Quantum ergodicity for electrons in two dimensions

TL;DR

This paper investigates how electron-electron interactions influence localization and delocalization in two-dimensional disordered systems, revealing a transition similar to the Anderson transition and connecting it to experimental metal-insulator phenomena.

Contribution

It provides analytical and numerical evidence of a transition from localized to delocalized states in 2D electron systems, highlighting the role of Coulomb interactions and spectral statistics.

Findings

Transition from Poisson to Wigner-Dyson spectral statistics

Localization-delocalization transition similar to 3D Anderson transition

Relation to 2D metal-insulator transition experiments

Abstract

We study the effect of electron-electron interaction on a two dimensional (2D) disordered lattice. For the case of two electrons the analytical estimates are presented showing a transition from localized to delocalized states in a way similar to the Anderson transition in 3D. The localized phase corresponds to large values of the parameter r_s, which is determined by the ratio of the Coulomb and Fermi energies. The numerical investigations of the spectral statistics P(s) in a system with up to N_p=30 spin polarized electrons show the transition from the Poisson to the Wigner-Dyson distribution at a total electron energy independent of N_p. The relation to experiments on the metal-insulator transition in 2D is also discussed.