the C-face it is shown that the SiC sublimation process results in the growth of long and isolated graphene ribbons (up to 600 μm) that are strain-relaxed and lightly p-type doped. In this case, combining the results of micro-Raman spectroscopy with micro-transmission measurements, we were able to ascertain that uniform monolayer ribbons were grown and found also Bernal stacked and misoriented bilayer ribbons. On the Si-face, the situation is completely different. A full graphene coverage of the SiC surface is achieved but anisotropic growth still occurs, because of the step-bunched SiC surface reconstruction. While in the middle of reconstructed terraces thin graphene stacks (up to 5 layers) are grown, thicker graphene stripes appear at step edges. In both the cases, the strong interaction between the graphene layers and the underlying SiC substrate induces a high compressive thermal strain and n-type doping
Properties of Graphene: A Theoretical Perspective
In this review, we provide an in-depth description of the physics of
monolayer and bilayer graphene from a theorist's perspective. We discuss the
physical properties of graphene in an external magnetic field, reflecting the
chiral nature of the quasiparticles near the Dirac point with a Landau level at
zero energy. We address the unique integer quantum Hall effects, the role of
electron correlations, and the recent observation of the fractional quantum
Hall effect in the monolayer graphene. The quantum Hall effect in bilayer
graphene is fundamentally different from that of a monolayer, reflecting the
unique band structure of this system. The theory of transport in the absence of
an external magnetic field is discussed in detail, along with the role of
disorder studied in various theoretical models. We highlight the differences
and similarities between monolayer and bilayer graphene, and focus on
thermodynamic properties such as the compressibility, the plasmon spectra, the
weak localization correction, quantum Hall effect, and optical properties.
Confinement of electrons in graphene is nontrivial due to Klein tunneling. We
review various theoretical and experimental studies of quantum confined
structures made from graphene. The band structure of graphene nanoribbons and
the role of the sublattice symmetry, edge geometry and the size of the
nanoribbon on the electronic and magnetic properties are very active areas of
research, and a detailed review of these topics is presented. Also, the effects
of substrate interactions, adsorbed atoms, lattice defects and doping on the
band structure of finite-sized graphene systems are discussed. We also include
a brief description of graphane -- gapped material obtained from graphene by
attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic
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