RESONANT SCATTERING IN A STRONG MAGNETIC-FIELD - EXACT DENSITY-OF-STATES

We study the structure of 2D electronic states in a strong magnetic fi eld in the presence of a large number of resonant scatterers. For an e lectron in the lowest Landau level, we derive the exact density of sta tes by mapping the problem onto a zero-dimensional field-theoretical m odel. We demonstrate that the interplay between resonant and nonresona nt scattering leads to a nonanalytic energy dependence of the electron Green function. In particular, for strong resonant scattering the den sity of states develops a gap in a finite energy interval. The shape o f the Landau level is shown to be very sensitive to the distribution o f resonant scatterers.