Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube

TL;DR

This study directly observes and spectroscopically characterizes a two-electron Wigner molecule in a clean carbon nanotube, demonstrating strong electron-electron interactions and spatial separation in a controllable one-dimensional quantum system.

Contribution

First direct measurement of a two-electron Wigner molecule's energy spectrum in a tunable, one-dimensional setting using a clean carbon nanotube.

Findings

Identification of seven low-energy states with distinct spin and isospin quantum numbers.

Observation of a small energy splitting indicating strong electron-electron interactions.

Demonstration of tunability of the two-electron state in space and for both electrons and holes.

Abstract

Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a strongly-interacting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the non-interacting value. Our ability to tune the two-electron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.