Effect of the confining potential on the magneto-optical spectrum of a quantum dot

The energy levels of electrons confined to a circular quantum well with hard walls are calculated in the presence of a perpendicular magnetic field. The results are compared with the case of soft-wall confinement (parabolic potential). There are important differences in the transition energies of the magneto-optical spectrum: (i) in contrast to the parabolic case where only two transition energies are found, in the hard-wall case there are many transitions possible which have different energies. Only a small number of them however have sufficient oscillator strength to be observable; (ii) with increasing magnetic field the energies approach the two-dimensional results much faster than for the soft-wall case. In quantum dots with many electrons we calculate the Fermi energy as a function of the magnetic field.