Statistics of Coulomb Blockade Peak Spacings within the Hartree-Fock Approximation

TL;DR

This paper investigates how electronic interactions influence the energy level distributions and conductance peak spacings in disordered two-dimensional quantum dots, revealing Gaussian distributions with large fluctuations and Wigner-Dyson statistics.

Contribution

It demonstrates that interactions cause Gaussian peak spacing distributions with large fluctuations and shows Hartree-Fock levels follow Wigner-Dyson statistics, advancing understanding of quantum dot spectra.

Findings

Peak spacings are Gaussian with large fluctuations.

Hartree-Fock levels follow Wigner-Dyson statistics.

Interactions increase fluctuations beyond non-interacting mean level spacing.

Abstract

We study the effect of electronic interactions on the addition spectra and on the energy level distributions of two-dimensional quantum dots with weak disorder using the self-consistent Hartree-Fock approximation for spinless electrons. We show that the distribution of the conductance peak spacings is Gaussian with large fluctuations that exceed, in agreement with experiments, the mean level spacing of the non-interacting system. We analyze this distribution on the basis of Koopmans' theorem. We show furthermore that the occupied and unoccupied Hartree-Fock levels exhibit Wigner-Dyson statistics.