Princeton University breakthrough research revives frozen electrons

Princeton University Researchers have discovered a strange form of matter that has eluded direct detection for about 90 years.

Although scientists have been studying electrons for more than a century, electrons—the infinitesimal particles known to move around atoms—continue to surprise scientists. Now, Princeton University physicists have pushed the boundaries of our understanding of these tiny particles by visualizing for the first time direct evidence of so-called Wigner crystals, strange substances made entirely of electrons.

The findings were published on April 11^th Journal issues nature, It confirmed a 90-year-old theory that electrons can assemble themselves into crystal-like structures without coalescing around atoms. This research may help discover new quantum phases of matter when electrons behave collectively.

Theoretical insights and early experiments

Al Yazdani, the James S. McDonald Distinguished University Professor, said: “Wigner crystals are one of the most fascinating quantum phases of matter ever predicted and are the subject of numerous studies claiming to have Finding the best indirect evidence of its formation “Visualizing this crystal not only allows us to observe its formation and confirm many of its properties, but we can also study it in ways we have not been able to do in the past. “

In the 1930s, Princeton University physics professor and 1963 Nobel Prize winner Eugene Wigner wrote a paper proposing the then-revolutionary idea that interactions between electrons could lead to They spontaneously arrange themselves into a crystal-like structure, or lattice, of tightly packed electrons. He speculated that this would only occur under conditions of low density and extremely cold temperatures, because they would repel each other.

“When you think of crystals, you typically think of the attraction between atoms as a stabilizing force, but this crystal forms purely because of the repulsion between electrons,” said Yasuda, the first co-director of the Princeton Quantum Institute. Zdani said.

The film depicts the process by which an electron Wigner crystal melts into its electron liquid phase. As the electron density (\nu, a measure of the number of electrons in a magnetic field, controlled by applying a voltage) increases, more electrons (dark blue sites) enter the field of view, and the periodic structure of a triangular lattice emerges. The periodic structure is melted first (close to \nu = 0.334), where the graph shows a uniform signal. It then reappears with a higher density \nu and eventually melts again (\nu = 0.414).Image credit: Yen-Chen Tsui, Princeton University

Progress in Electronic Crystal Research

For a long time, however, Wigner’s strange electronic crystals remained in the realm of theory. It was not until a series of later experiments that the concept of electronic crystals moved from conjecture to reality. The first experiments were conducted in the 1970s, when scientists at Bell Labs in New Jersey created a “classical” electron crystal by spraying electrons onto the surface of helium and found that they responded in a rigid manner like a crystal. However, the electrons in these experiments were far apart and behaved more like single particles than cohesive structures. A true Wigner crystal does not follow the familiar laws of physics from everyday life, but instead follows the laws of quantum physics, in which electrons behave less like single particles and more like single waves.

This led to a series of experiments over the next few decades proposing various methods of making quantum Wigner crystals.These experiments came a long way in the 1980s and 1990s, when physicists discovered how to use semiconductor. Applying a magnetic field to this layered structure also causes electrons to move in circles, creating favorable conditions for crystallization. But these experiments never allowed direct observation of the crystals. They can only hint at its existence or infer it indirectly from how electrons flow through the semiconductor.

A breakthrough in direct imaging

“There are literally hundreds of scientific papers that have studied these effects and claimed that these results must be caused by Wigner crystals, but we can’t know for sure because none of these experiments actually see such crystals,” Yazdani said. .

An equally important consideration, Yazdani noted, is that some researchers believe evidence of Wigner crystals could be the result of inherent defects or other periodic structures in the materials used in the experiments. “If there are any defects or some form of periodic substructure in the material, it would be possible to trap electrons and find experimental features that are not due to the formation of self-organized ordered Wigner crystals themselves, but are due to electrons being ‘stuck’ ‘Due to the structure of the material, the defects are close or trapped,” he said.

With these factors in mind, Yazdani and his research team set out to investigate whether Wigner crystals could be imaged directly using a scanning tunneling microscope (STM), a device that relies on a technique called “quantum tunneling” rather than light. Observe Wigner crystals.They also decided to use Graphenea surprising material discovered in the 21st century^Yingshi century and has been used in many experiments involving novel quantum phenomena. However, in order to carry out the experiment successfully, the researchers had to make the graphene as pristine and defect-free as possible. This is key to eliminating the possibility of any electronic crystals forming due to defects in the material.

Uncovering the nature of quantum

The results are impressive. “Our team has been able to create unprecedentedly clean samples that made this work possible,” Yazdani said. “Looking through our microscopes, we can confirm that there are no atomic defects in the sample’s graphene atomic lattice. Nor are there foreign atoms in a region with hundreds of thousands of atoms on its surface.”

To create pure graphene, the researchers peeled off two sheets of graphene carbon, creating a structure called Bernal stacked bilayer graphene (BLG).They then cooled the sample to extremely low temperatures – just a fraction of a degree hotter than the original absolute zero— and applying a magnetic field perpendicular to the sample, creating a two-dimensional electron gas system within the thin layer of graphene. This way, they could adjust the electron density between the two layers.

“In our experiment, we can image the system while adjusting the number of electrons per unit area,” said Yen-Chen Tsui, a graduate student in physics and first author of the paper. “You can initiate this phase transition simply by changing the density and find electrons spontaneously forming ordered crystals.”

Explore crystal structures and their dynamics

Tsui explains that this happens because at low densities, electrons are far apart from each other and they are arranged in a disordered, unorganized way. However, as density increases and electrons become closer together, their natural repulsive tendencies kick in and begin to form an organized lattice. Then, when the density increases further, the crystalline phase will melt into the e-liquid.

Minhao He, a postdoctoral researcher and co-first author 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 limited density, the electrons cannot spread infinitely apart. The result is that they form a tightly packed, regularized lattice structure, with each localized electron occupying a certain amount of space.

As this transformation forms, the researchers were able to visualize it using STM. “Our work provides the first direct image of such a crystal. We demonstrated that the crystal does exist and that we can see it,” Xu said.

Future directions of Wigner crystal research

However, just observing the crystals is not the end of the experiment. The specific images of the crystals allowed them to distinguish some of the crystal’s features. They found that the structure of the crystal is triangular, which can continuously adjust with the density of the particles. This led to the realization that Wigner crystals are actually quite stable over long ranges, a conclusion contrary to what many scientists had suspected.

“By continuously adjusting its lattice constant, experiments have shown that the crystal structure is the result of pure repulsion between electrons,” Yazdani said.

The researchers also discovered some other interesting phenomena that undoubtedly deserve further study in the future. They found that where each electron was positioned in the lattice appeared somewhat “blurred” in the image, as if the position was defined not by a point but by the range of positions in the lattice where the electron was confined. . The paper describes it as the “zero point” motion of electrons, a phenomenon related to the Heisenberg uncertainty principle. The degree of blur reflects the quantum nature of Wigner crystals.

“Electrons, even when frozen in a Wigner crystal, should exhibit strong zero-point motion,” Yazdani said. “It turns out that this quantum motion covers one-third of the distance between them, making the Wigner crystal a new type of quantum crystal.”

Yazdani and his team are also studying how Wigner crystals melt and transform into other exotic liquid phases of electrons interacting in magnetic fields. The researchers hope to image these phases much like they imaged Wigner crystals.

Reference: “Direct Observation of Magnetic Field-Induced Wigner Crystals,” by Yen-Chen Tsui, Minhao He, Yuwen Hu, Ethan Lake, Taige Wang, Kenji Watanabe, Takashi Taniguchi, Michael P. Zaletel, and Ali Yazdani, 2024 April 10, nature.
DOI: 10.1038/s41586-024-07212-7

Graduate student Yen-Chen Tsui, postdoctoral researcher Minhao He, and Yuwen Hu, who received his Ph.D. from Princeton’s Department of Physics in 2023 and is now a postdoctoral fellow at Stanford University, all contributed equally to this work. Other collaborators include theoretical physicists Ethan Lake, Taige Wang, and Professor Michael Zaletel of the University of California, Berkeley, who are also members of the Materials Sciences Division at Lawrence Berkeley National Laboratory, as well as Kenji Watanabe and the National Institute of Physics from the National Institute of Physics. Takashi Taniguchi. is the Center for Materials Science and International Materials Nanostructures.

This work at Princeton University was primarily supported by DOE-BES grant DE-FG02-07ER46419 and the Gordon and Betty Moore Foundation’s EPiQS Program grant GBMF9469. NSF-MRSEC provided additional support to the Princeton experimental infrastructure through the Princeton Complex Materials Center NSF6 DMR-2011750, ARO MURI (W911NF-21-2-0147), and ONR N00012-21-1-2592.

The team also thanks the warm hospitality of the Aspen Physics Center, which is supported by National Science Foundation grant PHY-1607611, where some of the work was performed. Work at UC Berkeley was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, and Materials Science and Engineering Division under Contract No. DE-AC02-05CH11231 under the Van der Waals Heterostructures Program (KCWF16).