Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

TL;DR

This paper investigates the transition to Wigner crystallization in a two-electron quantum dot system, using a roto-vibrational model and various theoretical approaches to characterize the crystallized state and its excitations.

Contribution

It introduces a quantitative roto-vibrational model for Wigner crystallization in two-electron quantum dots, including effects of magnetic fields and phase diagrams.

Findings

Crystallization occurs when rotational motion decouples from vibrational motion.

The Wigner molecule's properties are characterized by its moment of inertia and rotational states.

Magnetic fields influence the crystallization and excitation spectrum.

Abstract

We provide a quantitative determination of the crystallization onset for two electrons in a parabolic two-dimensional confinement. This system is shown to be well described by a roto-vibrational model, Wigner crystallization occurring when the rotational motion gets decoupled from the vibrational one. The Wigner molecule thus formed is characterized by its moment of inertia and by the corresponding sequence of rotational excited states. The role of a vertical magnetic field is also considered. Additional support to the analysis is given by the Hartree-Fock phase diagram for the ground state and by the random-phase approximation for the moment of inertia and vibron excitations.