Effects of screening on the Hofstadter butterfly

We study, within the Hartree approximation, the effects of the electron-electron interaction on the energy spectrum of a two-dimensional electron gas in a perpendicular homogeneous magnetic field and a lateral superlattice potential with square symmetry. Due to the strong screening effects, the bandwidth of the Landau bands oscillates strongly with their filling. For short enough periods and strong enough modulation of the superlattice potential, the miniband structure of the Landau bands can be resolved in the thermodynamic density of states.