Electronic structure of antidot superlattices in commensurate magnetic fields

We present a treatment of an interacting two-dimensional electron system mo ving in a bidirectionally periodic potential and a perpendicular magnetic f ield. Employing symmetry considerations based on the ray-group of magnetotr anslation operators and a canonical coordinate transformation, we derive an efficient scheme for calculating energy levels and states in arbitrary 'ra tional' magnetic fields. Applying this scheme to a superlattice of strongly localized antidots we reveal the possibility to split off an isolated and sufficiently broad cluster of subbands from a Landau band. The implications of the existence of such subbands to the experimental detection of the sub band structure and in particular quantum Hall effect measurements in period ic superlattices are discussed.