Three-particle correlation from a Many-Body Perspective: Trions in a Carbon Nanotube

TL;DR

This paper presents a new ab-initio many-body theoretical approach to study three-particle trion states in carbon nanotubes, revealing their energy shifts and detailed physical properties, aligning with experimental observations.

Contribution

It extends existing $GW$ and Bethe-Salpeter methods to accurately model trions in nanostructures, providing new insights into their spectra and wave functions.

Findings

Trions are red-shifted by ~130 meV compared to excitons.

The method confirms experimental energy shifts in carbon nanotubes.

Detailed analysis of trion spectra and wave functions is provided.

Abstract

Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are red-shifted by $\sim 130$ meV compared to the excitons, confirming experimental findings for similar tubes. Moreover, our method provides detailed insights in the physical nature of trion states. In the prototypical carbon nanotube we find a variety of different excitations, discuss the spectra, energy compositions, and correlated wave functions.