Weak localization and electron-electron interactions in a two-dimensional grid lateral surface superlattice

Low-field magnetoresistance measurements were performed on a two-dimensional grid lateral surface superlattice (LSSL) fabricated on a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterojunction. From a one-parameter fit to the two-dimensional weak-localization theory we have obtained the effective inelastic scattering length at different temperatures. By subtracting the weak-localization term, we have also investigated the electron-electron interactions in this system. Both localization and interaction effects saturate at low temperatures when the inelastic scattering length and thermal diffusion length are longer than the period of the LSSL. At higher temperatures, when the thermal diffusion length becomes comparable to the period of the LSSL, the electron-electron interaction term causes the conductivity to decrease logarithmically with temperature. These results can be explained in terms of coherent backscattering of the electrons in a fraction of the electron puddles formed below the superlattice gate. Disorder ensures that the cells showing these results are not neighbors, so that this effect is an ensemble average of many unit cells several periods apart.