Envelope of commensurability magnetoresistance oscillation in unidirectional lateral superlattices

The envelope of the commensurability magnetoresistance oscillation (Weiss oscillation) has been studied for lateral superlattices prepared from two-dimensional electron gas (2DEG) wafers with varying mobility mu. and spacer-layer thickness d(s). When the 2DEG has a high enough mu and a large enough d(s), the envelope is well described by the formula given by Peeters and Vasilopoulos in a first-order perturbation theory [Phys. Rev. B 46, 4667 (1992).]. For smaller mu or d(s), the oscillation diminishes faster than the formula at lower B. The damping can be accounted for by an additional factor of the form [pi/(mu B-W)]/sinh[pi/(mu B-W)]. The parameter mu (W) is found to be proportional to the mean free path L of the 2DEG, and the coefficient of proportionality increases with d(s). The magnitude of mu (W), as well as its dependence on d(s) and the electron areal density n(s), is close to that of mu (Q), the mobility corresponding to the total scattering time.