Magnetotransport in two-dimensional lateral superlattices with smooth disorder: Quasiclassical theory of commensurability oscillations

Commensurability oscillations in the magnetoresistivity of a two-dimensional electron gas in a two-dimensional lateral superlattice are studied in the framework of quasiclassical transport theory. It is assumed that the impurity scattering is of small-angle nature characteristic for currently fabricated high-mobility heterostructures. The shape of the modulation-induced magnetoresistivity $\Delta {\rho }_{\mathrm{xx}}$ depends on the value of the parameter $\gamma \equiv {\eta }^{2}ql/4,$ where η and q are the strength and the wave vector of the modulation, and l is the transport mean free path. For $\gamma \ll 1,$ the oscillations are described, in the regime of not too strong magnetic fields B, by perturbation theory in $\eta$ as applied earlier to the case of one-dimensional modulation. At stronger fields, where $\Delta {\rho }_{\mathrm{xx}}$ becomes much larger than the Drude resistivity, the transport takes the advection-diffusion form (Rayleigh-Bénard convection cell) with a large Péclet number, implying a much slower $\left(\propto B^{3/4}\right)$ increase of the oscillation amplitude with B. If $\gamma \gg 1,$ the transport at low B is dominated by the modulation-induced chaos (rather than by disorder). The magnetoresistivity drops exponentially and the commensurability oscillations start to develop at the magnetic fields where the motion takes the form of the adiabatic drift. Conditions of applicability, the role of the type of disorder, and the feasibility of experimental observation are discussed.