Effective models for excitons in carbon nanotubes

TL;DR

This paper investigates the low energy exciton spectrum in carbon nanotubes using a simplified one-dimensional model that becomes accurate as the nanotube radius decreases, providing exact solutions.

Contribution

It introduces a one-dimensional effective Hamiltonian for excitons in carbon nanotubes and demonstrates its exact solvability in the small radius limit.

Findings

Effective 1D Hamiltonian accurately describes low energy spectrum

Exact solutions obtained for the simplified model

Model applicable to small radius nanotubes

Abstract

We analyse the low lying spectrum of a model of excitons in carbon nanotubes. Consider two particles with an attractive Coulomb self-interaction, placed on an infinitely long cylinder. If the cylinder radius becomes small, the low lying spectrum is well described by a one-dimensional effective Hamiltonian which is exactly solvable.