Magnetism induced by electric impurities: A one-body problem with half the physics of the fractional quantum Hall effect

We study spectra for a 2D electron in the lowest Landau level with randomly distributed, repulsively correlated electric impurities. The lowest energy band reflects an effective magnetic field downshifted by an integer multiple of the impurity density. The downshift is precisely half that for the corresponding electron density in the composite-fermion picture of the fractional quantum Hall regime.