Discrete charging of metallic grains: Statistics of addition spectra

We analyze the statistics of electrostatic energies (and their differences) for a quantum dot system composed of a finite number $K$ of electron islands (metallic grains) with random capacitance-inductance matrix $C$, for which the total charge is discrete, $Q=Ne$ (where $e$ is the charge of an electron and $N$ is an integer). The analysis is based on a generalized charging model, where the electrons are distributed among the grains such that the electrostatic energy E(N) is minimal. Its second difference (inverse compressibility) $\chi_{N}=E(N+1)-2 E(N)+E(N-1)$ represents the spacing between adjacent Coulomb blockade peaks appearing when the conductance of the quantum dot is plotted against gate voltage. The statistics of this quantity has been the focus of experimental and theoretical investigations during the last two decades. We provide an algorithm for calculating the distribution function corresponding to $\chi_{N}$ and show that this function is piecewise polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract and Introduction

Non-Gaussian distribution of nearest-neighbour Coulomb peak spacings in metallic single-electron transistors

The distribution of nearest-neighbour spacings of Coulomb blockade oscillation peaks in normal conducting aluminum single-electron transistors is found to be non-Gaussian. A pronounced tail to reduced spacings is observed, which we attribute to impurity-specific parametric charge rearrangements close to the transistor. Our observation may explain the absence of a Wigner-Dyson distribution in the experimental nearest-neighbour spacing distributions in semiconductor quantum dots