Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2005-07-27
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
21 pages, no figures, mathematical nomenclature (except for Abstract and Introduction)
Scientific paper
10.1088/0305-4470/39/18/002
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.
Avishai Yshai
Berend Daniel
Bromberg Luba
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