Low-field magnetotransport study of localization in a mesoscopic antidot array

Low-field negative magnetoresistance has been studied on ${\mathit{G}}_{\mathit{a}}^{+}$ ion focused-ion-beam-patterned GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As heterojunctions as a function of carrier density and temperature. The negative magnetoresistance (NMR) is very large at low densities and decreases with increasing carrier density, giving a magnetoconductance linear in T at low densities but closer to a lnT dependence at higher values. The NMR of this grid structure is well explained using weak localization modified by boundary scattering in an array of one-dimensional point contacts. The NMR disappears after illumination as the patterning is screened by the increased electron density. From this model, we fit the phase-breaking rate as 1/${\mathrm{\tau }}_{\mathrm{\phi }}$=A+BT, where the constant term is attributed to boundary scattering and the linear temperature dependence arises from electron-electron scattering.