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The recently observed resistance oscillations of a two-dimensional (2D) electron system subject to a weak lateral 2D superlattice potential and a perpendicular magnetic field are investigated theoretically. Generalizing previous work on 1D superlattices, we develop a magnetotransport theory based on a quantum-mechanical picture taking consistently into account the effect of the lateral superlattice on the energy spectrum and the effect of randomly distributed impurities on collision broadening and transport scattering rate. The superlattice lifts the degeneracy of the Landau levels and leads to Landau bands with an oscillatory width and a complicated internal subband structure, visualized by the famous self-similar ``Hofstadter butterfly.'' The interplay between this peculiar energy spectrum and collision broadening effects is shown to provide the key for the understanding of all the characteristic features of the magnetotransport oscillations reported in recent experimental work.
Pfannkuche et al. (Sun,) studied this question.