Physicists Create All-Electron Wigner Crystal

Wigner Crystal
Wigner Crystal

In 1934, quantum mechanics pioneer Eugene Wigner theorized a strange type of matter, a crystal made of electrons. This idea proved that such a thing could not happen. Physicists have tried many tricks over eighty years to poke electrons to form these so-called Wigner crystals, but with limited success. But in June, two independent groups of physicists reported in Nature the most direct experimental observations of Wigner crystals ever. "Wigner crystallization is a very old idea," said Brian Skinner, a physicist at Ohio State University who was not involved in the study. “It was really nice to see it this clean.”

Crystal Structure Composed of Electrons

For the electrons to form a Wigner crystal, it might seem like enough for a physicist to cool them, but the electrons repel each other, thus reducing their cooling energy and freezing them in a lattice as the water turns into ice. Still, cold electrons obey the strange laws of quantum mechanics - they behave like waves. Rather than being fixed in place in a neatly arranged grid, wave-like electrons will also tend to wander around and bump into their neighbors. What should happen in a crystal is that it is expected to turn into something more like a puddle.

One of the teams responsible for the new study found a Wigner crystal almost by accident. Researchers in a group at Harvard University led by Hongkun Park were experimenting with electron behavior in a "sandwich" consisting of an extremely thin layer of semiconductor separated by a material that electrons cannot pass through. Physicists cooled this semiconductor sandwich below -230 degrees Celsius and played with the number of electrons in each layer.

The team observed that when there is a certain number of electrons in each layer, they all mysteriously become dormant. “Somehow, the electrons inside the semiconductors couldn't move. This was a truly surprising discovery,” says You Zhou, lead author of the new study.

Zhou shared his results with fellow theorists who finally remembered an old idea of ​​Wigner's. Wigner had calculated that electrons in a two-dimensional flat material would take on a pattern similar to a floor perfectly covered with triangular tiles. This crystal would prevent the electrons from moving completely. In Zhou's crystal, the repulsive forces between electrons in each layer and between layers worked together to place the electrons in Wigner's triangular grid. These forces were strong enough to prevent the electron spillage and churning predicted by quantum mechanics. But this behavior only occurred when the number of electrons in each layer was such that the upper and lower crystal grids were aligned: Smaller triangles in one layer had to exactly fill the void inside larger ones in the other. Park called the electron ratios that lead to these conditions "explanatory signs of double-layered Wigner crystals."

After the Harvard team realized they had a Wigner crystal on their hands, they melted the crystal, forcing electrons to adopt its quantum wave nature. We can compare the melting of a Wigner crystal to a quantum phase transition, which is similar to an ice cube becoming water, but without any heating.

Theorists have already predicted the conditions necessary for the process to occur, but the new experiment is the first to confirm this through direct measurements. Past experiments have found hints of Wigner crystallization, but new studies offer the most direct evidence due to a new experimental technique. The researchers blasted the semiconductor layers with laser light to create a particle-like entity called an exciton. The material then reflected or re-emitted this light.

What is an exciton?

An exciton is a bonded state of an electron and an electron hole attracted to each other by the electrostatic Coulomb force. It is an electrically neutral semi-particle found in insulators, semiconductors, and some liquids. The exciton is considered a fundamental excitation of condensed matter, which can carry energy without carrying a net electric charge.

An exciton can be formed when a material absorbs a photon with energy higher than the band gap. This excites an electron from the valence band to the conduction band. In turn, this leaves a positively charged electron hole (an abstraction for the position an electron is moving from). The electron in the conduction band is less attracted to this localized hole due to the repulsive Coulomb forces from the many electrons surrounding the hole and the excited electrons. These driving forces provide a balancing energy balance. As a result, the exciton has slightly less energy than the unbonded electron and hole. The wave function of the bound state is said to be hydrogenic, an exotic atomic state similar to that of the hydrogen atom. However, the binding energy is much smaller and the particle size is much larger than a hydrogen atom.

This is due to both the scanning of the Coulomb force (i.e., its relative permittivity) by other electrons in the semiconductor and the small effective masses of the excited electron and hole. The recombination of electron and hole, that is, the decay of the exciton, is limited by the resonance stabilization due to the overlap of the electron and hole wave functions, resulting in a longer lifetime for the exciton.

By analyzing the light, the researchers were able to tell whether excitons interact with ordinary free-flowing electrons or with electrons frozen in a Wigner crystal. "We actually have direct evidence that it's a Wigner crystal," said Park of Harvard. "You can also see that it's actually a crystal with this triangular structure." A second research team led by Ataç İmamoğlu at the Swiss Federal Institute of Technology Zurich also used this technique to observe the formation of a Wigner crystal.

The new study circumvents the negativity of many interacting electrons to form crystals. When you put a large number of electrons in a small space, they all repel each other and it becomes impossible to keep track of all the mutually intertwined forces.

Physicist Phillips of the University of Illinois at Urbana-Champaign identified Wigner crystals as an archetype for all such systems. He noted that the only problem involving electrons and electric forces that physicists know how to solve with only pen and paper is the problem of a single electron in a hydrogen atom. Even in atoms with one more electron, the problem of predicting what the interacting electrons will do becomes inextricable. Many interacting electron problems have long been considered one of the most difficult in physics.


Günceleme: 16/08/2021 15:46

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