Optical phonons in carbon nanotubes: Kohn anomalies, Peierls distortions, and dynamic effects (original) (raw)
Related papers
Kohn anomalies and nonadiabaticity in doped carbon nanotubes
Physical Review B, 2007
The high-frequency Raman-active phonon modes of metallic single-walled carbon nanotubes (SWNTs) are thought to be characterized by Kohn anomalies (KAs), which are expected to be modified by the doping-induced tuning of the Fermi energy level epsilonF\epsilon_FepsilonF, obtained through the intercalation of SWNTs with alkali atoms or by the application of a gate potential. We present a Density-Functional Theory (DFT) study of the phonon properties of a (9,9) metallic SWNT as a function of electronic doping. For such study, we use, as in standard DFT calculations of vibrational properties, the Born-Oppenheimer (BO) approximation. We also develop an analytical model capable of reproducing and interpreting our DFT results. Both DFT calculations and this model predict, for increasing doping levels, a series of EPC-induced KAs in the vibrational mode parallel to the tube axis at the mathbfGamma\mathbf\GammamathbfGamma point of the Brillouin zone, usually indicated in Raman spectroscopy as the G−G^-G− peak. Such KAs would arise each time a new conduction band is populated. However, we show that they are an artifact of the BO approximation. The inclusion of non-adiabatic (NA) effects dramatically affects the results, predicting KAs at mathbfGamma\mathbf\GammamathbfGamma only when epsilonF\epsilon_FepsilonF is close to a band crossing EXE_{X}EX. For each band crossing a double KA occurs for epsilonF=EXpmhbaromega/2\epsilon_F=E_{X}\pm \hbar\omega/2epsilonF=EXpmhbaromega/2, where hbaromega\hbar\omegahbaromega is the phonon energy. In particular, for a 1.2 nmnmnm metallic nanotube, we predict a KA to occur in the so-called G−G^-G− peak at a doping level of about Nel/C=pm0.0015N_{el}/C=\pm 0.0015Nel/C=pm0.0015 atom ($\epsilon_F\approx \pm 0.1 ~eV$). Furthermore, we predict that the Raman linewidth of the G−G^-G− peak significantly decreases for ∣epsilonF∣geqhbaromega/2|\epsilon_F| \geq \hbar\omega/2∣epsilonF∣geqhbaromega/2.
JPCC 2008 112 8219 Systematic Comparison of the Raman Spectra of Metallic and Semiconducting SWNTs
Raman spectra of individual SWNTs were systematically investigated by comparing the behavior of 21 semiconducting and 32 metallic SWNTs. It is found that, compared to semiconducting SWNTs, the RBM of metallic ones is softened, which exhibits chirality dependence. There are significant differences in the line shape of the G-band between semiconducting and metallic SWNTs, which was attributed to electron-phonon coupling previously. However, we found that the differences cannot be explained only by the electron-phonon coupling via the Kohn anomaly mechanism. Curvature effect and other unknown reasons appear to also contribute to the dissimilarities. As for the D-band, the frequency of metallic SWNTs does not show a softening effect when compared with that of semiconducting SWNTs, which is not consistent with theoretical predictions.
Physical Review B, 2014
We present resonant Raman scattering experiments on nanotube samples enriched in metallic armchair single-wall carbon nanotubes (SWCNTs). We establish the transverse optical (AT O) phonon frequency for the (5,5) through (10,10) armchair species, ranging in diameter from 0.68 to 1.36 nm. The frequencies show a strong diameter dependence similar to that previously observed in semiconducting nanotubes. We show that the AT O frequencies in armchair SWCNTs are dramatically upshifted from those of semiconducting SWCNTs. Furthermore, using electrochemical doping, we demonstrated that the AT O frequencies in armchair SWCNTs are independent of the position of the Fermi level. These results suggest that the upshift is a result of a Kohn anomaly involving a forward-scattering mechanism of electrons close to the Fermi level. This is in contrast to the wellknown Kohn anomaly that dominates the downshift of the ALO and E2g phonons in non-armchair metallic SWCNTs and graphene, respectively.
Electronic structure of single-wall carbon nanotubes studied by resonant inelastic X-ray scattering
Applied Physics A: Materials Science & Processing, 1998
Carbon nanotubes have in recent years attracted increasing interest as a new modification of carbon, related to the fullerenes and graphite. Especially for single wall carbon nanotubes (SWNTs) interesting electronic properties have been predicted early on. [1] For these nanotubes, the electronic structure strongly depends on the chirality vector defining the type of nanotube: (n, n) tubes ("armchair" type) are predicted to be metallic, while (n, m) tubes with n ≠ m are wide-gap or narrow-gap semiconductors, depending on the particular m and n. If 2n+m or n+2m is an integer multiple of 3, the SWNT is predicted to be a narrow-gap semiconductor with good room temperature conductivity.
2015
In this work, a quick and effective method to calculate the second and third optical transition energies of metallic armchair single-wall carbon nanotubes (SWCNT) is presented. In this proposed method, the transition energy of any armchair SWCNT can be predicted directly by knowing its one chiral index as both of its chiral indices are same. The predicted results are compared with recent experimental data and found to be accurate over a wide diameter range from 2 to 4.8 nm. The empirical equation proposed here is also compared with that proposed in earlier works. The proposed way may help the research works or applications where information of optical transitions of armchair metallic nanotubes is needed.
Empirical prediction of optical transitions in metallic armchair SWCNTs
Cogent Physics, 2015
In this work, a quick and effective method to calculate the second and third optical transition energies of metallic armchair single-wall carbon nanotubes (SWCNT) is presented. In this proposed method, the transition energy of any armchair SWCNT can be predicted directly by knowing its one chiral index as both of its chiral indices are same. The predicted results are compared with recent experimental data and found to be accurate over a wide diameter range from 2 to 4.8 nm. The empirical equation proposed here is also compared with that proposed in earlier works. The proposed way may help the research works or applications where information of optical transitions of armchair metallic nanotubes is needed.
Detail study of the Raman-active modes in carbon nanotubes
Physica Status Solidi B-basic Solid State Physics, 2007
The Raman-active A 1 -modes in carbon nanotubes are often used for characterizing nanotube samples. The fully-symmetric radial-breathing mode and the high-energy mode (HEM) have small non-radial and nontangential components, respectively. Neglecting these components results in errors for phonon frequency and electron -phonon coupling calculations. We present a model to estimate these non-radial components. For the HEM we find an anharmonicity that stems from the three-fold coordination of the C atoms.
Resonant Raman study of the structure and electronic properties of single-wall carbon nanotubes
Chemical Physics Letters, 2000
. We investigate the laser-energy dependence of the Raman profile of single-wall carbon nanotube SWNT samples with various distributions of diameters. We show that resonant Raman is an efficient tool for the study of the structure and electronic properties of SWNT. The tube diameter distribution is derived from the comparison between the experimental Ž . frequencies of the radial A breathing mode range RBM and the calculated RBM frequency of SWNT bundles. Metallic 1g or semi-conducting tubes are identified in the light of calculations of allowed optical transitions. The assignments are Ž . confirmed by the observation absence of a Breit-Wigner-Fano-like lineshape for the tangential graphite-like modes of Ž . metallic semiconducting nanotubes. q
Crystals
In this study, the optical refractive constants of the (5, 5) SWBNNT and (5, 5) SWCNT systems were calculated in both parallel and perpendicular directions of the tube axis by using Quantum ESPRESSO and YAMBO code. It also extended the optical behaviors of (5, 5) SWCNT and (5, 5) SWBNNT to both perpendicular and parallel directions instead of the parallel directions reported in the literature. It also looked at the effects of the diameter of the nanotube on the optical properties instead of chiral angles. From our results, the best optical reflection was found for (5, 5) SWBNNT, while the best optical refraction was found with (5, 5) SWCNT. It was observed that the SWCNT demonstrates refraction in both parallel and perpendicular directions, while (5, 5) SWBNNT shows perfect absorption in perpendicular direction. These new features that appeared for both nanotubes in perpendicular directions were due to new optical band gaps, which appear in the perpendicular directions to both nanot...