One of the simplest quantum mechanical systems is that of two electrons on a string. When the two electrons interact strongly, a Wigner molecule ground state is formed. Here, the two particles repulse each other to the opposite ends of the string. Named after Eugene Wigner, who predicted the existence of this quantum crystallization phenomenon back in 1934, this unique state of matter is very difficult to observe in experiments.

Cleanest conceivable condensed matter setup

The Wigner molecule is a very fragile quantum state and is held together only by the weak forces between electrons. These weak forces can easily be disturbed by the millions of other nearby electrons and atoms existing in the host material.

“To observe the molecule, we used the cleanest conceivable condensed matter setup,” explained team member Sharon Pecker of the Weizmann Institute of Science in Israel. “We started with an electrically neutral nanotube suspended in vacuum that was touching nothing but two metal electrodes, and we charged it exactly with two electrons. By then passing electrical current through the nanotube, we could infer how the two electrons were interacting.”

Using a technique called “transport spectroscopy”, the researchers found that, as predicted by Wigner, the electrons pushed each other apart such that each electron sat on one side of the nanotube, forming a molecule. When they then deliberately squeezed the two electrons to one side of the nanotube the electrons still kept themselves some distance apart. “Pushing the electrons from side to side also proved that the molecule forms as a result of intrinsic electron interactions and not merely because it is being affected by its surrounding environment,” Pecker told

Ordered Wigner crystal

According to quantum mechanics, electrons always tend to spread out and fill any given volume, he explains. However when the repulsive interactions between electrons are strong enough, they can overcome this tendency to spread. In this situation, the electrons form an ordered Wigner crystal of equally distanced, well-spaced electrons, says Pecker.

"Besides confirming Wigner’s old theoretical prediction, our work also demonstrates how an extremely clean system, like a carbon nanotube, can be used to manipulate delicate electronic states in a controlled way,” he adds. “More generally, it proves that nanotubes can today be synthesized with extremely high purity and are one of the most pristine solid state systems that actually exist now.

“If we could use these nanotubes to extend our control over more than two electrons, this could herald a new wave of precision experiments using these materials. We would then be able to exploit them as pristine condensed-matter ‘laboratories’ for studying fundamental quantum mechanical phenomena on the nanoscale.”

The present research was performed by Shahal Ilani’s group at the Weizmann Institute, Paul McEuen’s and Dan Ralph’s teams at Cornell University in the US and Massimo Rontani and colleagues at the CNR-NANO Research Centre in Italy. The researchers published their work in Nature Physics doi:10.1038/nphys2692.

Further reading

Carbon nanotubes clean up their act (Apr 2009)
Nanotubes set to shine for solar energy (Sep 2009)
Graphene simulations hint at future electronics (Oct 2007)