Chirality-dependent G-band Raman intensity of carbon nanotubes

R. Saito,G. Dresselhaus,J. H. Hafner,M. Hunter,C. M. Lieber,M. S. Dresselhaus,T. McClure,A. Jorio

doi:10.1103/physrevb.64.085312

Abstract

The chirality-dependent G-band Raman intensity of single wall carbon nanotubes is calculated using a nonresonant theory for the Raman tensor. We obtain six or three intense Raman modes, respectively, for chiral or achiral nanotubes, whose relative intensities depend on the chiral angle of the nanotube. The longitudinal and transverse optical phonon modes in two-dimensional graphite become, respectively, transverse and longitudinal optical phonon modes in a one-dimensional nanotube. Confocal micro-Raman measurements of individual single wall carbon nanotubes show chirality-dependent spectra of the G-band intensity, as predicted by this theory.

Highlights

Resonant Raman spectroscopy has provided a powerful tool for observing diameter-selective phonon modes in single wall carbon nanotubesSWNTs4,5 and in multiwall carbon nanotubesMWNTs6,7 containing different diameters within the sample
The RBM frequency is inversely proportional to the diameter of the SWNT dt because the RBM frequency depends on the number of carbon atoms around the circumferential direction
The other values of n correspond to phonon modes at kϭ0 in the 1D BZ, which are not Raman active, and do not contribute to the first-order Raman spectra

Summary

Introduction

Carbon nanotubes have aroused world-wide interest in the quantum properties of electrons and phonons and in a variety of nanotube applications. Resonant Raman spectroscopy has provided a powerful tool for observing diameter-selective phonon modes in single wall carbon nanotubesSWNTs4,5 and in multiwall carbon nanotubesMWNTs6,7 containing different diameters within the sample. The Raman-active G band consists of two A, two E1, and two E2 phonon modes for chiral nanotubes, and of one A1g , one E1g , and one E2g mode for achiralarmchair or zigzagnanotubes, as predicted by group theory and phonon frequency calculations.. We expect six or three G-band spectral features for chiral and achiral nanotubes, respectively, if all Raman-active modes have sufficient intensity to be observed and can be spectrally resolved. Since the phonon frequencies of both the RBM and the G band depend mainly on dt , previous theoretical works were performed mainly for achiral carbon nanotubes without considering any chirality dependence. The present work shows that this difference in behavior is related to the chirality dependence of the G-band features discussed in this paper

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Results

Discussion

Conclusion