A new strange substance once again confirms the wonder of quantum mechanics.
Written by | Yu Huai
Atoms can form a regular lattice, and many solid substances, from the ubiquitous metal to the silicon inside a chip, are the product of the regular arrangement of atoms (crystals). Further subdividing downwards, atoms contain positively charged nuclei and negatively charged electrons. So, is there a crystal lattice that is produced only by the regular arrangement of electrons?
Ninety years ago, the famous physicist Eugene Wigner theoretically gave the prediction of electronic crystals. The mutual repulsion of electrons keeps them away from each other, and a certain electron density prevents them from moving away from each other without limitation. When such conflicting interactions are balanced, the electrons tend to align into a regular lattice to reduce the energy of the interaction. This lattice is also known as the "Wigner crystal".
Now, this theoretical prediction has finally been directly observed by scientists. Researchers from Princeton University, published a paper in the journal Nature, for the first time, directly photographed the Wigner lattice.
Physicists have been trying to bring Wigner crystals to life. Fabrication of Wigner crystals often requires extremely low temperatures and low dimensions, as the interaction of electrons is more pronounced in both cases. The earliest experiments can be traced back to the work of Bell Labs in the 70s of the last century. The researchers ejected electrons on the surface of liquid helium, moving them away from each other to form a crystal lattice. But such electrons are closer to independent particles, and in a true Wigner crystal, all the electrons should form a whole, acting collectively like waves.
In the decades that followed, physicists made a series of explorations. For example, semiconductors are used to limit the motion of electrons to two dimensions, and magnetic fields are used to circle electrons to help form crystals. Evidence of the existence of Wigner's lattice has been indirectly observed in many works. However, people have not been able to "take a picture" of the Wigner lattice and achieve direct observation.
To "photograph" such a subatomic structure, the researchers chose scanning tunneling microscopy (STM). The basic principle of this microscope is to detect the extremely weak current generated by quantum effects between the probe and the sample, thus revealing the characteristics of the sample after scanning. This method makes it possible to clearly observe the scale of atomic size, thus making "photography" possible at the atomic level.
Iron atoms arranged in circles on a copper surface photographed by STM, cover image of Physics Today, November 1993
After determining the means of shooting, the preparation of samples was also a major challenge. First of all, the sample must be extremely clean and free of impurities. A Vigner crystal is a crystal made up of only electrons. All electrons interact with each other under quantum mechanics and act in unison. Even the presence of an impurity particle has the potential to form a trap that binds electrons, thus breaking such an interaction.
Researchers at Princeton University chose stacked bilayer graphene as a sample, cooled it, and applied a magnetic field perpendicular to the direction of the sample to create an electronic gas that moves in two dimensions. This also makes it easy to adjust the electron density.
With all these efforts, the results are amazing. Through a tunneling scanning microscope, scientists saw for the first time a Wigner crystal made up of only electrons. Due to the ultra-high resolution of the microscope, it can be determined that no impurities are present in this. These electronic regularities that make up the lattice are arranged in tight triangles, and the size of the triangles also changes when the electron density is adjusted. This further establishes that the lattice is formed by electronic interactions and is not affected by impurities.
Wigner Crystal丨Source: References[1]
Scientists have also found that these electrons, which should be regularly arranged in the crystal lattice, are somewhat blurry. The researchers explain that this is due to the electron's "zero-point energy" – the lowest energy of a system described by quantum mechanics – related to Heisenberg's uncertainty principle. Such a blurry electronic image shows that the captured Wigner crystal was formed due to quantum mechanical effects.
One of the goals of physicists is to continuously explore these novel phases, realize them and record them, and understand how different phases are transformed to better understand the quantum world.
bibliography
[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
Producer: Popular Science China
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