Electronic and optical properties of a superlattice in a parabolic potential

The electronic and optical properties of a superimposed parabolic and superlattice potential are calculated within the local-density approximation for a range of superlattice periods d. For small d, the properties are similar to those of a parabolic quantum well containing electrons with effective masses corresponding to the underlying superlattice. The ``effective-mass approximation'' is valid in this regime. For larger d, the spacing of the ideal-parabolic-well energy levels becomes comparable to the superlattice miniband width, and the effective-mass approximation breaks down.