Excitons in narrow-gap carbon nanotubes

TL;DR

This paper calculates exciton binding energies in narrow-gap carbon nanotubes considering relativistic effects, showing no transition to excitonic insulator phase and confirming their potential for THz applications.

Contribution

It provides exact analytical solutions for the relativistic two-body problem in nanotubes and clarifies excitonic behavior in quasi-metallic nanotubes.

Findings

Binding energy scales with band gap

No excitonic insulator transition in quasi-metallic nanotubes

Feasibility of THz applications in these nanotubes

Abstract

We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for the quasi-relativistic dispersion of electrons and holes. Exact analytical solutions of the quantum relativistic two-body problem are obtain for several limiting cases. We show that the binding energy scales with the band gap, and conclude on the basis of the data available for semiconductor nanotubes that there is no transition to an excitonic insulator in quasi-metallic nanotubes and that their THz applications are feasible.