Weak localization and conductance fluctuations in complex mesoscopic geometries

We extend the theory of weak localization and conductance fluctuations in mesoscopic samples to more complex measurement-probe configurations using the network formalism of Douçot and Rammal. Large measurement probes reduce both the amplitude of the localization contribution and the characteristic field scale of the low-field magnetoresistance. We present a simple and physically intuitive picture to explain these results. Our calculations on the length dependence of the conductance fluctuations for wires with narrow measurement probes agree with previous theoretical work, but allow us to make predictions for samples with more complex probe geometries. Furthermore, the detailed shape of the field autocorrelation function is strongly dependent on the geometry of the probes, reminiscent of the weak-localization magnetoresistance. The results of our experiments on weak localization and conductance fluctuations in short Ag wires confirm many of these predictions. We also discuss the relevance of our calculations for the determination of important microscopic parameters such as the electron phase coherence length.