Commensurability oscillations due to pinned and drifting orbits in a two-dimensional lateral surface superlattice

We have simulated conduction in a two-dimensional electron gas subject to a weak two-dimensional periodic potential, $V_x \cos(2\pi x/a) + V_y \cos(2\pi y/a)$. The usual commensurability oscillations in $\rho_{xx}(B)$ are seen with $V_x$ alone. An increase of $V_y$ suppresses these oscillations, rather than introducing the additional oscillations in $\rho_{yy}(B)$ expected from previous perturbation theories. We show that this behavior arises from drift of the guiding center of cyclotron motion along contours of an effective potential. Periodic modulation in the magnetic field can be treated in the same way.