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

Abstract

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 G8 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 G8-band frequencies are dependent on the wave vector kii where the electrons are confined in the one-dimensional subbandi of the electronic structure of SWNTs. By making use of the (n,m) assignment for each tube, we theoretically correlate the observed frequency dependences for the D- and G8-band modes with the electronic structure predicted for each ( n,m) pair and we determine the dependence of v D and v G8 on the diameter and chirality for individual electronic transitions Eii for nanotube bundles. We use the D- and G8-band dependence on electron wave vector k ii to predict the dominant phonon wave vector q selected by the quantum-confined electronic statekii and to explain the anomalous dispersion observed for v D and v G8 in SWNT bundles as a function of laser excitation energy, yielding excellent agreement between experiment and theory.