Quasiclassical magnetotransport in a random array of antidots

We study theoretically the magnetoresistance ${\rho }_{\mathrm{xx}}\mathrm{}\left(B\right)\mathrm{}$ of a two-dimensional electron gas scattered by a random ensemble of impenetrable discs in the presence of a long-range correlated random potential. We believe that this model describes a high-mobility semiconductor heterostructure with a random array of antidots. We show that the interplay of scattering by the two types of disorder generates new behavior of ${\rho }_{\mathrm{xx}}\mathrm{}\left(B\right)\mathrm{}$ which is absent for only one kind of disorder. We demonstrate that even a weak long-range disorder becomes important with increasing B. In particular, although ${\rho }_{\mathrm{xx}}\mathrm{}\left(B\right)\mathrm{}$ vanishes in the limit of large B when only one type of disorder is present, we show that it keeps growing with increasing B in the antidot array in the presence of smooth disorder. The reversal of the behavior of ${\rho }_{\mathrm{xx}}\mathrm{}\left(B\right)\mathrm{}$ is due to a mutual destruction of the quasiclassical localization induced by a strong magnetic field: specifically, the adiabatic localization in the long-range Gaussian disorder is washed out by the scattering on hard discs, whereas the adiabatic drift and related percolation of cyclotron orbits destroys the localization in the dilute system of hard discs. For intermediate magnetic fields in a dilute antidot array, we show the existence of a strong negative magnetoresistance, which leads to a nonmonotonic dependence of ${\rho }_{\mathrm{xx}}\mathrm{}\left(B\right).$