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

Shiue-Yuan Shiau , Monique Combescot (1) , Yia-Chung Chang

1 INSP - Institut des Nanosciences de Paris

We solve the Schrodinger equation for two electrons plus one hole by writing it in the electron-exciton basis. One 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 Schrodinger 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. This restricted electron-hole basis already gives results in reasonable agreement with those obtained through the best variational methods using free carriers. The main advantage of the electron-hole basis is to allow us to reach the bound and unbound trion excited states as easily as the ground state. Through the trion wave functions, we also derive the optical absorption spectrum in the presence of hot carriers for two-dimensional 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.

Domaines: Matière Condensée [cond-mat]

Shiue-Yuan Shiau, Monique Combescot, Yia-Chung Chang. Trion ground state, excited states, and absorption spectrum using electron-exciton basis. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2012, 86 (11), ⟨10.1103/PhysRevB.86.115210⟩. ⟨hal-01229186⟩