Excitons in Cd 1− x Mn x Te quantum wells with a parabolic confining potential

Excitons in Cd 1− x Mn x Te and Cd 1− x −y Mg y Mn y Te parabolic and half-parabolic quantum wells are investigated by magnetooptical methods. The diagonal and nondiagonal (in the harmonic oscillator quantum numbers) transitions are observed. Apart from 1s excitons we observed also 2s and 3s states in the presence of a magnetic field. The results are discussed in terms of a simple variational calculation of the exciton energy. It is shown that a parabolic confining potential very effectively reduces the dimensionality of the excitons leading to large values of their binding energy even in relatively wide quantum wells. The truly parabolic shape of the confining potential in the investigated structures is proved by an analysis of spin splitting of the exciton states.