Fermi energy dependence of theG-band resonance Raman spectra of single-wall carbon nanotubes

Abstract

The Fermi energy dependence of the G-band resonance Raman spectra of single-wall carbon nanotubes ͑SWNTs͒ is calculated, including the Kohn anomaly effect for metallic tubes. The gate voltage dependence of the G-band Raman spectra for SWNTs shows chirality-dependent G + / G − spectra, reflecting their dependence on the eigenvector direction of the optical ͑LO and TO͒ phonon modes and the nanotube chirality. The G-band Raman spectra of single-wall carbon nanotubes ͑SWNTs͒ arise from the first-order, one-phonon, and intravalley G-band Raman-scattering processes, 1,2 which have been widely utilized for characterizing SWNTs and graphene. The G-band spectra of a SWNT consist of a higher-frequency peak ͑G + ͒ near 1580ϳ 1590 cm −1 and a lower-frequency peak ͑G − ͒ in the range 1550ϳ 1570 cm −1 . For semiconducting tubes ͑S-SWNT͒, the G + and G − peaks can be assigned to longitudinal-optical ͑LO͒ and transverseoptical ͑TO͒ phonon modes, respectively, while the G + and G − peaks of metallic tubes ͑M-SWNTs͒ are assigned to TO and LO phonon modes, respectively, because of the Kohn anomaly ͑KA͒ effect for phonons at the ⌫ point. [3][4][5][6][7][8] For the KA effect, the self-energy correction to the LO and TO phonon modes by the virtual excitation of an electron-hole pair causes a softening and a hardening of the LO and TO phonon frequencies, respectively. [7][8][9] Recently Nguyen et al. 7 and Farhat et al. 8 observed the Fermi energy ͑E F ͒ dependence of the phonon-softening effect of SWNTs by using an electrochemical gate, and their results clearly show that the LO phonon mode softens as a function of E F . Thus the E F -dependent Raman spectra measurement is important for SWNT field effect transistor operation. However, the observed G-band Raman spectra of an individual SWNT show an anomalous behavior depending on the chirality ͑n , m͒ of a SWNT, 10 caused in part by the dependence of the relative intensity of the Raman G + to G − -band features ͑I G + / I G −͒ on the chirality and diameter. 11 For S-SWNTs, the G + peak is dominant at the zigzag chiral angle ͑ =0°͒, while both the G + and G − peaks appear at other chiral angles ͑0°Ͻ Ͻ 30°͒. It has been known that the k-dependent electron-phonon ͑el-ph͒ interaction gives rise to the chirality dependence of both the G-band ͑Refs. 9 and 12͒ and radial breathing mode ͑RBM͒ ͑Ref. 12͒ Raman intensities. Thus the G-band spectral analysis is still not well understood, even though the G band has been studied for many years. In this Rapid Communication, resonance Raman spectra of SWNTs as a function of E F are calculated in order to understand and interpret the chirality and E F -dependent G-band spectra. We show here that the k-dependent el-ph interaction affects both the I G + / I G − relative Raman intensity and their spectral widths.The self-energy corrections to the G-band phonon frequencies due to the KA affect not only the LO mode but also the TO mode, and both the LO and TO phonon frequencies depend on the chiral angle . The G-band Raman intensity I is calculated as a f...

Fundamental optical processes in armchair carbon nanotubes

“…27,87,91,[137][138][139][140] The absence of the LO phonon feature for armchair tubes is consistent with some theoretical studies (e.g., References 27 and 145), i.e., it is not Raman active in armchair SWCNTs (although this still does not eliminate the presence of a Kohn anomalyonly its Raman activity), while it is inconsistent with more recent theories. 90,146 In conclusion, using resonant Raman measurements of macroscopic ensembles of ν = 0 enriched SWCNT samples, we have demonstrated that the appearance of a broad G − peak is due to the presence of non-armchair "metallic" tubes. More importantly, the G-band of the truly gapless armchair tubes consists of a single, narrow G + component and serves as a further diagnostic for their identification.…”

“…Returning to the G-band mode, experimental studies by Wu et al, 87 Telg et al, 88 Fouquet et al, 89 Michel et al, 77 and Park et al 90 attempted to correlate G-band line shape with specific (n, m), especially in light of a new explanation for the origin of the broad G − feature in metallic nanotubes as arising from the Kohn anomaly 91 (discussed later in Section VII). Raman measurements were made on individual, (n, m)-identified tubes.…”

Defect characterization in graphene and carbon nanotubes using Raman spectroscopy

“…Recently, Sasaki et al (2010) showed that the phonon softening effect of the G can characterize the graphene edge structure. In the presence of free electrons, the G band and the radial breathing mode (RBM) phonon in single-walled carbon nanotubes (SWNTs) becomes soft as a function of the Fermi energy position, through an effect which is known as the Kohn anomaly (Sasaki et al 2008a,b;Farhat et al 2009;Kalbac et al 2009;Park et al 2009). These phenomena occur preferentially at graphene edges, since the electron wave function forms a standing wave by mixing elastically scattered waves at the edge where the momentum along the edge (perpendicular to the edge) is conserved (changes its sign).…”

On the charge transfer between single-walled carbon nanotubes and graphene

“…The various changes in the Raman spectra due to doping include differences in the intensity ratios between the G -and G + peaks, broadening/stiffening of the peaks, and frequency shifts. 14,16,26 Moreover, the asprepared SWNT bundles contain a mixture of semiconducting and metallic SWNTs, …”

“…8,9 Raman spectroscopy is a powerful tool that has been used extensively to study charge transfer in SWNTs and in graphene. [10][11][12][13][14][15][16][17][18][19] Adsorption of electron donating and accepting molecules cause shifts in the Raman peak frequencies, which are proportional to the amount of carriers injected. 10 While charge transfer in SWNTs and graphene due to molecular dopants has been studied separately, there is very little work on the electronic interaction between SWNTs and graphene.…”