Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes

TL;DR

This paper investigates how the diameter and chirality of semiconducting carbon nanotubes influence exciton properties such as binding energies, sizes, and splittings, providing analytical models to guide experimental understanding.

Contribution

It introduces a symmetry-based variational method using effective-mass and envelope-function approximations to analytically describe exciton properties in carbon nanotubes based on diameter and chirality.

Findings

Binding energies scale as 1/d with diameter.

Exciton sizes scale linearly with diameter.

Bright-dark exciton splittings scale as 1/d^2.

Abstract

We calculate the diameter and chirality dependences of the binding energies, sizes, and bright-dark splittings of excitons in semiconducting single-wall carbon nanotubes (SWNTs). Using results and insights from {\it ab initio} calculations, we employ a symmetry-based, variational method based on the effective-mass and envelope-function approximations using tight-binding wavefunctions. Binding energies and spatial extents show a leading dependence with diameter as $1/d$ and $d$, respectively, with chirality corrections providing a spread of roughly 20% with a strong family behavior. Bright-dark exciton splittings show a $1/d^2$ leading dependence. We provide analytical expressions for the binding energies, sizes, and splittings that should be useful to guide future experiments.