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 $\xi$ and the elastic mean free path $l$, which can be estimated from microscopic models. For the experimentally relevant case in which $\xi$ 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 $\xi$ 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.