Inverse flux quantum periodicity in the amplitudes of commensurability oscillations in two-dimensional lateral surface superlattices

We report strong, amplitude modulated, commensurability oscillations in the magnetoresistance of short period, square, two-dimensional, lateral surface superlattices with symmetric potentials. The amplitude of the oscillations is strongly enhanced when one magnetic-flux quantum (h/e) passes through an integral number of cells of the superlattice. The temperature dependence of the strong oscillations agrees with the theory for commensurability oscillations in one-dimensional superlattices, but the smaller oscillations between these are more rapidly attenuated by increasing temperature. Although the structure we observe has the same flux periodicity as expected for the Landau-level substructure known as the Hofstadter butterfly, such substructure will not be resolved at the temperatures of measurement (1-10 K). We compare our data instead to a recent theoretical model which treats exactly this case, and find significant points of agreement.