Magnetotransport in lateral superlattices with small-angle impurity scattering: Low-field magnetoresistance

An analytical study of the low-field magnetoresistance of a two-dimensional electron gas subject to a weak periodic modulation is presented. We assume small-angle impurity scattering characteristic for high-mobility semiconductor heterostructures. It is shown that the condition for existence of the strong low-field magnetoresistance induced by so-called channeled orbits is $\eta^{3/2}ql\gg 1$, where $\eta$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport mean free path. Under this condition, the magnetoresistance scales as $\eta^{7/2}$.