Effects of Chirality and Defect-Density on the Intermediate Frequency

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C: Physical Processes in Nanomaterials and Nanostructures

Effects of Chirality and Defect-Density on the Intermediate Frequency Raman Modes of Individually-Suspended Single-Walled Carbon Nanotubes Takumi Inaba, Yuichirou Tanaka, Satoru Konabe, and Yoshikazu Homma J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01017 • Publication Date (Web): 09 Apr 2018 Downloaded from http://pubs.acs.org on April 9, 2018

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The Journal of Physical Chemistry

Effects of Chirality and Defect Density on the Intermediate Frequency Raman Modes of Individually-Suspended Single-Walled Carbon Nanotubes Takumi Inaba⁎1, Yuichirou Tanaka1, Satoru Konabe2, and Yoshikazu Homma1,2 1

Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku Tokyo 162-

8601, Japan 2

Research Institute of Science and Technology, Tokyo University of Science, 6-3-1 Niijuku,

Katsushika Tokyo 125-8585, Japan

ACS Paragon Plus Environment

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ABSTRACT

The intermediate frequency Raman mode (IFM) in the range from 300 to 500 cm-1 of individually-suspended single-walled carbon nanotubes (SWCNTs) was assessed to determine the effects of chirality and defect density. Photoluminescence spectroscopy was employed to confirm isolation and chirality of the SWCNTs. The IFM frequency exhibited a positive correlation with the nanotube diameter as expected from prior studies. Raman and photoluminescence measurements were conducted simultaneously with the introduction of defects into an SWCNT. The photoluminescence intensity showed the largest reduction rate among all optical peaks analyzed. Furthermore, the intensity of the IFM increased with defect creation, and showed almost the same behavior as the D-mode intensity. These results can be explained by the increase of the exciton-phonon coupling in the defective SWCNTs. Unambiguous chirality assignment using photoluminescence spectroscopy, along with the employment of individually-suspended samples that minimizes environmental effects, enabled us to investigate the intrinsic nature of the IFM.


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1.

INTRODUCTION

Single-walled carbon nanotubes (SWCNTs) are nanomaterials that can provide a model for the examination of quantum effects. The low mass density of these structures, in conjunction with the robust bonding of carbon atoms as well as the well-defined crystalline structure of SWCNTs, are difficult to obtain using top-down synthetic techniques. These properties make SWCNTs one of the most useful materials for assessing our understanding of the quantum of lattice vibration: the phonon. Phonons in SWCNTs have been investigated extensively using Raman spectroscopy.1,2 Raman spectroscopy can drive a quantum transducer because Raman processes involve several of the major quanta in solid-state physics, including phonons, photons and excitons.1 Studies of phonons also contribute to our knowledge of exciton dynamics because excitons are always exposed to phonon fields.3 As an example, the self-trapping of excitons is one of the primary consequences of lattice relaxation. However, the observation of self-trapping requires a homogeneous sample, and thus may possibly be achieved via the Raman spectroscopic analysis of individually suspended SWCNTs. The Raman spectroscopy of SWCNTs can involve the analysis of graphene-based Raman modes as well as modes exclusive to SWCNTs including the radial breathing mode (RBM) and the G–-mode, which can be observed as a result of the tubular structure of SWCNTs.2 The RBM is of special interest because it is a nanotube-specific feature for which the phonon frequency varies with the diameter of the SWCNT. The RBM has therefore been used to determine diameter distributions in nanotube samples. Establishing nanotube diameters is crucial to the practical application of SWCNTs because many physical properties depend on the diameter. In


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addition to the RBM and the G–-mode, SWCNTs generate an additional and less intense Raman peak that is often referred to as the intermediate frequency mode (IFM) in the frequency range from 300 to 1000 cm-1. These peaks have been investigated using ensemble samples.4-9 In addition, reports regarding minor Raman peaks generated by individual SWCNTs on a substrate have been published.10, 11 These prior papers emphasized the importance of employing isolated SWCNTs to demonstrate the chirality effects. In fact, SWCNTs having atomically-thin tubular structures have been shown to interact significantly with their environment.12-16 Therefore, the intrinsic properties of these structures can best be determined by examining individuallysuspended SWCNTs rather than ensemble samples. Although Raman peaks in the intermediate frequency range have already been analyzed in the prior works described above, none of these studies employed chirality-assigned, individually-suspended SWCNTs. We emphasize that contact with a substrate can also result in an environmental effect in the case of low-frequency Raman peaks, as reported in studies investigating the RBM.16 In prior research, the IFM was attributed to K-momentum phonons and, as discussed herein, our results support this conclusion.7, 11 In this respect, the ability to probe low-frequency phonons (i.e., acoustic phonons) having non-zero momentum with photons is important because SWCNTs do not generate Raman peaks that are simultaneously acoustic and have non-zero momentum. Although applications that treat phonons having different energy levels or momentum values separately remain challenging, the IFM could provide possible future applications of phonons in SWCNTs. In the present work, the Raman spectra of individually-suspended SWCNTs, whose chiralities were assigned based on photoluminescence spectroscopy, were obtained to assess the


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IFM in the frequency range from 300 to 500 cm-1. The use of photoluminescence spectroscopy

Figure 1 (a) Scanning electron microscopy image of an individually-suspended SWCNT. (b) Photoluminescence excitation map obtained from an individually-suspended (11,3) nanotube. (c, d) Photoluminescence images of the SWCNT shown in (b) and that of another (10,5) nanotube. (color online) for the chirality assignment provided a well-defined data set for IFM analysis.

2.

Experimental Section 2.1

Sample Preparation

Individual SWCNTs were suspended between a pair of micropillars to acquire sufficiently intense Raman and photoluminescence spectra.17 These SWCNTs were synthesized via alcoholcatalytic chemical vapor deposition.18 The same substrate configuration used in our previous study was employed.19 This substrate is characterized by a thin silicon film that covers the surface, with the exception of the tops of the micropillars, such that the SWCNTs grow only from these locations. This technique is based on the synthesis of SWCNTs using metal nanoparticles on silicon dioxide, since the synthesis will not take place on pure silicon due to the silicidation of the metal nanoparticles.20 Here, we employed cobalt as the metal nanoparticles. A typical


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scanning electron microscopy image of an individually-suspended SWCNT is shown in Figure 1a. A single SWCNT suspended between two micropillars can be seen in the Figure 1a. The undesired growth of excess SWCNTs that could interfere with the subsequent optical measurements was successfully suppressed. It should also be noted that none of the samples employed in the following optical measurement were assessed by scanning electron microscopy because the electron beam irradiation would likely damage the as-grown SWCNTs.21 Photoluminescence excitation maps were acquired to assign the chirality of each individually-suspended SWCNT, using a tunable Ti:sapphire laser system for E22 excitation of the samples. This instrument was capable of generating laser light with wavelengths from 700 to 840 nm, and the wavelength of the excitation laser was varied in 10 nm steps to acquire the photoluminescence excitation maps. The laser spot size on the substrate was approximately 1.6 µm in diameter, and the laser power was as low as possible (~10 µW) so that photoinduced bleaching did not take place prior to the subsequent Raman measurements.19,

22, 23

Photoluminescence ranging from 1000 to 1500 nm was collected using an InGaAs multiarray photodetector coupled to a spectrometer. The wavelength resolution of the optical apparatus was less than 0.6 nm, and the resulting photoluminescence spectra were calibrated using a mercury lamp. SWCNTs that produced a single intense peak within the detectable range were carefully selected and the chirality of each specimen was assigned, referencing reported E11 and E22 values in air.12 Semiconducting SWCNTs with diameters of approximately 0.87 to 1.25 nm, roughly corresponding to (11,0) to (11,7) nanotubes, could potentially be analyzed using this optical apparatus. The possibility that our samples contained bundled SWCNTs whose E22 and E11 energies were outside the detection range, or were bundled with metallic SWCNTs was excluded by employing photoluminescence spectroscopy. In the case of bundling with semiconducting


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SWCNTs, the photoluminescence excitation map would be expected to exhibit multiple spots or redshifting of the emission wavelength, based on prior reports.14 Furthermore, bundling with metallic SWCNTs would significantly reduce the luminescence from the semiconducting SWCNTs because of exciton energy transfer to metallic SWCNTs and subsequent non-radiative decay. A typical photoluminescence excitation map is shown in Figure 1b as an example. The maximum intensity in this map occurs at an excitation wavelength of 778 nm and emission wavelength of 1178 nm, corresponding to the E22 and E11 of an (11,3) nanotube, respectively.12 In this case, these wavelengths were estimated via curve fitting to the photoluminescence excitation map. Photoluminescence images of chirality-assigned SWCNTs were obtained with E22 excitation of the samples. The laser spot was defocused so as to simultaneously illuminate the entire suspended area. A near-infrared image of the illuminated region was captured using a 2D InGaAs diode array defector coupled with an acousto-optic tunable filter, which can continuously tune a wavelength passing through the filter, adjusted to the emission wavelength of the sample. Examples of photoluminescence images obtained from the (11,3) nanotube in Figure 1b and another (10,5) nanotube are shown in Figure 1c and 1d, respectively. The image of the (11,3) nanotube shows a photoactive region at the center of the image, corresponding to the center of the two micropillars, that is smaller than the spacing of the two micropillars. This might have resulted from bundling with other SWCNTs at both edges of the (11,3) nanotube or from insufficient suspension in the central regions of the tapered micropillars. Although the SWCNTs grew only at the top of each micropillar, they descended from that point and thus could occasionally attach to another micropillar. Raman analyses were subsequently conducted only


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within the photoactive region using focused laser, so that environmental and bundling effects were excluded. The sample preparation process employed in this study ensured that individual SWCNTs free from other nanotubes and substrate were obtained. Because our Raman instrumentation was optimized for laser excitation at 785 nm,24 five chiralities with corresponding E22 were selected for analysis: (12,1), (11,3), (10,5), (9,7), and (9,8). 2.2 Simultaneous Raman and Photoluminescence Assessments

The Raman and photoluminescence spectra of the individual SWCNTs were simultaneously acquired, using the same 785 nm excitation laser focused on each SWCNT. The Raman scattering and photoluminescence emissions from each specimen were separated using a dichroic mirror.24 The photoluminescence was collected with the optical setup described above, while the Raman scattering was collected via a charge coupled device detector coupled to the spectrometer. The frequency resolution of the Raman instrumentation was less than 1.6 cm-1 and this instrument was calibrated using a mercury argon lamp. The intensity of the excitation laser was set to 100 µW so that photoinduced bleaching of the photoluminescence from the SWCNTs in air could be observed.19,

22, 23

The power density of the excitation laser was 3 kW/cm2.

Compared to a prior study,22 the laser power used in this work was relatively low, so as to allow the observation of photoinduced bleaching. However, the minimum laser power required for bleaching largely depends on atmospheric parameters, such as the concentration of ions in the ambient air.19 3.

Results and Discussion


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3.1

Peak Analysis


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Figure 2 (a) Photoluminescence and (b) Raman scattering spectra generated by the (11,3) nanotube shown in Figure 1b. Spectra obtained from the as-grown sample are shown in black, while those acquired from the bleached sample are in red (color online). Table 1 Figure 2.

Fitting parameters for the Raman and photoluminescence spectra shown in

Figure 2 presents the Raman scattering and photoluminescence spectra of the (11,3) nanotube whose photoluminescence excitation map is shown in Figure 1b. The lower energy light exhibited in Figure 2a is photoluminescence spectra, while higher energy light which is close to the energy of the excitation laser is due to Stokes scattering from the same SWCNT. Although the horizontal axis scales for these spectra are in the units of energy to allow for ready comparison, the corresponding photoluminescence wavelengths and Raman shifts are also provided above each figure. The black and red spectra are those acquired before and after photoinduced bleaching, respectively. In Figure 2b, Raman peaks originating from the wellknown RBM,13, 25 D-mode26-28 and G-modes29 are clearly evident at 231, 1284 and 1590 cm-1,


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respectively. In addition, two minor Raman peaks are also observed, with the less intense peak at 855 cm-1 and the other at 425 cm-1. The 855 cm-1 peak is assigned to the out-of-plane transverse optical (oTO) phonon mode,1,5, 10 while the 425 cm-1 peak is attributed to the IFM.1, 4-7, 9-11 The following discussion addresses the relatively strong D-mode intensity generated by the as-grown SWCNTs. The assignment of the oTO peak is based on its Raman shift, which is very close to that reported in earlier studies.1,

5, 10

The intensity of this peak

evidently decreased with increases in the defect density. Typically, decreases in intensity with rising defect density are observed for zero-momentum phonon modes such as the RBM and the G-mode because of a reduction in optical absorbance.30 The effect of the defect density on the intensity of the Raman peak observed in the present work is also in agreement with the oTO assignment. 3.2 Figure 3 (a) Intensities of the Raman and photoluminescence peaks in Figure 2b as functions of time. (b) Relationships between the Raman and photoluminescence intensities shown in (a). (color online)

Effects of Defect Density on Raman

Scattering and Photoluminescence

As shown in Figure 2a, bleaching caused a weakening of the photoluminescence intensity, a redshift of the photoluminescence peak position, and

broadening of the peak. Furthermore, a very weak emission was generated in the range of 200 to


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300 nm below the E11 peak, as shown in the inset to Figure 2a. These results are in agreement with photoinduced bleaching reported from earlier studies.19, 22, 23 It should be noted that the photoinduced bleaching in this study was not a temporary reduction in optical absorption but the permanent degradation of the SWCNTs. Conversely, the only major change in the Raman spectra after bleaching was in the peak intensity. These spectral changes are summarized in Table 1. The peak positions as well as the full width at half maximum (FWHM) value for each peak were determined by fitting with a Lorenz curve. It is not possible to directly compare the Raman scattering and photoluminescence intensities because different optical setups were employed to obtain these spectra and, of course, the origins of those spectra are different. However, there are still some similarities between these spectra. These spectra, for instance, are enhanced by the same resonance. Furthermore, the reduction of photoluminescence intensity due to the enhancement of exciton-phonon coupling, which also determines the Raman intensity, was predicted.31 Therefore, a comparison of the relative intensity changes in the Raman and photoluminescence spectra can compensate for the effect of optical absorption and demonstrate the influence of exciton-phonon coupling on the peak intensities. The intensities of each Raman and photoluminescence peak in Figures 2a and 2b are plotted as functions of the duration of intense laser illumination in Figure 3a. Here, the intensities have been normalized to those of the unbleached states, corresponding to the black lines in Figure 2. The photoluminescence immediately decreased and eventually plateaued at a value approximately one fifth the original level. Although an evaluation of the reason for this plateau is outside the scope of this paper, this effect may have resulted from a redshift of the E22 while the wavelength of the excitation laser was fixed during the observation period. The photoluminescence intensity showed the largest reduction rate among all peaks, which indicates


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that the photoluminescence was more sensitive to defect creation, or possibly affected to a greater extent by changes in exciton-phonon coupling compared to the Raman scattering. The Raman scattering intensities are plotted against the photoluminescence intensities in Figure 3b. The intensities of zero-momentum phonons, in particular pure optical modes such as the oTO mode and G-mode, are seen to decrease linearly as the photoluminescence intensity increases.


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Figure 4 Typical Raman spectra of (a) (12,1), (b) (11,3), (c) (10,5), (d) (9,7), and (e) (9,8) nanotubes after the bleaching of photoluminescence. (color online) Synchronous changes in the IFM and D-mode intensities can be clearly seen in Figure 3a. This result strongly supports the assignment of the IFM origin in prior studies.7, 11 In particular, one of those studies concluded that the IFM originates from an acoustic-like phonon mode with a K-momentum like D-mode.11 In that prior analysis, the momentum of the IFM was determined from the well-known facts that the optical absorption of SWCNTs is enhanced by a van-Hove singularity, and that elastic scattering caused at defects.27, 28 However, the synchronous change shown in Figure 3a provides additional experimental support for the assignment of the IFM momentum. The effects of defect creation on the IFM were already assessed in the prior study but the synchronous changes in the IFM and D-mode intensities were not reported.7 In fact, other assignments for the Raman peak in the IFM range have been proposed in prior studies,4,

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but these are unlikely to explain the IFM observed in the present research


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because of the effects of the defect introduction on the IFM intensity (Figure 3). It should also be noted that it is possible for RBM overtone modes to appear in the IFM range, but we did not observe such peaks.8 3.3

Chirality Dependence of the IFM

Typical Raman spectra for the five chiralities employed in this study are provided in Figure 4. The IFM can be clearly observed in the range of 300 to 500 cm-1 in each case, and the IFM frequency evidently depends on the chirality. The SWCNT diameter (dt) dependence of each Raman frequency is presented in Figure 5. The effects of dt on the IFM frequency (ωIFM) are summarized in Figure 5d and demonstrate a positive correlation as given by ୍߱୊୑ = ‫ܣ‬/݀୲ + ‫ܤ‬,

(1)

where A = -312 cm-1·nm, and B =732 cm-1. The diameters in Figure 5 were calculated from the assigned chirality of each sample, with the diameters ascending in the order of (12,1), (11,3), (10,5), (9,7), and (9,8). The fitting curve represented by Equation 1 is also plotted as the green line in Figure 5d. Although, in the present work, we employed an inversely proportional relationship between ωIFM and dt as in prior studies,6, 9 the curvature of the plot of our current data is evidently greater than that predicted by Equation 1. In contrast, the RBM frequency was well fitted by using an inversely proportional function as shown by the green line in Figure 5e. In this case, the coefficient for the inverse diameter is 227 cm-1·nm, which is in good agreement with prior studies.13, 15 The other peaks do not show a systematic effect of diameter on the Raman frequency. Although the D-mode frequency was expected to vary systematically with diameter based on previous reports,26, 27 the


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range over which the D-mode varied was less than 12 cm-1 wide, so the variation of this mode was not as significant as that of the IFM. This difference is clearly because the D-mode is associated with the optical phonon mode of graphene, while the IFM originates from acousticlike phonon mode.9, 11 The photoluminescence images of these SWCNTs demonstrate that the length of the photoactive region was not relevant to our results. That is, the photoactive regions of some SWCNTs plotted in Figure 5 were shorter than the suspended length (see, as an example, Figure 1c), while others were photoactive over the entire suspended length (as in Figure 1d). However, the IFM frequencies for each chirality converged similar to the other major Raman peaks. Therefore, the results obtained in this work appear to reflect the intrinsic characteristics of these SWCNTs rather than the recently reported quantum-dot-like behavior of oxygen-doped SWCNTs.32 The diameter dependence of the IFM was Figure 5 Effects of the SWCNT diameter on the phonon frequencies for the (a) G-mode, (b) D-mode, (c) oTO mode, (d) IFM, and (e) RBM. The data for five chiralities are plotted; (12,1), (11,3), (10,5), (9,7) and (9,8) in ascending order of diameter. (color online)

nicely explained in the prior study.11 In the case of E22 excitation of the (n-m)mod 3 = 2 family, the phonon frequency of the IFM increases with the


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diameter. This is because the momentum transfer of intervalley elastic scattering at E22

ሬሬሬሬԦ of the graphene Brillouin zone with increases in the diameter, and because of approaches the ሬΓK the upward band bending of the acoustic-like phonon mode with increasing momentum. As a result, the phonon frequency increases along with the diameter of SWCNTs. For this reason, the data for the (9,8) nanotube should be treated separately from the other specimens because, within our experimental samples, only the (9,8) nanotube belongs to the (n-m)mod 3 = 1 family, while all the others are in the (n-m)mod 3 = 2 family. Removing the results for the (9,8) nanotube changes the fitting parameters A and B to -342 cm-1·nm and 762 cm-1, respectively. The fitting curve obtained using these parameters is shown in orange in Figure 5d. In this case, the data point for the (9,8) nanotubes does not lie on the fitting curve, but there is a better fit of the remaining data.. 3.4

Intensities of K-momentum Phonons

The intensity of the IFM is typically not significant and, for this reason, has not been the focus of most prior Raman studies of SWCNTs. In the present work, we successfully observed intense IFM peaks generated by as-grown SWCNTs exhibiting relatively high photoluminescence and RBM intensities. Therefore, we believe that the intensity of the IFM peaks is not simply correlated with the defect density. Interestingly, the D-mode peaks, which are typically observed in the case of defective sp2 hybridized carbon-based materials, exhibited intensities comparable to those of the G-mode peaks. Although the G/D ratio was only as high as 2.4 for the as-grown SWCNTs, we observed an intense photoluminescence emission with a FWHM of 15.2 nm, as shown in Figure 2. This value was 30% higher than, but still consistent with, the reported FWHM values for pristine SWCNTs at room temperature.33 Given that both the IFM and the D-


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mode originate from similar mechanisms, the intense IFM peaks evidently resulted from the same circumstances that produced relatively low G/D ratio for the as-grown SWCNTs. Figure 4 demonstrates an intriguing result; the IFM intensities of these 5 samples are different from each other. The RBM intensities, compared to the G-mode intensities, also changes with chiralities. In prior studies, an effect of chirality on the RBM intensity was both theoretically predicted and experimentally verified using chirality-sorted SWCNTs in solution.34, 35

Spectra for each chirality in Figure 4 show a decrease in IRBM/IG with increases in the chiral

angle which increase from (12,1) to (9,7). Furthermore, the (9,8) nanotube, which belongs to the (n-m)mod 3 = 1 family, had the smallest IRBM/IG ratio. The results obtained with our individually suspended SWCNTs are in good agreement with data reported in the prior studies.34, 35 In the case of the IFM, the intensity ratio IIFM/IG is slightly confusing because defects introduction probably affects the ratio. The ratio IIFM/ID would provide better index to interpret the IFM intensity. The ratios IIFM/ID for each chiralities in Figure 4 decrease from top to bottom, which is similar to IRBM/IG. Although we do not have enough theoretical background to discuss the chirality dependence of the IFM intensities this time, the discussion may enable us to quantitatively analyze K-momentum phonons.

4. Conclusion

This work determined the effects of variations in chirality and defect density on the IFM peaks generated by individually-suspended SWCNTs. The IFM frequency showed a positive correlation with the diameter of the SWCNT, while optical defects induced in the SWCNTs increased the IFM intensity. These results were made possible by the unambiguous assignment


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of chirality using photoluminescence spectroscopy and provides a well-defined data-set that should assist in the future interpretation of nanotube phonons. Although the D-mode is often observed in the Raman spectra of SWCNTs, the observation of an intense IFM as shown in Figure 2 herein is rare. Additional studies regarding the IFM intensity will further improve our understanding of the physics of K-momentum phonons.

AUTHOR INFORMATION Corresponding Author *Takumi Inaba: Phone: +81-3-3260-4271 (Ext. 2478), mail: [email protected] Author Contributions The manuscript was written through contributions of all authors, with all authors contributing equally. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors gratefully acknowledge helpful discussions with Prof. Shohei Chiashi. This work was partly supported by a MEXT Grant-in-Aid for Scientific Research on Innovative Areas as part of the “Science of Hybrid Quantum Systems” program (no. 15H05869). ABBREVIATIONS IFM, intermediate frequency mode; SWCNTs, single-walled carbon nanotubes; RBM, radial breathing mode; PL, photoluminescence; oTO, out-of-plane transverse optical phonon; FWHM, full width half maximum REFERENCES


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TOC Graphics


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Figure 2 (a) Photoluminescence and (b) Raman scattering spectra generated by the (11,3) nanotube shown in Figure 1b. Spectra obtained from the as-grown sample are shown in black, while those acquired from the bleached sample are in red (color online). 52x17mm (300 x 300 DPI)



Figure 4 Typical Raman spectra of (a) (12,1), (b) (11,3), (c) (10,5), (d) (9,7), and (e) (9,8) nanotubes after the bleaching of photoluminescence. (color online) 112x62mm (300 x 300 DPI)


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Figure 1 (a) Scanning electron microscopy image of an individually-suspended SWCNT. (b) Photoluminescence excitation map obtained from an individually-suspended (11,3) nanotube. (c, d) Photoluminescence images of the SWCNT shown in (b) and that of another (10,5) nanotube.¬ (color online) 47x14mm (300 x 300 DPI)



Figure 3 (a) Intensities of the Raman and photoluminescence peaks in Figure 2b as functions of time. (b) Relationships between the Raman and photoluminescence intensities shown in (a). (color online) 150x281mm (300 x 300 DPI)


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Figure 5 Effects of the SWCNT diameter on the phonon frequencies for the (a) G-mode, (b) D-mode, (c) oTO mode, (d) IFM, and (e) RBM. The data for five chiralities are plotted; (12,1), (11,3), (10,5), (9,7) and (9,8) in ascending order of diameter. (color online) 170x361mm (300 x 300 DPI)



Table 1 Fitting parameters for the Raman and photoluminescence spectra shown in Figure 2. 412x178mm (72 x 72 DPI)


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Effects of Chirality and Defect-Density on the Intermediate Frequency

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