Smooth-disorder effects in ballistic microstructures

We analyze the effect of weak residual disorder in microstructures defined on high-mobility heterojunctions, where the classical electron motion is ballistic. We parameterize the disorder by its correlation length ξ and the elastic mean free path l, which can be estimated from microscopic models. For the experimentally relevant case in which ξ is not negligible with respect to the size of the microstructure, we present a perturbative semiclassical approach demonstrating that the reduction due to disorder of a two-point Green-function observable, like the average magnetic susceptibility, is intrinsically different from the bulk (power law depending on l and ξ instead of an exponential damping governed uniquely by l). The very weak damping that we obtain supports the use of clean (no disorder) models for the ballistic regime. Our analytical findings are confirmed by exact numerical calculations.