Effect of quantized electronic states on the dispersive Raman features in individual single-wall carbon nanotubes

This work reports how resonance Raman experiments are used to study details of the electronic structure of individual single-wall carbon nanotubes (SWNTs) by measuring the phonon spectra and how the quantized electronic structure affects the dispersive Raman features of SWNTs. We focus our analysis on the dispersive D and (formula presented) bands observed in the Raman spectra of isolated semiconducting nanotubes. By using a laser excitation energy of 2.41 eV, we show that both the D-band and (formula presented)-band frequencies are dependent on the wave vector (formula presented) where the electrons are confined in the one-dimensional subband i of the electronic structure of SWNTs. By making use of the (formula presented) assignment for each tube, we theoretically correlate the observed frequency dependences for the D- and (formula presented)-band modes with the electronic structure predicted for each (formula presented) pair and we determine the dependence of (formula presented) and (formula presented) on the diameter and chirality for individual electronic transitions (formula presented) for nanotube bundles. We use the D- and (formula presented)-band dependence on electron wave vector (formula presented) to predict the dominant phonon wave vector q selected by the quantum-confined electronic state (formula presented) and to explain the anomalous dispersion observed for (formula presented) and (formula presented) in SWNT bundles as a function of laser excitation energy, yielding excellent agreement between experiment and theory.