The trion as an exciton interacting with a carrier

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 excitons and electrons. 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.