Effect of fermionic components on trion-electron scattering

TL;DR

This paper investigates how the composite nature of trions affects their scattering with electrons, finding that at low momentum transfer, trions behave like elementary fermions, but deviations appear at higher transfers.

Contribution

It introduces a detailed calculation of trion-electron scattering using composite-exciton many-body theory, highlighting the conditions under which trions mimic elementary fermions.

Findings

Trion behaves as an elementary fermion at low momentum transfer.

The direct scattering channel is described by Coulomb potential with a form factor.

The exchange channel is affected by the trion's composite nature at all momentum transfers.

Abstract

To test the validity of replacing a composite fermion by an elementary fermion, we here calculate the transition rate from a state made of one free electron and one trion to a similar electron-trion pair, through the time evolution of such a pair induced by Coulomb interaction between elementary fermions. To do it in a convenient way, we describe the trion as one electron interacting with one exciton, and we use the tools we have developed in the new composite-exciton many-body theory. The trion-electron scattering contains a direct channel in which ``in'' and ``out'' trions are made with the same fermions, and an exchange channel in which the ``in'' free electron becomes one of the ``out'' trion components. As expected, momenta are conserved in these two channels. The direct scattering is found to read as the bare Coulomb potential between elementary particles multiplied by a form factor which depends on the ``in'' and ``out'' trion relative motion indices $\eta$ and $\eta'$, this factor reducing to $\delta_{\eta\eta'}$ in the zero momentum transfer limit: In this direct channel, the trion at large distance reacts as an elementary particle, its composite nature showing up for large momentum transfer. On the contrary, the fact that the trion is not elementary does affect the exchange channel for all momentum transfers. We thus conclude that a 3-component fermion behaves as an elementary fermion for direct processes in the small momentum transfer limit only.