Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by scanning probe technique

TL;DR

This study uses numerical simulations to evaluate how effectively scanning probe techniques can map charge densities in strongly-correlated two-dimensional quantum dots, revealing insights into electron arrangements and the limitations of the method.

Contribution

It demonstrates the accuracy and limitations of charge density mapping in various quantum dot geometries, especially under strong electron-electron correlations.

Findings

Wigner molecules form in circular quantum dots and are detectable by the mapping.

The mapping accurately reproduces charge densities, with some underestimation or overestimation depending on tip potential.

Charge densities in lower-symmetry dots with single-electron islands are well-resolved by the technique.

Abstract

We perform a numerical simulation of mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schr\"odinger equation with the exact diagonalization approach and evaluate the energy maps in function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are confronted with the original ones. The present study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limit case. We concentrate on large quantum dots for which strong electron-electron correlations appear. For circular dots the correlations lead to formation of Wigner molecules that in the presence of the tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for repulsive tip potential and overestimated for the attractive tip. In lower-symmetry quantum dots the Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of the tip. These charge densities are well resolved by the mapping. The single-electron islands appear in the laboratory frame provided that classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.