Diluted magnetic semiconductor quantum dots: An extreme sensitivity of the hole Zeeman splitting on the aspect ratio of the confining potential

The valence band states confined in infinitely deep quantum dots made of diluted magnetic semiconductors (DMS) are considered theoretically. A complex anisotropic structure of the valence bands in DMSs with cubic symmetry described by the full Luttinger Hamiltonian is taken into account. It is found that the Zeeman splitting is very sensitive to the shape of the confining potential and, in particular, to its orientation relative to the direction of an external magnetic field. This sensitivity has its origin in a mixing of different spin components of a hole wave function which takes place for finite hole wave vectors k. Several consequences of the effect are discussed, including a possibility to control the interdot tunneling by an external magnetic field. It is shown also that the polarizations of optical transitions in a single DMS quantum dot depend on details of geometry of its confining potential as well as on the strength of the magnetic field.