MAGNETORESISTANCE OSCILLATIONS IN A 2-DIMENSIONAL ELECTRON-GAS SUBJECT TO A WEAK LATERAL SUPERLATTICE POTENTIAL

Recent progress of our understanding of the novel magnetoresistance oscillations observed on two-dimensional electron gases with a weak lateral superlattice is reviewed. The discussion is based on a quantum mechanical single-electron picture, taking consistently into account the effect of the superlattice on the energy spectrum and the effect of randomly distributed impurities on collision broadening and transport scattering rate. This, first, allows to explain the original results of Weiss et al. on high-mobility AlxGa1-xAs-GaAs heterostructures with an unidirectional modulation potential produced by holographic illumination: the large-amplitude oscillations of rho-xx, measured when the current flows in the direction of the modulation, are attributed to a bandconductivity sigma-yy, and the weaker antiphase oscillations of rho-yy (proportional sigma-xx, current parallel to equipotentials) are shown to result from quantum oscillations of the scattering rate. Second, for the case of a modulation with square symmetry, where the energy spectrum is given by Hofstadter's famous "butterfly", it explains the dramatic suppression of the bandconductivity, which has recently been observed on high-mobility samples, as a consequence of the splitting of Landau levels into the Hofstadter-type subbands.