Nonequilibrium Green's functions approach to strongly correlated few-electron quantum dots

TL;DR

This paper uses nonequilibrium Green's functions to study how electron-electron interactions affect the properties of few-electron quantum dots, revealing the transition from Fermi liquid to Wigner molecule behavior.

Contribution

It introduces a self-consistent Green's function approach with a conserving self-energy approximation to analyze electron correlations in quantum dots.

Findings

Charge density and spectral functions are computed at various temperatures.

The study observes the crossover from Fermi liquid to Wigner crystal states.

Results include energy and distribution functions for different electron numbers.

Abstract

The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's functions theory. The ground and equilibrium state is self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for the zero and finite temperature charge carrier density, the orbital-resolved distribution functions and the self-consistent total energies and spectral functions for isotropic, two-dimensional parabolic confinement as well as for the limit of large anisotropy--quasi-one-dimensional entrapment. For the considered quantum dots with N=2, 3 and 6 electrons, the analysis comprises the crossover from Fermi gas/liquid (at large carrier density) to Wigner molecule or crystal behavior (in the low-density limit).