LANDAU-LEVELS IN THE PRESENCE OF DILUTE SHORT-RANGE SCATTERERS

We consider an electron in a magnetic field interacting with low densi ty of short-range scatterers in two dimensions and develop a perturbat ion theory in the scatterer range. When the number of flux quanta per scatterer phi is much greater than 1, each Landau band splits into nar row and close (but clearly distinct) subbands, accommodating one or tw o states per scatterer each. In a model in which there is no electron- electron interaction, the subbands can yield large oscillations in the density of states at the Fermi level, and consequently in the heat ca pacity, magnetic susceptibility, and, perhaps, transport properties, w hen phi changes by 1 or 2.