Charged-Exciton Complexes in Quantum Dots

It is known experimentally that stablecharged-exciton complexes can existin low-dimensional semiconductor nanostructures. Much less is known aboutthe properties of such charged-exciton complexes since three-body problemsare very difficult to be solved, even numerically. Here we introduce thecorrelated hyperspherical harmonics as basis functions to solve thehyperangular equation for negatively and positively charged excitons(trions) in a harmonic quantum dot. By using this method, we have calculatedthe energy spectra of the low-lying states of a charged exciton as afunction of the radius of quantum dot. Based on symmetry analysis, the levelcrossover as the dot radius increases can be fully explained as the resultsof symmetry constraint.