Wigner molecules in carbon-nanotube quantum dots

TL;DR

This paper demonstrates the formation of Wigner molecules in carbon nanotube quantum dots, showing electrons localize in ordered structures and their excitations resemble collective vibrations, with some features observed experimentally.

Contribution

It provides exact diagonalization calculations and a simple vibrational wave function model to describe electron localization and excitations in nanotube quantum dots.

Findings

Electrons form ordered Wigner molecules in nanotube quantum dots.

Localized electron wave functions resemble nuclei in molecules.

Low-energy excitations are collective vibrational modes.

Abstract

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a `Wigner molecule'. Our exact diagonalisation calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy -indeed some of them have already been observed by Deshpande and Bockrath [Nature Phys. 4, 314 (2008)]. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions.