Universal transport properties of quantum dots with chiral symmetry

Abstract

We present a stochastic model to describe universal transport characteristics of quantum dots with sublattice (chiral) symmetry, coupled to two electron reservoirs via identical point contacts. The joint distribution of transmission eigenvalues is deduced from a maximum-entropy principle and is shown to comply with the classification of geometric correlations in terms of classical symmetric spaces. A Brownian motion ensemble is presented to calculate transport characteristics for an arbitrary number of propagating channels. Exact distributions of the conductance and shot-noise power are obtained in the single-mode case. We derive semiclassical formulas for calculating the average and the variance of arbitrary cumulants of the charge-counting statistics.