Trion Binding Energies and Wave Functions in Doped Quantum Wells

Abstract

The energy spectra of negative trions (X − = 2e + h) in one-sided doped GaAs quantum wells are calculated. The maps of the trion binding energy ∆ as a function of well width w, electron concentration n, and the magnetic field B are obtained. The dependence of the trion ground state ("bright singlet" versus "dark triplet") on those parameters is established.

Exact-diagonalization studies of trion energy spectra in high magnetic fields

“…29 The singlet-triplet crossover occurs in rather high magnetic fields, 30 and it is fairly sensitive to the parameters. [31][32][33] ͑iii͒ Additional, less strongly bound trions occur at intermediate fields, including the "bright triplet" X tb − with S = 1 and M =0. 31 All three trions were later confirmed by several independent calculations 32,34 and experiments.…”

“…[31][32][33] ͑iii͒ Additional, less strongly bound trions occur at intermediate fields, including the "bright triplet" X tb − with S = 1 and M =0. 31 All three trions were later confirmed by several independent calculations 32,34 and experiments. 27,28,35,36 Trions were also identified beyond the "dilute regime," in PL spectra of the fractional quantum Hall states.…”

“…Compared to the earlier studies, [30][31][32][33][34] asymmetry of the quantum well caused by one-sided doping is fully taken into account by self-consistent calculation of the subband wave functions and by inclusion of up to three subbands along with several Landau levels in the Hilbert space. Especially for the the singlet trion and for doped wells, the results are significantly different from the previous, less accurate models.…”

“…In this paper we address this problem by extensive realistic numerical calculations of the binding energies of (negative and positive) trions in doped GaAs quantum wells in high magnetic fields. Compared to the earlier studies, 30,31,32,33,34 asymmetry of the quantum well caused by one-sided doping is fully taken into account by self-consistent calculation of the subband wave functions and by inclusion of up to three subbands along with several Landau levels in the Hilbert space. Especially for the the singlet trion and for doped wells, the results are significantly different from the previous, less accurate models.…”

Fractional Quasiexcitons in Photoluminescence of Quantum Hall Liquids

“…In order to correctly estimate the overall impact of the electric field on the structure, first we calculated the trion binding energies for a w = 20 nm AlGaAs/GaAs well [5]. The energies were obtained by exact diagonalization of the 2e + h system in the presence of magnetic field B perpendicular to the well.…”