Interactions in chaotic nanoparticles: Fluctuations in Coulomb blockade peak spacings

We use random matrix models and a Fermi-liquid approach to investigate the ground state energy of electrons confined to a nanoparticle. Our expression for the energy includes the charging effect, the single-particle energies, and the residual screened interactions treated in Hartree-Fock. This model is applicable to chaotic quantum dots or nanoparticles—in these systems the single-particle statistics follows random matrix theory at energy scales less than the Thouless energy. We find the distribution of Coulomb blockade peak spacings first for a large dot in which the residual interactions can be taken constant: the spacing fluctuations are of order the mean level separation $\Delta .$ Corrections to this limit are studied using the small parameter ${1/k}_{F}L:$ both the residual interactions and the effect of the changing confinement on the single-particle levels produce fluctuations of order $\Delta /\sqrt{k_{F}L}.$ The distributions we find are qualitatively similar to the experimental results. Thus, models beyond Fermi-liquid theory are not needed to describe this quantity.