The trion: two electrons plus one hole versus one electron plus one exciton

We first show that, for problems dealing with trions, it is totally hopeless to use the standard many-body description in terms of electrons and holes and its associated Feynman diagrams. We then show how, by using the description of a trion as an electron interacting with an exciton, we can obtain the trion absorption through far simpler diagrams, written with electrons and \emph{excitons}. These diagrams are quite novel because, for excitons being not exact bosons, we cannot use standard procedures designed to deal with interacting true fermions or true bosons. A new many-body formalism is necessary to establish the validity of these electron-exciton diagrams and to derive their specific rules. It relies on the commutation technique'' we recently developed to treat interacting close-to-bosons. This technique generates a scattering associated to direct Coulomb processes between electrons and excitons and a dimensionless scattering’’ associated to electron exchange inside the electron-exciton pairs – this scattering'' being the original part of our many-body theory. It turns out that, although exchange is crucial to differentiate singlet from triplet trions, this scattering’’ enters the absorption explicitly when the photocreated electron and the initial electron have the same spin – \emph{i}. \emph{e}., when triplet trions are the only ones created – \emph{but not} when the two spins are different, although triplet trions are also created in this case. The physical reason for this rather surprising result will be given.