Selection Rules for One- and Two-Photon Absorption by Excitons in Carbon Nanotubes

TL;DR

This paper derives symmetry-based selection rules for one- and two-photon optical transitions involving excitons in carbon nanotubes, aiding the interpretation of experimental spectra.

Contribution

It provides a group-theoretic approach to determine excitonic optical transition rules in carbon nanotubes, addressing limitations of previous symmetry analyses.

Findings

Derived selection rules for excitonic transitions

Clarified the role of symmetry in two-photon experiments

Enhanced understanding of optical spectra interpretation

Abstract

Recent optical absorption/emission experiments showed that the lower energy optical transitions in carbon nanotubes are excitonic in nature, as predicted by theory. These experiments were based on the symmetry aspects of free electron-hole states and bound excitonic states. The present work shows, however, that group theory does not predict the selection rules needed to explain the two photon experiments. We obtain the symmetries and selection rules for the optical transitions of excitons in single-wall carbon nanotubes within the approach of the group of the wavevector, thus providing important information for the interpretation of theoretical and experimental optical spectra of these materials.