Scaling of exciton binding energy with external dielectric function in carbon nanotubes

TL;DR

This paper presents a model linking exciton binding energy to external dielectric screening in carbon nanotubes, showing how environmental changes affect electronic interactions and optical properties.

Contribution

The study introduces a scaling relationship that quantifies how external dielectric environments influence exciton binding energies in carbon nanotubes.

Findings

Screening reduces particle interaction energies by up to 50%.

Electron-electron interactions are larger than electron-hole interactions in the unscreened state.

The model explains the observed 'ratio problem' in optical transitions.

Abstract

We develop a scaling relationship between the exciton binding energy and the external dielectric function in carbon nanotubes. We show that the electron-electron and electron-hole interaction energies are strongly affected by screening yet largely counteract each other, resulting in much smaller changes in the optical transition energy. The model indicates that the relevant particle interaction energies are reduced by as much as 50 percent upon screening by water and that the unscreened electron-electron interaction energy is larger than the unscreened electron-hole interaction energy, in agreement with explanations of the "ratio problem." We apply the model to measurements of the changes in the optical transistion energies in single, suspended carbon nanotubes as the external dielectric environment is altered.