Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network

We investigate weak localization in metallic networks etched in a two dimensional electron gas between $25:$mK and $750:$mK when electron-electron (e-e) interaction is the dominant phase breaking mechanism. We show that, at the highest temperatures, the contributions arising from trajectories that wind around the rings and trajectories that do not are governed by two different length scales. This is achieved by analyzing separately the envelope and the oscillating part of the magnetoconductance. For $Tgtrsim0.3:$K we find $Lphi^mathrm{env}propto{T}^{-1/3}$ for the envelope, and $Lphi^mathrm{osc}propto{T}^{-1/2}$ for the oscillations, in agreement with the prediction for a single ring cite{LudMir04,TexMon05}. This is the first experimental confirmation of the geometry dependence of decoherence due to e-e interaction.