(ORDO NEWS) — The unequivocal discovery of the Wigner crystal was based on a new technique for studying the internal structure of complex materials.
In 1934, Eugene Wigner, a pioneer of quantum mechanics, put forward a theory about a strange kind of matter – a crystal of electrons.
The idea was simple, but it was not easy to prove it. For eight decades, physicists have tried in many ways to push electrons to form what are known as Wigner crystals, with limited success. However, in June, two independent teams of physicists reported in the journal Nature the most direct experimental observations of Wigner crystals.
“Wigner crystallization is such an old idea,” said Brian Skinner, a physicist at Ohio State University who was not involved in the work. “To see it in such a pure form was very nice.”
To make electrons form a Wigner crystal, it would seem that physicists simply need to cool them down. Electrons repel each other, so cooling will reduce their energy and freeze them into a lattice, much like water turns to ice.
However, cold electrons obey the strange laws of quantum mechanics – they behave like waves. Instead of being fixed in place in a neat, ordered lattice, the undulating electrons tend to get mixed up and crash into their neighbors. What should be a crystal turns into something more like a puddle.
One of the groups responsible for the new work discovered the Wigner crystal almost by accident. Researchers in a team led by Hongkun Park at Harvard University experimented with the behavior of electrons in a “sandwich” of extremely thin sheets of semiconductor separated by a material through which the electrons could not move.
The physicists cooled this semiconductor sandwich to below -230 degrees Celsius and played with the number of electrons in each layer.
The team noticed that when each layer had a certain number of electrons, they all mysteriously remained stationary. “Somehow, the electrons inside the semiconductors couldn’t move. It was a really amazing find,” said Yu Zhou, lead author of the new study.
Zhou shared his results with fellow theorists, who eventually remembered Wigner’s old idea. Wigner calculated that electrons in a flat two-dimensional material would have a floor-like pattern perfectly covered with triangular tiles. Such a crystal completely stops the movement of electrons.
In the Zhou crystal, the repulsive forces between the electrons in each layer and between the layers worked together to arrange the electrons into a triangular Wigner lattice. These forces were strong enough to prevent the scattering of electrons predicted by quantum mechanics.
But this behavior only happened when the number of electrons in each layer was such that the top and bottom crystal lattices aligned: The smaller triangles in one layer had to exactly fill the space inside the larger triangles in the other. Park called the electron ratio that led to these conditions “signs of two-layer Wigner crystals.”
Realizing that they had a Wigner crystal in their hands, the Harvards made it melt, forcing the electrons to assume their quantum wave nature. The melting of a Wigner crystal is a quantum phase transition, similar to how an ice cube turns into water, but without any heating.
Theorists have previously predicted the conditions necessary for this process, but the new experiment is the first to confirm this with direct measurements. “It was very, very interesting to see in the experimental data what we learned from textbooks and articles,” Park said.
Past experiments have found hints of Wigner crystallization, but new research offers the most direct evidence thanks to a new experimental technique. The researchers irradiated semiconductor layers with laser light to create an exciton-like particle.
The material then reflected or re-emitted this light. By analyzing the light, the researchers could determine whether the excitons interacted with ordinary free-flying electrons or with electrons frozen in the Wigner crystal. “We have direct evidence for the existence of the Wigner crystal,” Park said. “You can see that it is a crystal that has a triangular structure.”
A second research team led by Atacha Imamoglu of the Swiss Federal Institute of Technology Zurich also used this technique to observe the formation of a Wigner crystal.
The new work highlights the infamous problem of many interacting electrons. When you put a lot of electrons in a small space, they all push against each other, and it becomes impossible to keep track of all the intertwining forces.
Philip Phillips, a physicist at the University of Illinois at Urbana-Champaign who was not involved in the experiment, called Wigner crystals the archetype of all such systems.
He noted that the only problem with electrons and electric forces that physicists can solve with pen and paper is the problem of one electron in a hydrogen atom. In atoms with one more electron, the problem of predicting what interacting electrons will do becomes intractable. The problem of many interacting electrons has long been considered one of the most difficult in physics.
Going forward, the Harvard team plans to use their system to answer unresolved questions about Wigner crystals and strongly correlated electrons. One open question is what exactly happens when a Wigner crystal melts; there are many competing theories.
In addition, the team observed Wigner crystals in their semiconductor sandwich at higher temperatures and for more electrons than theorists predicted. Exploring the reasons for this could lead to new insights into the behavior of strongly correlated electrons.
Eugene Demler, a Harvard theorist who contributed to both new studies, believes this work will resolve old theoretical disputes and inspire new questions. “It’s always much easier to work on a problem when you can find the answers at the end of a book,” he said. “And having additional experiments is like looking for an answer.”
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