Radial breathing mode of single-walled carbon nanotubes: Optical transition energies and chiral-index assignment

TL;DR

This paper systematically assigns chiral indices to carbon nanotubes using resonant Raman scattering, providing a comprehensive, parameter-free method to determine optical transition energies, analyze tube properties, and relate vibrational modes to diameter.

Contribution

It introduces a unique, empirical-parameter-free approach for chiral-index assignment and optical transition energy determination in carbon nanotubes using resonant Raman spectroscopy.

Findings

Chiral indices assigned for over 50 nanotubes.

Empirical fits for transition energies and breathing modes.

Insights into electron-phonon coupling from Raman intensities.

Abstract

We present a comprehensive study of the chiral-index assignment of carbon nanotubes in aqueous suspensions by resonant Raman scattering of the radial breathing mode. We determine the energies of the first optical transition in metallic tubes and of the second optical transition in semiconducting tubes for more than 50 chiral indices. The assignment is unique and does not depend on empirical parameters. The systematics of the so-called branches in the Kataura plot are discussed; many properties of the tubes are similar for members of the same branch. We show how the radial breathing modes observed in a single Raman spectrum can be easily assigned based on these systematics. In addition, empirical fits provide the energies and radial breathing modes for all metallic and semiconducting nanotubes with diameters between 0.6 and 1.5 nm. We discuss the relation between the frequency of the radial breathing mode and tube diameter. Finally, from the Raman intensities we obtain information on the electron-phonon coupling.