Numerical studies of free exciton and trion wave functions in high magnetic fields

Abstract

Wave functions of excitons and negative and positive trions confined in GaAs quantum wells and subject to high magnetic fields are studied by exact numerical diagonalization in Haldane spherical geometry. 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 multiple electron and hole subbands and Landau levels in the configuration-interaction basis. The main results regard the interaction-induced mixing of electron and hole single-particle levels, normal charge density profiles, in-plane correlation functions, and optical oscillator strengths. These characteristics are calculated for the exciton and different trion states, in terms of their dependence on the quantum-well width, carrier concentration, and magnetic field.