WEAK-LOCALIZATION IN LATERAL SURFACE SUPERLATTICES

We present a theoretical investigation of weak localization in a two-dimensional electron gas with unidirectional modulation by a cosine potential. By lowering the electron density the system gradually turns from a weakly modulated electron gas into an array of almost isolated quantum wires of finite width. A dimensional transition occurs in such a system due to the decreasing widths of the resulting minibands; The reduction of the dimensionality of interference effects takes place when coherent tunneling of electrons between adjacent wires is suppressed. In this case we find a pronounced enhancement of the weak-localization correction to the conductivity. Its functional dependence on the phase coherence length develops from a logarithmic behavior to a linear one, typical for one dimension. Close to the transition to strong localization the correction due to interference effects becomes additive in the resistance. The localization length deduced from the calculations exhibits a continuous change from an exponential to a linear dependence on the scattering length at the dimensional transition. Numerical results are discussed for GaAs structures with different electron densities.