The trion as an exciton interacting with a carrier

TL;DR

This paper develops a theoretical framework to describe the X$^-$ trion as an exciton-electron complex, overcoming the challenge of exciton-electron interaction potential by using a commutation technique that accounts for the composite nature of excitons.

Contribution

It introduces a novel commutation technique to exactly handle exciton-electron interactions and derives the trion creation operator and ladder diagram for future many-body studies.

Findings

Derived the X$^-$ trion creation operator in terms of exciton and electron

Obtained the exciton-electron ladder diagram

Provided foundational tools for many-body trion research

Abstract

The X$^-$ trion is essentially an electron bound to an exciton. However, due to the composite nature of the exciton, there is no way to write an exciton-electron interaction potential. We can overcome this difficulty by using a commutation technique similar to the one we introduced for excitons interacting with excitons, which allows to take exactly into account the close-to-boson character of the excitons. From it, we can obtain the X$^-$ trion creation operator in terms of exciton and electron. We can also derive the X$^-$ trion ladder diagram between an exciton and an electron. These are the basic tools for future works on many-body effects involving trions.