It’s not often that messing around in the lab has produced a fundamental breakthrough, à la Michael Faraday with his magnets and prisms. Even more uncommon is the discovery of the same thing by two research teams at the same time: Newton and Leibniz come to mind. But every so often, even the rarest of events does happen. The summer of 2021 has been a banner season for condensed-matter physics. Three separate teams of researchers have created a crystal made entirely of electrons — and one of them actually did it by accident.

The researchers were working with single-atom-thick semiconductors, cooled to ultra-low temperatures. One team, led by Hongkun Park along with Eugene Demler, both of Harvard, discovered that when very specific numbers of electrons were present in the layers of these slivers of semiconductor, the electrons stopped in their tracks and stood “mysteriously still.” Eventually colleagues recalled an old idea having to do with Wigner crystals, which were one of those things that exist on paper and in theory but had never been verified in life. Wigner had calculated that because of mutual electrostatic repulsion, electrons in a monolayer would assume a tri-grid pattern.

Park and Demler’s group was not alone in its travails. “A group of theoretical physicists led by Eugene Demler of Harvard University, who is moving to ETH [ETH Zurich, in Switzerland] this year, had calculated theoretically how that effect should show up in the observed excitation frequencies of the excitons – and that’s exactly what we observed in the lab,” said Ataç Imamoğlu, himself from ETH. Imamoğlu’s group used the same technique to document the formation of a Wigner crystal.

Electrons act like magnetic poles in a way: like repels like. In solids, electrons help create regular, repeating crystal lattices. But it’s a different story in liquids. Because liquid electrons are so easily disturbed, when left to their own devices their collective waveform is chaotic, full of shifting, uneven interference.

Getting them to settle requires a perfect confluence of extreme conditions. First, it’s easier when there aren’t many other electrons to cause disturbance in the pattern. Also, a neatly divisible number of electrons can be arranged in a perfect grid. An independent group of researchers, including corresponding author Feng Wang of UC Berkeley, were working with a semiconductor made of atom-thin layers of tungsten disulfide and tungsten diselenide. The atoms in those compounds are slightly different distances apart, so the overlapping layers created a “honeycomb-shaped moiré pattern” of very slightly lower-energy regions, which also helped the electrons to settle down.

A Wigner crystal of electrons (red) inside a semiconductor material (blue/grey). Credit: ETH Zurich

Then there’s temperature. Everything slows down when it’s very cold, so bringing the temperature within a few degrees of absolute zero helps to keep flighty electrons where they’re supposed to be. This is where quantum phenomena start to supersede classical electron behavior. Instead of acting like wavefronts in water, the electrons start acting more in accord with their particle-like nature. But once it’s cold and still enough, all of a sudden containing the electrons gets much easier. It becomes less like herding cats, and more like those acoustic sand-plate patterns. With the right number of electrons, they actually line up by themselves.

(Author’s note: Do give this a watch if you want a cool A/V demo of particles and waves self-organizing to avoid certain places and concentrate in others. Warning: turn the volume way down. It’s like a combination of microphone feedback and an air raid siren.)

Electrons are the functional unit of electricity. So, it might seem like if you get a whole ton of electrons together, what you’d have is maybe something like ball lightning: a potent, condensed, highly powerful quantity of electricity just waiting to zap something. But that’s not what happens in a Wigner crystal. Electricity results from the movement of electrons, not just their presence. Corralling electrons together in a neat atomic tri-grid means that there’s little movement of electrons within that material. It’s also the definition of an insulator. That’s how the researchers knew they’d created an electron crystal: where they’d expected their semiconductor to semi-conduct, it wouldn’t. Held inside their pigeonholes, the electrons weren’t moving, so neither was electricity. These “crystals” are 100% electron, but they’re insulators.

Quantum fluctuations near absolute zero cause quantum-phase transitions, between free-flowing liquids and quantum crystals like Wigner crystals. These quantum transitions are believed to be important in many other quantum systems. Once they knew they had a Wigner crystal, to explore its properties, the Harvard team decided to put it through “quantum melting,” which is apparently just like regular melting, but on a scale so tiny it’s quantum…

“Do you guys just put the word quantum in front of everything?” (Image: Marvel’s “Ant-Man and the Wasp”)

All this excitement took place on a scale so small the scientists couldn’t visually image it even using the best light microscopes. But initial attempts to use a scanning tunneling microscope destroyed the delicate surface of the crystal. In a flash of insight, Wang’s team overlaid the semiconductor with a single-atom-thick sheet of graphene. The Wigner crystals underneath very slightly altered the electron structure of the graphene, which the scanning-tunneling microscope could pick up. To verify that they’d created a Wigner crystal, the physicists had to ping it with individual photons, knocking an electron loose and creating a thing called an “exciton,” which they were able to detect.

“This is right at the border of matter of [sic] changing from partially quantum material to partially classical material and has many unusual and interesting phenomena and properties,” said Demler in a statement. Exactly what those are will take some time to work out.