Paul van Gerven
13 October 2021

Scientists have snapped a picture of the Bigfoot of condensed matter physics: a crystal made solely from electrons.

In 1934, Hungarian-born theoretical physicist Eugene Wigner pondered what would happen if electrons would chill out for once. If they slowed down enough, he figured, the repulsion between their negative charges would start to dominate their behavior. Scrambling to minimize their total energy, electrons would then freeze in place, forming what became known as Wigner crystal.

Wigner’s prediction remained purely theoretical for decades, until Harvard scientists stumbled upon it by accident earlier this year. Working with atomically thin sheets of 2D semiconductors at cryogenic temperatures, a team of physicists noticed that their material stack inexplicably turned into an insulator sometimes.

Stumped by these observations, the researchers turned to their theorist colleagues, one of whom eventually recalled Wigner’s work. Together, they figured out what made the electrons stop dead in their tracks, other than the low temperature: it was their number.

ETH Wigner crystal
A Wigner crystal of electrons (red) inside a 2D semiconductor (blue and grey). Credit: ETH Zurich


One would expect that cooling would be enough for the repulsive forces to take over and force electrons – locked inside a 2D environment – to form a lattice. But it’s not as easy as that, because electrons also behave as waves. Even when more or less fixed into place, electron waves constantly crash into each other, breaking up the grid.

Inadvertently, however, the Harvard researchers had created a stabilizing environment. Inside the two sheets of molybdenum selenide (MoSe2), separated by an insulating layer of boron nitride, the electrons not only experience repulsive forces from their lateral neighbors, but also from the ones in the other layer. At specific ratios between the number of electrons in the top and bottom layer, the crystal grids they form would align in such a way that they stabilize each other.

Independently, researchers at the ETH Zurich also managed to ‘grow’ a Wigner crystal inside MoSe2 around the same time as their Harvard counterparts. The two papers detailing the findings have been posted on the Nature website on the same date.

Too aggressive

Making Wigner crystals is one thing, proving that you made one another. The matter is very fragile and ‘melts’ when probed too aggressively. Both groups gathered evidence by gently firing laser pulses at the semiconductor layers, creating electron-hole entities called excitons. By analyzing re-emitted light, the researchers could tell what they had been shooting at: electrons that were moving about or that were bound in a crystalline state.

This is solid evidence, but neither research group can claim they actually saw the elusive Wigner crystal. And that’s why researchers at the University of California, Berkeley got to work. “If you say you have an electron crystal, show me the crystal,” teases Feng Wang, Berkeley professor of physics.

Berkeley Wigner crystal
Scanning tunneling microscope image revealing a Wigner crystal that formed underneath a graphene sheet. Credit: Hongyuan Li and Shaowei Li, courtesy of Nature

Wang’s team recently published a scanning tunneling microscope (STM) snapshot of the ‘electron ice,’ this time inside a bilayer of tungsten disulfide and tungsten diselenide. The atoms in those compounds are slightly different distances apart. Thanks to this mismatch, which creates a honeycomb ‘moiré pattern,’ electrons settle down even more quickly.

Tracing the STM needle across the bilayer directly proved too aggressive. After adding a layer of graphene, however, the presence of the Wigner crystal was clearly revealed through a change in the graphene’s electron structure. As predicted, the electrons settled into a crystal arrangement with a separation nearly a hundred times greater than the separation of atoms in the semiconductor sheets.