192 research outputs found
Phonon renormalisation in doped bilayer graphene
We report phonon renormalisation in bilayer graphene as a function of doping.
The Raman G peak stiffens and sharpens for both electron and hole doping, as a
result of the non-adiabatic Kohn anomaly at the point. The bilayer has
two conduction and valence subbands, with splitting dependent on the interlayer
coupling. This results in a change of slope in the variation of G peak position
with doping, which allows a direct measurement of the interlayer coupling
strength.Comment: 5 figure
Electron Transport and Hot Phonons in Carbon Nanotubes
We demonstrate the key role of phonon occupation in limiting the high-field
ballistic transport in metallic carbon nanotubes. In particular, we provide a
simple analytic formula for the electron transport scattering length, that we
validate by accurate first principles calculations on (6,6) and (11,11)
nanotubes. The comparison of our results with the scattering lengths fitted
from experimental I-V curves indicates the presence of a non-equilibrium
optical phonon heating induced by electron transport. We predict an effective
temperature for optical phonons of thousands Kelvin.Comment: 4 pages, 1 figur
Kohn Anomalies and Electron-Phonon Interaction in Graphite
We demonstrate that graphite phonon dispersions have two Kohn anomalies at
the Gamma-E_2g and K-A'1 modes. The anomalies are revealed by two sharp kinks.
By an exact analytic derivation, we show that the slope of these kinks is
proportional to the square of the electron-phonon coupling (EPC). Thus, we can
directly measure the EPC from the experimental dispersions. The Gamma-E_2g and
K-A'1 EPCs are particularly large, whilst they are negligible for all the other
modes at Gamma and K.Comment: 4 pages, 2 figure
Phonon Linewidths and Electron Phonon Coupling in Nanotubes
We prove that Electron-phonon coupling (EPC) is the major source of
broadening for the Raman G and G- peaks in graphite and metallic nanotubes.
This allows us to directly measure the optical-phonon EPCs from the G and G-
linewidths. The experimental EPCs compare extremely well with those from
density functional theory. We show that the EPC explains the difference in the
Raman spectra of metallic and semiconducting nanotubes and their dependence on
tube diameter. We dismiss the common assignment of the G- peak in metallic
nanotubes to a Fano resonance between phonons and plasmons. We assign the G+
and G- peaks to TO (tangential) and LO (axial) modes.Comment: 5 pages, 4 figures (correction in label of fig 3
Optical Phonons in Carbon Nanotubes: Kohn Anomalies, Peierls Distortions and Dynamic Effects
We present a detailed study of the vibrational properties of Single Wall
Carbon Nanotubes (SWNTs). The phonon dispersions of SWNTs are strongly shaped
by the effects of electron-phonon coupling. We analyze the separate
contributions of curvature and confinement. Confinement plays a major role in
modifying SWNT phonons and is often more relevant than curvature. Due to their
one-dimensional character, metallic tubes are expected to undergo Peierls
distortions (PD) at T=0K. At finite temperature, PD are no longer present, but
phonons with atomic displacements similar to those of the PD are affected by
strong Kohn anomalies (KA). We investigate by Density Functional Theory (DFT)
KA and PD in metallic SWNTs with diameters up to 3 nm, in the electronic
temperature range from 4K to 3000 K. We then derive a set of simple formulas
accounting for all the DFT results. Finally, we prove that the static approach,
commonly used for the evaluation of phonon frequencies in solids, fails because
of the SWNTs reduced dimensionality. The correct description of KA in metallic
SWNTs can be obtained only by using a dynamical approach, beyond the adiabatic
Born-Oppenheimer approximation, by taking into account non-adiabatic
contributions. Dynamic effects induce significant changes in the occurrence and
shape of Kohn anomalies. We show that the SWNT Raman G peak can only be
interpreted considering the combined dynamic, curvature and confinement
effects. We assign the G+ and G- peaks of metallic SWNTs to TO
(circumferential) and LO (axial) modes, respectively, the opposite of
semiconducting SWNTs.Comment: 24 pages, 21 figures, submitted to Phys. Rev.
The Raman Fingerprint of Graphene
Graphene is the two-dimensional (2d) building block for carbon allotropes of
every other dimensionality. It can be stacked into 3d graphite, rolled into 1d
nanotubes, or wrapped into 0d fullerenes. Its recent discovery in free state
has finally provided the possibility to study experimentally its electronic and
phonon properties. Here we show that graphene's electronic structure is
uniquely captured in its Raman spectrum that clearly evolves with increasing
number of layers. Raman fingerprints for single-, bi- and few-layer graphene
reflect changes in the electronic structure and electron-phonon interactions
and allow unambiguous, high-throughput, non-destructive identification of
graphene layers, which is critically lacking in this emerging research area
Edge-functionalized and substitutional doped graphene nanoribbons: electronic and spin properties
Graphene nanoribbons are the counterpart of carbon nanotubes in
graphene-based nanoelectronics. We investigate the electronic properties of
chemically modified ribbons by means of density functional theory. We observe
that chemical modifications of zigzag ribbons can break the spin degeneracy.
This promotes the onset of a semiconducting-metal transition, or of an
half-semiconducting state, with the two spin channels having a different
bandgap, or of a spin-polarized half-semiconducting state -where the spins in
the valence and conduction bands are oppositely polarized. Edge
functionalization of armchair ribbons gives electronic states a few eV away
from the Fermi level, and does not significantly affect their bandgap. N and B
produce different effects, depending on the position of the substitutional
site. In particular, edge substitutions at low density do not significantly
alter the bandgap, while bulk substitution promotes the onset of
semiconducting-metal transitions. Pyridine-like defects induce a
semiconducting-metal transition.Comment: 12 pages, 5 figure
Raman Spectroscopy of Graphene Edges
Graphene edges are of particular interest since their orientation determines the electronic properties. Here we present a detailed Raman investigation of graphene flakes with edges oriented at different crystallographic directions. We also develop a real space theory for Raman scattering to analyze the general case of disordered edges. The position, width, and intensity of G and D peaks are studied as a function of the incident light polarization. The D-band is strongest for polarization parallel to the edge and minimum for perpendicular. Raman mapping shows that the D peak is localized in proximity of the edge. For ideal edges, the D peak is zero for zigzag orientation and large for armchair, allowing in principle the use of Raman spectroscopy as a sensitive tool for edge orientation. However, for real samples, the D to G ratio does not always show a significant dependence on edge orientation. Thus, even though edges can appear macroscopically smooth and oriented at well-defined angles, they are not necessarily microscopically ordered
Effect of Holstein phonons on the optical conductivity of gapped graphene
We study the optical conductivity of a doped graphene when a sublattice
symmetry breaking is occurred in the presence of the electron-phonon
interaction. Our study is based on the Kubo formula that is established upon
the retarded self-energy. We report new features of both the real and imaginary
parts of the quasiparticle self-energy in the presence of a gap opening. We
find an analytical expression for the renormalized Fermi velocity of massive
Dirac Fermions over broad ranges of electron densities, gap values and the
electron-phonon coupling constants. Finally we conclude that the inclusion of
the renormalized Fermi energy and the band gap effects are indeed crucial to
get reasonable feature for the optical conductivity.Comment: 12 pages, 4 figures. To appear in Eur. Phys. J.
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