Interference effects and magnetoresistance oscillations in normal-metal networks:1-weak localization approach

A general formalism is outlined for the calculation of the transport coefficients of a normal-metal network in the weak-localization regime. Simple circuits such as loops and ladders are used to illustrate our approach. Closed expressions for the magnetoresistance of infinite regular networks (square, honeycomb,...) are derived. The case of an infinite fractal network (Sierpinski gasket) is also investigated. We show that the localization correction to the magnetoresistance Δ R/R is given in general by a weighted sum over the eigenvalues of the underlying linear problem. We find in particular that, in contrast with superconducting networks, no fine structure due to interference effects between adjacent loops is expected. The obtained results are shown to agree very well with recent experimental results on the magnetoresistance oscillations in normal-metal networks.