Correlation between electrons and vortices in quantum dots

TL;DR

This paper computes exact many-body wave functions for small quantum dots to analyze electron-vortex correlations, revealing structured vortex distributions without multiple zeros, and compares these with rotating electron molecule models.

Contribution

It provides the first detailed analysis of vortex distributions in exact wave functions for quantum dots with up to four electrons, highlighting correlation rules and validating REM wave functions.

Findings

Zeros are strongly correlated and follow specific distribution rules.

No multiple zeros (vorticity > 1) are observed.

Comparison shows good agreement with rotating electron molecule models.

Abstract

Exact many-body wave functions for quantum dots containing up to four interacting electrons are computed and we investigated the distribution of the wave function nodes, also called vortices. For this purpose, we evaluate the reduced wave function by fixing the positions of all but one electron and determine the locations of its zeros. We find that the zeros are strongly correlated with respect to each other and with respect to the position of the electrons and formulate rules describing their distribution. No multiple zeros are found, i.e. vortices with vorticity larger than one. Our exact calculations are compared to results extracted from the recently proposed rotating electron molecule (REM) wave functions.