We consider an electron in a magnetic field interacting with low density of short-range scatterers in two dimensions and develop a perturbation theory in the scatterer range. When the number of flux quanta per scatterer φ is ≫1, each Landau band splits into narrow and close (but clearly distinct) subbands, accommodating one or two 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 capacity, magnetic susceptibility, and, perhaps, transport properties, when φ changes by 1 or 2.

• Received 14 June 1995

DOI:https://doi.org/10.1103/PhysRevB.52.14098