Positively charged magnetoexcitons in a semiconductor quantum well

A variational calculation of the lower singlet and triplet states of positively charged excitons (trions), confined to a single quantum well and in the presence of a perpendicular magnetic field, is presented. All the three particles of the exciton complex are treated within the effective-mass approximation. We study the dependence of the energy levels and of the binding energy on the well width and on the magnetic-field strength. Our results are compared with the available experimental data, and show a good qualitative and quantitative agreement. A singlet-triplet crossing is found which for a $200-\AA$-wide GaAs is predicted to occur for $B=15\mathrm{}\hspace{0.5em}\mathrm{T}.$