Weak localization in arrays of metallic quantum dots: Combined scattering matrix formalism and nonlinearσmodel

Abstract

Combining scattering-matrix formalism with nonlinear $\ensuremath{\sigma}$-model technique we analyze weak localization effects in arrays of chaotic quantum dots connected via barriers with arbitrary distribution of channel transmissions. With the aid of our approach we evaluate magnetoconductance of two arbitrarily connected quantum dots as well as of $N\ifmmode\times\else\texttimes\fi{}M$ arrays of identical quantum dots. Our results can be directly used for a quantitative decription of magnetoconductance measurements in structures containing metallic quantum dots.