Diameter dependence of TO phonon frequencies and the Kohn anomaly in armchair single-wall carbon nanotubes

We performed tunable resonance Raman spectroscopy on samples highly enriched in the (5,5), (6,6), (7,7), and (8,8) armchair structures of metallic single-wall carbon nanotubes. We present Raman excitation profiles (REPs) for both the radial breathing mode and G-band phonons of these species. G-band excitation profiles are shown to resolve the expected incoming and outgoing resonances of the scattering process. Notably, the profiles are highly asymmetric, with the higherenergy outgoing resonance weaker than the incoming resonance. These results are comparable to the asymmetric excitation profiles observed previously in semiconducting nanotubes, introduce a new electronic type, and broaden the structural range over which the asymmetry is found to exist. Modeling of the behavior with a third-order quantum model that accounts for the k -dependence in energies and matrix elements, without including excitonic effects, is found to be insufficient for reproducing the observed asymmetry. We introduce an alternative fifth-order model in which the REP asymmetry arises from quantum interference introduced by phonon-mediated state-mixing between the E M 11 and K-momentum excitons. Such state-mixing effectively introduces a nuclear coordinate dependence in the transition dipole moment and thus may be viewed as a non-Condon effect from a molecular perspective. This result unifies a molecular-like picture of nanotube transitions (introduced by their excitonic nature) with a condensed matter approach for describing their behavior.

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“…The TO frequencies are 1573, 1581, 1586, and 1588 cm −1 for the (5,5), (6,6), (7,7), and (8,8) structures, respectively (see also Ref. 31).…”

Section: Resultsmentioning

confidence: 99%

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

et al. 2015

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“…If more than one (n,m) are available, ESI † needs to be taken into account. For example, the G band shape and frequency, 14,32,36,37 IFM features, 33 and simultaneous excitation under multiple laser lines.…”

Section: Procedures For (Nm) Assignmentsmentioning

confidence: 99%

(n,m) Assignments and quantification for single-walled carbon nanotubes on SiO₂/Si substrates by resonant Raman spectroscopy

Zhang

Yang

et al. 2015

Nanoscale

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The single-walled carbon nanotubes (SWNTs) on silicon substrates are a promising candidate for the next generation of electronic and photoelectronic devices, therefore an easy, convenient, and nondestructive method for characterizing such samples is quite important and strongly needed. In this study, we provide in detail such a method to assign (n,m) indices with considerable accuracy through resonant Raman spectra analysis. We developed an equation of ωRBM = 235.9/dt + 5.5 for SWNTs grown by Ni, Co, and Fe catalysts on SiO2/Si substrates in the dt range of 1.2-2.1 nm. This method was further utilized to make (n,m) assignments and quantification for our SWNTs catalyzed by W6Co7, which is highly enriched with (12,6). The less abundant chiralities in the samples were also assigned and the contents were analyzed using a counting-based method. Moreover, these chirality-specified samples allowed us to collect 1330 RBM data for the single chirality (12,6) and the RBM variation was found to be no larger than ±2.5 cm(-1). A step-by-step procedure is also provided as a general guide for (n,m) assignments.

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“…41 However, unlike chiral CNTs, demonstrating the G-band splitting into G + and G − components with longitudinal and circumferential motions of carbon atoms, armchair CNTs exhibit only one narrow G + -band in resonance Raman spectra, presumably due to the A1g(2) mode with circumferential atomic dsplacements. 42,[45][46][47][48][49] In the (5, 5) CNT, such G + feature was detected at 1573 cm −1 , whereas the RBM mode is found at 338 cm −1 (Ref. 42 ).…”

Section: Normal Mode Analysis For C100-d5dmentioning

confidence: 99%

“…42,[45][46][47][48][49] In the (5, 5) CNT, such G + feature was detected at 1573 cm −1 , whereas the RBM mode is found at 338 cm −1 (Ref. 42 ). While the resonance enhancement is extremely useful for CNTs as it enables the measurement of tiny sample amounts, down to a single nanotube, it also imposes a limitation on the information obtained from such spectra as it only attests to enhanced modes.…”

Section: Normal Mode Analysis For C100-d5dmentioning

confidence: 99%

Vibrational anatomy of C₉₀, C₉₆, and C₁₀₀ fullertubes: probing Frankenstein's skeletal structures of fullerene head endcaps and nanotube belt midsection

et al. 2022

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Diameter dependence of TO phonon frequencies and the Kohn anomaly in armchair single-wall carbon nanotubes

Cited by 6 publications

References 46 publications

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

(n,m) Assignments and quantification for single-walled carbon nanotubes on SiO₂/Si substrates by resonant Raman spectroscopy

Vibrational anatomy of C₉₀, C₉₆, and C₁₀₀ fullertubes: probing Frankenstein's skeletal structures of fullerene head endcaps and nanotube belt midsection

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Diameter dependence of TO phonon frequencies and the Kohn anomaly in armchair single-wall carbon nanotubes

Cited by 6 publications

References 46 publications

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

(n,m) Assignments and quantification for single-walled carbon nanotubes on SiO2/Si substrates by resonant Raman spectroscopy

Vibrational anatomy of C90, C96, and C100 fullertubes: probing Frankenstein's skeletal structures of fullerene head endcaps and nanotube belt midsection

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(n,m) Assignments and quantification for single-walled carbon nanotubes on SiO₂/Si substrates by resonant Raman spectroscopy

Vibrational anatomy of C₉₀, C₉₆, and C₁₀₀ fullertubes: probing Frankenstein's skeletal structures of fullerene head endcaps and nanotube belt midsection