Trion ground state, excited states and absorption spectrum using electron-exciton basis

TL;DR

This paper introduces a novel electron-exciton basis to accurately compute trion states and absorption spectra in 2D quantum wells, improving the understanding of bound and unbound trion excitations.

Contribution

It develops and applies an electron-exciton basis with a composite boson formalism to analyze trion states and optical absorption, offering advantages over traditional methods.

Findings

Reasonable agreement with variational methods for ground state energies.

Effective identification of bound and unbound trion excited states.

Clear characterization of optical absorption peaks related to trion and electron-exciton scattering.

Abstract

We solve the Schr\"{o}dinger equation for two electrons plus one hole by writing it in the electron-exciton basis. The main advantage of this basis is to eliminate the exciton contribution from the trion energy in a natural way. The interacting electron-exciton system is treated using the recently developed composite boson many-body formalism which allows an exact handling of electron exchange. We numerically solve the resulting electron-exciton Schr\"{o}dinger equation, with the exciton levels restricted to the lowest $1s, 2s$ and $3s$ states, and we derive the trion ground state energy as a function of the electron-to-hole mass ratio. While our results are in reasonable agreement with those obtained through the best variational methods using free carrier basis, this electron-exciton basis is mostly suitable to easily reach the bound and unbound trion excited states. Through their wave functions, we here calculate the optical absorption spectrum in the presence of hot carriers for 2D quantum wells. We find large peaks located at the exciton levels, which are attributed to electron-exciton (unbound) scattering states, and small peaks identified with trion bound states.