Correlation between electrons and vortices in quantum dots

Abstract

The exact many-body wave function for small numbers $N<5$ of two-dimensional Coulomb-interacting electrons trapped in a parabolic potential placed in a perpendicular magnetic field are investigated. The reduced wave function of this system, which is obtained by fixing the positions of $N\ensuremath{-}1$ electrons, exhibits strong correlations between the fixed electrons and the zeros of the wave function. These zeros are often called vortices. The wave functions are obtained from an exact-diagonalization scheme and the results are compared with results obtained from the recently proposed rotating electron molecule (REM) theory. We find that the vortices cluster around the fixed electrons and repel each other, which is the case to a much lesser extent for the REM results.