Binding Energy and Lifetime of Excitons in Metallic Nanotubes

TL;DR

This paper develops a theory for excitons in metallic nanotubes, showing their binding energy and lifetime are influenced by screening effects and gapless subbands, aligning with experimental data.

Contribution

The paper introduces a novel theoretical framework for excitons in metallic nanotubes, accounting for their large radius, binding energy, and finite lifetime due to gapless subband interactions.

Findings

Exciton binding energy is approximately 0.08v/R.

Excitons have a finite lifetime due to scattering into gapless subbands.

Theoretical results agree with experimental measurements.

Abstract

The difficulty of describing excitons in semiconducting SWNTs analytically lies with the fact that excitons can neither be considered strictly 1D nor 2D objects. However, the situation changes in the case of metallic nanotubes where, by virtue of screening from gapless metallic subbands, the radius of the exciton becomes much larger than the radius of the nanotube $R_\text{ex}\gg R$. Taking advantage of this, we develop the theory of excitons in metallic nanotubes, determining that their binding energy is about $0.08v/R$, in agreement with the existing experimental data. Additionally, because of the presence of the gapless subbands, there are processes where bound excitons are scattered into unbound electron-hole pairs belonging to the gapless subbands. Such processes lead to a finite exciton lifetime and the broadening of its spectral function. We calculate the corresponding decay rate of the excitons.