A crystal composed entirely of electrons? This prediction was made 90 years ago, and it really happened this time.

A new exotic substance once again proves the magic of quantum mechanics.

Written by Yu Huai

Atoms can form a regularly arranged lattice. From metals that can be seen everywhere to silicon inside chips, many solid substances are the product of regularly arranged atoms (crystals). Further subdivided, atoms contain positively charged nuclei and negatively charged electrons. So, is there a lattice that is produced only by the regular arrangement of electrons?

90 years ago, the famous physicist Eugene Wigner theoretically predicted the electron crystal. The mutual repulsion between electrons will make them move away from each other, while a certain electron density will prevent them from moving away from each other indefinitely. When such conflicting interactions are balanced, electrons tend to arrange into a regular lattice to reduce the energy brought by the interaction. This lattice is therefore named "Wigner crystal".

Now, this theoretical prediction has finally been directly observed by scientists. Researchers from Princeton University published a paper in the journal Nature, directly photographing the Wigner lattice for the first time.

Physicists have been trying to make Wigner crystals a reality. Making Wigner crystals usually requires extremely low temperatures and low dimensions, because the interactions between electrons are more significant in these two conditions. The earliest experiments can be traced back to the work of Bell Labs in the 1970s. Researchers sprayed electrons on the surface of liquid helium, causing the electrons to move away from each other and form a lattice. But such electrons are closer to independent particles. In a real Wigner crystal, all electrons should form a whole and act collectively like waves.

In the following decades, physicists have made a series of explorations. For example, they have used semiconductors to confine the movement of electrons to two dimensions, and used magnetic fields to make electrons circle to help form crystals. Many works have indirectly observed evidence of the existence of Wigner lattices. However, people have not been able to "take a picture" of Wigner lattices and realize direct observation.

In order to "take pictures" of such subatomic structures, the researchers chose the scanning tunneling microscope (STM). The basic working principle of this microscope is to detect the extremely weak current generated by quantum effects between the probe and the sample, thereby displaying the characteristics of the sample after scanning. This method can clearly observe the scale of atomic size, making atomic-level "photography" possible.

Iron atoms arranged in a circle on a copper surface, photographed using an STM. This is the cover image of Physics Today, November 1993.

After determining the shooting method, sample preparation is also a big problem. First of all, the sample must be extremely clean and free of impurities. Wigner crystals are crystals composed only of electrons. All electrons interact with each other under quantum mechanics and act in unison. Even the existence of an impurity particle may form a trap that binds electrons, thus breaking such interactions.

The Princeton researchers chose stacked double-layer graphene as a sample, cooled it, and then applied a magnetic field perpendicular to the sample direction to create an electron gas moving in two dimensions. This also makes it easy to adjust the electron density.

After all the efforts, the results are amazing. Through the tunnel scanning microscope, scientists saw for the first time a Wigner crystal composed only of electrons. Due to the ultra-high resolution of the microscope, it can be determined that there are no impurities in it. The electrons that make up the lattice are regularly arranged into tight triangles, and the size of the triangles will change when the electron density is adjusted. This further confirms that the lattice is formed by the interaction of electrons, rather than being affected by impurities.

Scientists also found that the electrons that should have been arranged regularly in the lattice were somewhat blurry. The researchers explained that this was due to the "zero-point energy" of the electrons, a system's lowest energy described by quantum mechanics, which is related to the Heisenberg uncertainty principle. Such blurry electron images show that the Wigner crystals captured were formed due to quantum mechanical effects.

Wigner crystal is a novel phase of matter. One of the goals of physicists is to continuously explore these novel phases, realize and record them, and understand how different phases transform in order to better grasp the quantum world.

References

[1] Tsui, YC., He, M., Hu, Y. et al. Direct observation of a magnetic-field-induced Wigner crystal. Nature 628, 287–292 (2024). https://doi.org/10.1038/s41586-024-07212-7

Produced by: Science Popularization China

Special Tips

1. Go to the "Featured Column" at the bottom of the menu of the "Fanpu" WeChat public account to read a series of popular science articles on different topics.

2. Fanpu provides a function to search articles by month. Follow the official account and reply with the four-digit year + month, such as "1903", to get the article index for March 2019, and so on.

Copyright statement: Personal forwarding is welcome. Any form of media or organization is not allowed to reprint or excerpt without authorization. For reprint authorization, please contact the backstage of the "Fanpu" WeChat public account.