ABSTRACT
This chapter examines the first excited level of a two-dimensional polar semiconductor quantum dot with parabolic confinement in the presence of an external magnetic field applied normal to the plane of the dot. The first excited level of a two-dimensional parabolic quantum dot potential is two-field degenerate. In a bulk polar material, one needs to have a hydrogenic impurity to observe Zeeman splitting, whereas in a quantum dot one can have Zeeman splitting even in the absence of any hydrogenic impurity because of the existence of the parabolic confinement potential. The first excited level of a two-dimensional parabolic quantum dot potential is two-field degenerate. This two-field degeneracy will be lifted in the presence of a magnetic field. For small values of the magnetic field, the behavior of the polaron self-energy as a function of the confinement length is qualitatively similar to what one would observe in the absence of the magnetic field.
