Unified description of floppy and rigid rotating Wigner molecules formed in quantum dots

TL;DR

This paper investigates the properties of rotating Wigner molecules in quantum dots, revealing their behavior as floppy rotors at high magnetic fields and rigid rotors at zero field, providing insights into their ground states and excitation spectra.

Contribution

It offers a unified description of floppy and rigid rotating Wigner molecules in quantum dots, clarifying their characteristics across different magnetic field regimes.

Findings

High magnetic fields lead to floppy rotor behavior with specific energy scaling.

Zero field and strong repulsion result in rigid rotor behavior with quadratic energy dependence.

The energy dependence serves as a diagnostic for the appropriate theoretical model for quantum dots.

Abstract

Restoration of broken circular symmetry is used to explore the characteristics of the ground states and the excitation spectra of rotating Wigner molecules (RWM's) formed in two-dimensional parabolic N-electron quantum dots. In high magnetic fields, the RWM's are floppy rotors with the energies of the magic angular momentum (L) states obeying aL + b/L^{1/2}. Under such fields the ground-state energies (referenced to the kinetic energy in the lowest Landau level) approach the electrostatic energy of N point charges in the classical equilibrium molecular configuration. At zero field and strong interelectron repulsion, the RWM's behave like quasiclassical rigid rotors whose energies vary as L^2. The particular L-dependence in high B is inherent and natural to a floppy rotating WM, and it can be used as a crucial diagnostic tool for resolving the recently posed question whether the composite-fermion or the RWM picture is appropriate for QD's.