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

TL;DR

This study uses advanced numerical methods to accurately calculate the energy spectra of trions in doped GaAs quantum wells under high magnetic fields, considering realistic well properties and multiple physical effects.

Contribution

It introduces a comprehensive exact diagonalization approach that incorporates well asymmetry, finite width, and multiple Landau levels for precise trion energy calculations.

Findings

Calculated trion binding energies as functions of magnetic field and well parameters.

Analyzed the effects of well asymmetry and finite width on trion energies.

Provided estimates of finite-size errors and convergence behavior.

Abstract

Binding energies of negative and positive trions in doped GaAs quantum wells in high magnetic fields are studied by exact numerical diagonalization in spherical geometry. Compared to earlier calculations, finite width of the quantum well and its asymmetry caused by one-sided doping are both fully taken into account by using self-consistent subband wave functions in the integration of Coulomb matrix elements, and by inclusion of higher subbands along with several Landau levels in the Hilbert space. Detailed analysis of the accuracy and convergence of the exact diagonalization scheme is presented, including dependence on Landau level and subband mixing, sensitivity to the (not well known) single-particle spectrum in the valence band, and the estimate of finite-size errors. The main results are the exciton dispersion and trion binding energy spectrum calculated as a function of the magnetic field, quantum well width, electron concentration, and the presence of an ionized impurity. As a complementary approach, a combination of the exact diagonalization in the quantum well plane and the variational calculation in the normal direction is used as well.