Curvature-induced Symmetry Lowering and Anomalous Dispersion of Phonons in Single-Walled Carbon Nanotubes
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Curvature-induced Symmetry Lowering and Anomalous Dispersion of Phonons in SingleWalled Carbon Nanotubes Jason Reppert1, Ramakrishna Podila1, Nan Li2, Codruta Z. Loebick2, Steven J. Stuart3, Lisa D. Pfefferle2 and Apparao M. Rao1 1
Department of Physics and Astronomy; Center for Optical Material Science and Engineering Technologies, Clemson University, Clemson, South Carolina, USA. 2 Department of Chemical Engineering, Yale University, New Haven, Connecticut, USA 3 Department of Chemistry, Clemson University, Clemson, South Carolina, USA ABSTRACT Here we report rich and new resonant Raman spectral features for several sub-nanometer diameter single wall carbon nanotubes (sub-nm SWNTs) samples grown using chemical vapor deposition technique operating at different temperatures. We find that the high curvature in subnm SWNTs leads to (i) an unusual S-like dispersion of the G-band frequency due to perturbations caused by the strong electron-phonon coupling, and (ii) an activation of diameterselective intermediate frequency modes that are as intense as the radial breathing modes (RBMs). Furthermore, an analytical approach which includes the effects of curvature into the overlap integral and the energy gap between the van Hove singularities is discussed. Lastly, we show that the phonon spectra for sub-nm SWNTs obtained from the molecular dynamic simulations which employs a curvature-dependent force field concur with our experimental observations. INTRODUCTION Resonant Raman scattering of single walled carbon nanotubes (SWNTs) has been studied extensively [1]. When laser excitation energy (Elaser) matches the energy gap (Eii) between a pair of ith van Hove singularities (vHS), one observes a resonance enhancement in the intensity of Raman-active modes such as the radial breathing mode (RBM) and the tangential stretching mode (G-band). Eii is often obtained from the zone-folding scheme using cutting lines to deduce the 1D electronic energy sub-bands for SWNTs [1,2]. Within the framework of the zone-folding scheme, most Raman features of SWNTs whose average diameter is > 1 nm have been well understood [1,2]. Here, we present strong spectroscopic evidence which suggests that curvature-induced effects lead to the activation of resonant intermediate frequency modes (IFMs). Previously, extremely weak IFMs (600-1100 cm-1) have been reported by several groups [3, 4] in SWNTs with average diameter in the range of 1.5±0.3 and 1.0±0.3 nm. For example, Fantini et al. observed a step-like dispersion of the IFMs in semiconducting and metallic SWNTs and attributed its origin to the creation of an optic phonon and annihilation of an acoustic phonon. We find that the intensity of the IFMs can equal that of the RBMs in chemical vapor deposition (CVD) grown sub-nm SWNTs. Interestingly, we also observe S-like dispersion for the G-band frequency which is a result of curvature-induced perturbation of the electron-phonon interaction. We show that by taking into account the chiral dependence of Eii, (obtained from the tightbinding method [4]) and
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