Magnetoresistance of a two-dimensional electron gas with spatially periodic lateral modulations: Exact consequences of Boltzmann's equation

On the basis of Boltzmann's equation, including anisotropic scattering in the collision operator, we investigate the effect of one-dimensional superlattices on two-dimensional electron systems. In addition to superlattices defined by static electric and magnetic fields, we consider mobility superlattices describing a spatially modulated density of scattering centers. We prove that magnetic and electric superlattices in the x direction affect only the resistivity component rho(xx) if the mobility is homogeneous, whereas a mobility lattice in the x direction in the absence of electric and magnetic modulations affects only rho(yy). Solving Boltzmann's equation numerically, we calculate the positive magnetoresistance in weak magnetic fields and the Weiss oscillations in stronger fields within a unified approach.