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

Abstract

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 ${\ensuremath{\rho}}_{\mathrm{xx}}$ if the mobility is homogeneous, whereas a mobility lattice in the $x$ direction in the absence of electric and magnetic modulations affects only ${\ensuremath{\rho}}_{\mathrm{yy}}.$ 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.