Confined excitons in a semiconductor quantum dot in a magnetic field

Magnetic field effects in a semiconductor quantum dot (QD) are studied theoretically. Magneto-optical effects originating from electron-hole pairs in the lowest and the higher excited states are discussed. The theory is based on the effective-mass approximation with the following effects taken into account: the direct Coulomb interaction, the electron-hole exchange interaction, and the valence-band mixing effect. A calculation is performed with a numerical diagonalization method. The transition from the quantum confined Zeeman effect for a weak magnetic field to the quantum confined Paschen-Back effect for a strong magnetic field is discussed. Special attention is paid to a magnetic field dependence of the optical transition probabilities which is found to be a pronounced effect for a CdSe QD, where the confinement by a potential and a magnetic field have competing contributions.