Scientists visualize electron crystals in a quantum superposition

The scientists are using innovative techniques to see the electrons in the single atomic layer of carbon atoms. They are finding that strong interactions between electrons in high magnetic fields drive them to form unusual crystal-like structures similar to those first recognized for benzene in the 1860s by chemist August Kekul. The spatial periodicity of these crystals correspond to electrons being in a quantum superposition. Experiments show that quantum crystals have defects that are different from those of ordinary crystals. The findings shed light on the interplay between electrons and their interaction, which underlies a wide range of phenomena in many materials.

Physicists learned how to control how electrons interact with one another by applying a strong magnetic field and stacking multiple layers of Graphene on top of each other. The discovery of graphene in the first decade of the 21st century opened a new arena for exploring the physics of electrons, especially for examining how electrons behave collectively.

The strong interaction between electrons in graphene drives them to form crystal structures with complex patterns determined by quantum superposition, which was discovered by a group of researchers led by the Class of 1909 Professor of Physics and director of the Center for Complex Materials at Princeton University. The novel quantum crystal has exotics that correspond to the twisting and winding of the electrons.

A single layer of carbon atoms is arranged in a honeycomb-like lattice. It is produced in a way that is easy to understand. A single-atom-thin layer of carbon is reached when the same material found in pencils is exfoliated strip by strip.

Researchers have been able to peer so deeply into the nature of quantum states with such spatial resolution.

The scanning tunneling microscope was used to achieve this level of resolution. This device relies on a phenomenon called quantum tunneling, where the electrons are funneled between the metallic tip of the microscope and the sample only a few meters away. The world of electrons on the atomic scale can be viewed using the tunneling current in the microscope. The microscopes operate in a high vacuum to keep the sample surface clean and at low temperatures to allow for high resolution measurements.

The microscope is able to see electrons in their lowest energy states.

The spatial structure of the quantized energy level can be determined by using the microscope.

The behavior of electrons in a magnetic field is one of the special properties of Graphene.

Classical physics allows continuous energy values, but quantum physics allows the creation of discrete values of energy, without any intermediate values.

The researchers focused their attention on the quantized level with the lowest energy in graphene, for which previous research first reported by Phuan Ong, Eugene Higgins Professor of Physics at Princeton, had revealed some unusual electrical properties. When the charge is neutral, this level dominates the electrical properties. When the charge is neutral, the electrons freeze and the graphene layer acts as an insulator. The nature of this frozen state of electrons in graphene has been a mystery for almost a decade.

The state that we found puzzled everyone and strongly challenged the prevailing theories at that time was the subject of 13 years of research. The new results resolve the puzzle in a very exciting fashion.

The lowest quantized energy level in the presence of a magnetic field was mapped using the microscope. The researchers were able to see patterns of electron waves when graphene was in a neutral state.

In metals, wavefunction is spread throughout the crystal, while in a normal insulator, electrons are frozen without any preference to the crystal structure of the atomic sites. At very low fields, the images showed the wavefunctions of Graphene choosing one of the sub-lattice sites over the other. By increasing the magnetic field, a bond-like pattern is observed, which corresponds to electrons in a quantum superposition. An electron occupies the two sites at the same time.

The image was similar to the structure first recognized by Kekul. There are alternating single and double bonds. One electron from each atom bonds with its neighbor electron in a single bond and two electrons from each atom bonds in a double bond.

"People have speculated that electrons may form such Kekul patterns, but now we're seeing it for the first time." One cannot distinguish this state of electrons unless it is imaged.

The researchers used the microscope to map the properties of the Kekul crystal and its defects in the Graphene. They found a pattern that evolved continuously around a near charge defect on the Graphene surface.

The team developed a method to extract the mathematical properties of the quantum wavefunction of electrons from the STM data. The analysis showed that one of the phase angles around the defect was winding and that the other angle was changing.

When the group applied their technique to measure the phase-angle above a defect in the substrate, they found a storm in the Kekul pattern, which is like a Hurricane around which the phase-angle winds around by 12.

The team believes that the techniques they have developed to uncover this unusual quantum crystal of electrons in a strong magnetic field can be applied elsewhere in the field. Other two-dimensional materials and their stack can have the same quantum crystals. The team wants to apply their methodology to more materials.

The authors of the study included Xiaomeng, Gelareh, and Cheng-Li Chiu, as well as Zlatko Papic, School of Physics and Astronomy.

The study shows broken symmetry and defects in a quantum Hall ferromagnet.

More information: Xiaomeng Liu et al, Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet, Science (2022). DOI: 10.1126/science.abm3770 Journal information: Science Citation: Scientists visualize electron crystals in a quantum superposition (2022, February 23) retrieved 23 February 2022 from https://phys.org/news/2022-02-scientists-visualize-electron-crystals-quantum.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.