Understanding double-resonant Raman scattering in chiral carbon nanotubes: Diameter and energy dependence of theDmode

Abstract

We present a theoretical model to describe the double-resonant scattering process in arbitrary carbon nanotubes. We use this approach to investigate the defect-induced D mode in CNTs and unravel the dependence of the D-mode frequency on the CNT diameter and on the energy of the resonant optical transition. Our approach is based on the symmetry of the hexagonal lattice and geometric considerations, hence the method is independent of the exact model that is chosen to describe the electronic band structure or the phonon dispersion. We finally clarify the diameter dependence of this Raman mode that was controversely discussed in the past and demonstrate that, depending on the experimental conditions, in general two different dependencies can be measured. We also prove that carbon nanotubes with arbitrary chiral index can exhibit a D mode in their Raman spectrum, in contrast to previous symmetry-based arguments. Furthermore, we give a direct quantification of the curvature-induced phonon frequency corrections of the D-mode in carbon nanotubes with respect to graphite.

Effects of Chirality and Defect Density on the Intermediate Frequency Raman Modes of Individually Suspended Single-Walled Carbon Nanotubes

“…This result strongly supports the assignment of the IFM origin in prior studies. , In particular, one of those studies concluded that the IFM originates from an acoustic-like phonon mode with a K-momentum-like D-mode . 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 is caused at defects. , However, the synchronous change shown in Figure a 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 …”

“…In this case, the coefficient for the inverse diameter is 227 cm –1 ·nm, which is in good agreement with prior studies. , 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, , the range over which the D-mode varied was less than 12 cm –1 wide; therefore, 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 an acoustic-like phonon mode. , …”

“…The black and red spectra are those acquired before and after photoinduced bleaching, respectively. In Figure b, Raman peaks originating from the well-known RBM, , D-mode, − and G-modes are clearly evident at 231, 1284, and 1590 cm –1 , 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 .…”

Diameter dependence of the defect-induced Raman modes in functionalized carbon nanotubes

“…A simulation of the (2)D-mode diameter dependence in nanotube ensembles and a description of the curvature induced jump between the optical transitions can be found in Ref. [40]. Ref.…”

Two-phonon Raman bands of single-walled carbon nanotubes: A case study

“…Recently, a step towards the understanding of the defectinduced D mode in nanotubes vs diameter and energy has been made using the hexagonal symmetry of graphene and geometrical considerations. 12,13 This approach allows assigning the two-phonon bands to pairs of definite phonons. However, the two-phonon band shape can only be predicted, taking into account the couplings and the electronic linewidth, and carrying out full integration over the Brillouin zone.…”