Counting statistics and an anomalous metallic phase in a network of quantum dots

Abstract

We report results relating to the transport properties of a quantum network formed by connecting chaotic quantum dots to each other and to electron reservoirs via barriers of arbitrary transparencies. We employ two representations of a generating function for charge counting statistics: a stochastic one, based on a random scattering matrix model for numerical simulations, and a field theoretic one, based on a Keldysh nonlinear σ-model for analytical calculations. We compute in the semiclassical regime the first four charge transfer cumulants: conductance, shot-noise power, skewness and kurtosis. We show that the variations in the transparencies of the barriers can induce qualitative changes in the transport properties of the networks, through topology controlled noise power modulation. We also show that a double-scaling limit, achieved by a combination of an infinite number of dots and full suppression of Fabry–Perot modes, leads to an anomalous metallic phase in the limit of thick wire. Finally, a powerful procedure is proposed for computing weak localization effects in the transport observables of the networks for all ranges of parameters, both for pure symmetry classes and for the crossover induced by an applied magnetic field and spin–orbit scattering.