203 research outputs found
Symmetry properties of vibrational modes in graphene nanoribbons
We present symmetry properties of the lattice vibrations of graphene
nanoribbons with pure armchair (AGNR) and zigzag edges (ZGNR). In
non-symmorphic nanoribbons the phonon modes at the edge of the Brillouin zone
are twofold degenerate, whereas the phonon modes in symmorphic nanoribbons are
non-degenerate. We identified the Raman-active and infrared-active modes. We
predict 3N and 3(N+1) Raman-active modes for N-ZGNRs and N-AGNRs, respectively
(N is the number of dimers per unit cell). These modes can be used for the
experimental characterization of graphene nanoribbons. Calculations based on
density functional theory suggest that the frequency splitting of the LO and TO
in AGNRs (corresponding to the E2g mode in graphene) exhibits characteristic
width and family dependence. Further, all graphene nanoribbons have a
Raman-active breathing-like mode, the frequency of which is inversely
proportional to the nanoribbon width and thus might be used for experimental
determination of the width of graphene nanoribbons.Comment: 10 pages, 5 figure
Chirality distribution and transition energies of carbon nanotubes
From resonant Raman scattering on isolated nanotubes we obtained the optical
transition energies, the radial breathing mode frequency and Raman intensity of
both metallic and semiconducting tubes. We unambiguously assigned the chiral
index (n_1,n_2) of approximately 50 nanotubes based solely on a third-neighbor
tight-binding Kataura plot and find omega_RBM=214.4cm^-1nm/d+18.7cm^-1. In
contrast to luminescence experiments we observe all chiralities including
zig-zag tubes. The Raman intensities have a systematic chiral-angle dependence
confirming recent ab-initio calculations.Comment: 4 pages, to be published in Phys. Rev. Let
The strength of the radial-breathing mode in single-walled carbon nanotubes
We show by ab initio calculations that the electron-phonon coupling matrix
element M of the radial breathing mode in single-walled carbon nanotubes
depends strongly on tube chirality. For nanotubes of the same diameter the
coupling strength |M|^2 is up to one order of magnitude stronger for zig-zag
than for armchair tubes. For (n,m) tubes M depends on the value of (n-m) mod 3,
which allows to discriminate semiconducting nano tubes with similar diameter by
their Raman scattering intensity. We show measured resonance Raman profiles of
the radial breathing mode which support our theoretical predictions
Graphene on Si(111)7x7
We demonstrate that it is possible to mechanically exfoliate graphene under
ultra high vacuum conditions on the atomically well defined surface of single
crystalline silicon. The flakes are several hundred nanometers in lateral size
and their optical contrast is very faint in agreement with calculated data.
Single layer graphene is investigated by Raman mapping. The G and 2D peaks are
shifted and narrowed compared to undoped graphene. With spatially resolved
Kelvin probe measurements we show that this is due to p-type doping with hole
densities of n_h \simeq 6x10^{12} cm^{-2}. The in vacuo preparation technique
presented here should open up new possibilities to influence the properties of
graphene by introducing adsorbates in a controlled way.Comment: 8 pages, 7 figure
Phonons in graphene with point defects
The phonon density of states (DOS) of graphene with different types of point
defects (carbon isotopes, substitution atoms, vacancies) is considered. Using a
solvable model which is based on the harmonic approximation and the assumption
that the elastic forces act only between nearest neighboring ions we calculate
corrections to graphene DOS dependent on type and concentration of defects. In
particular the correction due to isotopic dimers is determined. It is shown
that a relatively small concentration of defects may lead to significant and
specific changes in the DOS, especially at low frequencies, near the Van Hove
points and in the vicinity of the K-points of the Brillouin zone. In some cases
defects generate one or several narrow gaps near the critical points of the
phonon DOS as well as resonance states in the Brillouin zone regular points.
All types of defects are characterized by the appearance of one or more
additional Van Hove peaks near the (Dirac) K points and their singular
contribution may be comparable with the effect of electron-phonon interaction.
Besides, for low frequencies and near the critical points the relative change
in density of states may be many times higher than the concentration of
defects.Comment: 19 pages, 7 figure
Exciton binding energies in carbon nanotubes from two-photon photoluminescence
One- and two-photon luminescence excitation spectroscopy showed a series of
distinct excitonic states in single-walled carbon nanotubes. The energy
splitting between one- and two-photon-active exciton states of different
wavefunction symmetry is the fingerprint of excitonic interactions in carbon
nanotubes. We determine exciton binding energies of 0.3-0.4 eV for different
nanotubes with diameters between 0.7 and 0.9 nm. Our results, which are
supported by ab-initio calculations of the linear and non-linear optical
spectra, prove that the elementary optical excitations of carbon nanotubes are
strongly Coulomb-correlated, quasi-one dimensionally confined electron-hole
pairs, stable even at room temperature. This alters our microscopic
understanding of both the electronic structure and the Coulomb interactions in
carbon nanotubes, and has direct impact on the optical and transport properties
of novel nanotube devices.Comment: 5 pages, 4 figure
The phonon dispersion of graphite by inelastic x-ray scattering
We present the full in-plane phonon dispersion of graphite obtained from
inelastic x-ray scattering, including the optical and acoustic branches, as
well as the mid-frequency range between the and points in the Brillouin
zone, where experimental data have been unavailable so far. The existence of a
Kohn anomaly at the point is further supported. We fit a fifth-nearest
neighbour force-constants model to the experimental data, making improved
force-constants calculations of the phonon dispersion in both graphite and
carbon nanotubes available.Comment: 7 pages; submitted to Phys. Rev.
Dependence of exciton transition energy of single-walled carbon nanotubes on surrounding dielectric materials
We theoretically investigate the dependence of exciton transition energies on
dielectric constant of surrounding materials. We make a simple model for the
relation between dielectric constant of environment and a static dielectric
constant describing the effects of electrons in core states, bonds and
surrounding materials. Although the model is very simple, calculated results
well reproduce experimental transition energy dependence on dielectric constant
of various surrounding materials.Comment: 5pages, 4 figure
Intersubband decay of 1-D exciton resonances in carbon nanotubes
We have studied intersubband decay of E22 excitons in semiconducting carbon
nanotubes experimentally and theoretically. Photoluminescence excitation line
widths of semiconducting nanotubes with chiral indicess (n, m) can be mapped
onto a connectivity grid with curves of constant (n-m) and (2n+m). Moreover,
the global behavior of E22 linewidths is best characterized by a strong
increase with energy irrespective of their (n-m) mod(3)= \pm 1 family
affiliation. Solution of the Bethe-Salpeter equations shows that the E22
linewidths are dominated by phonon assisted coupling to higher momentum states
of the E11 and E12 exciton bands. The calculations also suggest that the
branching ratio for decay into exciton bands vs free carrier bands,
respectively is about 10:1.Comment: 4 pages, 4 figure
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