Groundbreaking research at Princeton University gives cryoelectrons a new lease of life

Researchers at Princeton University have detected a strange form of matter that has not been directly detected for about 90 years. Even though scientists have been studying electrons for more than a century, electrons – infinitesimally small particles known to swim around atoms – still surprise scientists.

Image of a triangular Wigner crystal taken by a scanning tunneling microscope. Researchers have revealed an elusive crystal that is formed entirely by the repulsive properties of electrons. Each site (blue circular area) contains a local electron. Source: Yanchen Xu and team, Princeton University

Now, physicists at Princeton University have pushed the boundaries of what we understand about these tiny particles, and for the first time directly demonstrated in a visual way the so-called Wigner crystal, a strange substance made entirely of electrons.

The finding, published in the April 11 issue of the journal Nature, confirms a 90-year-old theory that electrons can combine themselves into crystal-like forms without condensing around atoms. This research may contribute to the discovery of new quantum phases of matter when electrons act collectively.

Theoretical insights and early experiments

"The Wigner crystal is one of the most fascinating quantum phases of matter that has been predicted, and is the subject of numerous studies that claim to find only circumstantial evidence of its formation at best," said Al Yazdani, James S. McDonnell Distinguished University Physics Professor at Princeton University and senior author of the study. "Visualizing this crystal not only allows us to observe its formation, confirm its many properties, but also to study it in ways that were not possible in the past. "

In the thirties of the 20th century, Eugene Wigner, a professor of physics at Princeton University who won the Nobel Prize in 1963 for his work on the principle of quantum symmetry, wrote a paper in which he proposed the revolutionary idea of the time that the interaction between electrons causes them to spontaneously arrange into crystal-like configurations, that is, a lattice of closely packed electrons. According to his theory, this is only possible at low density and at very low temperatures, due to the mutual repulsion of electrons.

Yazdani, the first co-director of the Princeton Quantum Institute and director of the Princeton Center for Complex Materials, said: "When you think of crystals, you usually think of the attraction between atoms as a stabilizing force, but the formation of this crystal is purely due to the repulsion between electrons. "

The video depicts the process by which an electron Vigner crystal melts into an electron-liquid phase. As the electron density (\nu, a measure of the number of electrons in a magnetic field, controlled by the application of voltage) increases, more electrons (dark blue dots) come into view, and a periodic structure of a triangular lattice emerges. The periodic structure is first melted (around \nu = 0.334), where the map shows a uniform signal. It then reappears at the more dense \nu and eventually melts again (\nu = 0.414). Source: Princeton University, Yanchen Xu

Advances in the study of electronic crystals

However, for a long time, Wigner's exotic electron crystals remained theoretical. It was not until a series of experiments later that the concept of an electron crystal went from conjecture to reality. The first experiments were carried out in the 70s of the 20th century, when scientists at Bell Labs in New Jersey created a "classic" electron crystal by ejecting electrons on the surface of helium and found that they reacted as stiff as crystals. However, the electrons in these experiments are far apart and behave more like a single particle than a cohesive structure. Instead of following the familiar laws of physics in everyday life, a true Vigner crystal follows the laws of quantum physics, in which electrons behave less like a single particle and more like a single wave.

Thus, in the following decades, a series of experiments were carried out, and various methods for making quantum Wigner crystals were proposed. In the 80s and 90s of the 20th century, physicists greatly advanced these experiments by discovering how semiconductors could be used to confine the motion of electrons to thin layers of atoms. Applying a magnetic field to this layered structure also causes the electrons to move in a circular motion, creating favorable conditions for crystallization. However, these experiments never made it possible to directly observe the crystals. They can only imply the presence of crystals, or indirectly infer the presence of crystals based on the way electrons flow in semiconductors.

A breakthrough in direct imaging

"There are literally hundreds of scientific papers studying these effects and claiming that these results must have been caused by the Wigner crystals," Yazdani said, "but we can't know for sure because none of these experiments actually saw the crystals." "

An equally important consideration, Yazdani noted, is that some researchers believe that evidence of Wigner crystals may be due to defects in the materials used in the experiments or other inherent periodic structures. "If there are any defects or some form of periodic substructure in the material, it is possible to trap electrons and discover experimental features that are not due to the formation of the self-organizing ordered Wegner crystal itself, but because the electrons are 'stuck' in the vicinity of the defect or due to the structure of the material," he said. "

With these factors in mind, Yazdani and his research team began investigating whether they could image Wigner crystals directly using scanning tunneling microscopy (STM), a device that relies on a technique called "quantum tunneling" instead of light to observe atoms and the subatomic world. They also decided to use graphene, a magical material discovered in the 21st century that has been used in many experiments involving new quantum phenomena. However, in order to be successful, researchers must make graphene as pure and blemish as possible. This is the key to eliminating the possibility of any electronic crystals forming due to material defects.

Unveiling the essence of quantum

The results are impressive. "Our team was able to produce unprecedentedly clean samples, which made this work possible," Yazdani said. With our microscope, we can confirm that these samples do not have any atomic defects in the graphene atomic lattice, nor do they have any foreign atoms on their surface, exceeding the region of hundreds of thousands of atoms. "

To make pure graphene, the researchers stripped two graphene carbon sheets into a structure called Bernal stacked bilayer graphene (BLG). They then cooled the sample to an extremely low temperature – only a fraction of absolute zero – and applied a magnetic field perpendicular to the sample, creating a two-dimensional electronic gas system within the graphene thin layer. In this way, they can adjust the electron density between the two layers of graphene.

"In our experiments, when we adjust the number of electrons per unit area, we can image the system," said Yen-Chen Tsui, a graduate student in physics and first author of the paper. "Just by changing the density, this phase transition can be initiated, and the electrons are found to spontaneously form ordered crystals."

Explore crystal structures and their dynamics

Tsui explains that this happens because at low density, the electrons are far apart from each other and their position is disordered, unorganized. However, as the density increases, the distance between the electrons gets closer and closer, and their natural tendency to repel comes into play and begins to form an organized lattice. Then, as the density increases further, the crystalline phase will melt into an e-liquid.

He Minhao, a co-first author and postdoctoral researcher of the paper, explained the process in more detail. "There is an inherent repulsion between electrons," he said. They want to push each other away, but at the same time, due to the limited density, the electrons cannot be separated indefinitely. As a result, they form a tightly packed regularized lattice structure, with each local electron occupying a certain space. "

When this transformation formed, the researchers were able to visualize it using STM: "Our work provides a direct image of this crystal for the first time. We proved that the crystal does exist, and we can see it. "

The future direction of Wigner's crystal research

However, just seeing the crystals is not the end of the experiment. Specific images of the crystals allow them to discern some of the characteristics of the crystals. They found that the crystal structure is triangular and can be adjusted over time as the particle density changes. This led them to realize that the Wigner crystals were actually quite stable over a long range, contrary to what many scientists had guessed.

"By constantly adjusting the lattice constant, experiments have shown that the crystal structure is the result of pure repulsion between electrons," Yazdani said.

The researchers also discovered a number of other interesting phenomena that undoubtedly merit further study in the future. They found that the position of each electron in the lattice appeared to a certain degree of "blurring" in the image, as if the position was not defined by a point, but rather that the electrons were confined to a range of positions in the lattice. The paper describes it as the "zero-point" motion of electrons, a phenomenon related to Heisenberg's uncertainty principle. This degree of ambiguity reflects the quantum nature of Wigner's crystals.

"Even if the electrons solidify into a Wigner crystal, they should exhibit a strong zero-point motion," Yazdani said. It turns out that this quantum motion covers a third of the distance between them, making the Vigner crystal a novel quantum crystal".

Yazdani and his team are also studying how Wigner crystals melt and transform into other exotic liquid phases where electrons interact in a magnetic field. The researchers hope to image these liquid phases in the same way that they did with Wigner crystals.

编译自/scitechdaily