Scientists Visualize Electron Crystals with Quantum Superposition

Illustration of two sites of graphene grid.Credit: Image courtesy: Researcher

Princeton scientists are using innovative technology to visualize the electrons in graphene, a single atomic layer of carbon atoms. They made them so that strong interactions between electrons in high magnetic fields form anomalous crystal-like structures similar to those first recognized in benzene molecules by chemist August Kekulé in the 1860s. I’m discovering to drive. These crystals exhibit spatial periodicity corresponding to the electrons being in quantum superposition. Experiments also show that Kekulé quantum crystals have defects that are not similar to those of ordinary crystals composed of atoms. These discoveries shed light on the complex quantum phases in which electrons can form due to the interactions that underlie a wide range of phenomena in many materials.

Physicists have learned to control how electrons interact with each other by applying a strong magnetic field, and more recently by stacking multiple layers of graphene on top of each other. In fact, with the discovery of graphene in the first decade of the 21st century, the 2010 Nobel Prize in Physics, the exploration of electron physics, especially how electrons behave collectively. A new field has been opened to find out.

Currently, Princeton researchers, led by Ali Yazdani, a professor of physics in 1909 and director of the Complex Materials Center at Princeton University, found a complex pattern in which strong interactions between electrons in graphene are determined by the quantum. I discovered that it drives to form a crystal structure that has. Superposition — Electrons that exist at multiple atomic sites at the same time. This experiment, recently published in Science, also shows that this new quantum crystal hosts an exotic transformation that corresponds to the twisting and winding of the electron’s wavefunction.

Graphene consists of a single layer of carbon atoms arranged in a two-dimensional hexagonal or honeycomb-like lattice. It’s seemingly simple, but it’s produced in a painstaking way. Graphite, the same material found in pencils, is gradually stripped strip by strip until it reaches the thin carbon layer of this single atom.

“Previous studies have shown that graphene exhibits new electrical properties,” says Yazdani. “But until now, researchers have never been able to study the properties of quantum states with such spatial resolution so deeply.”

To achieve this unparalleled level of resolution, Yazdani’s group Scanning tunneling microscope (STM). This device relies on a phenomenon called “quantum tunneling”. This phenomenon uses voltage to send electrons between a sharp metal chip in a microscope and a sample just a few angstroms away. The microscope uses this tunneling current instead of light to display the world of electrons on an atomic scale. Yazdani’s microscopes operate in very high vacuums, keep sample surfaces clean, and operate at very low temperatures, allowing high resolution measurements without the effects of thermal agitation.

The microscope can also display the electrons as they reach them. Lowest energy state It is dominated by their quantum properties.

In the presence of a magnetic field, a microscope can be used to determine the spatial structure of quantized energy levels.

“One of the special properties of graphene is its behavior in the magnetic field as the electrons are forced to orbit around the magnetic field in a circular motion,” says Yazdani. “This quantizes the energy and the electrical properties of graphene.”

Quantization of energy refers to the creation of discrete values ​​of energy without the intermediate values ​​that are characteristic of quantum physics, as opposed to classical physics, where continuous energy values ​​are allowed.

Researchers have focused on the lowest-energy quantization level of graphene. A previous study first reported by Puan On, a professor of physics at Princeton University’s Eugene Higgins, revealed some anomalous electrical properties. This level dominates the electrical properties when graphene is not overcharged or removed, that is, when the charge is neutral. Ong showed that when the charge is neutral, the electrons “freeze” and the graphene layer acts as an insulator upon application of a magnetic field. The nature of this frozen electron in graphene has been a mystery for almost a decade since Ong’s first discovery.

Scientists Visualize Electron Crystals with Quantum Superposition

Kekulé pattern vortex. The left panel shows the changes in the Kekulé pattern in space. The lower right panel shows the texture of the vortex extracted from the left panel, similar to a hurricane.Credit: Image courtesy: Researcher

“The insulation we found confused everyone and strongly challenged the general theory of the time,” said Ong, who was not involved in the current study. “Until Yazdani gave beautiful results, it remained a permanent puzzle for 13 years. The new results solve the puzzle in a very exciting way.”

Yazdani and his team used a microscope to map the wavefunction of the lowest quantization energy level in the presence of a magnetic field.Researcher found Complex pattern Changes in electron waves when graphene is tuned to a neutral state at a nearby electrical gate.

In metals, the wavefunction of electrons spreads throughout the crystal, but in ordinary insulators, electrons are frozen without prioritizing the crystal structure of the atomic site. At very low magnetic fields, STM images showed that graphene’s electron wavefunction selects one of the other sublattice sites. More importantly, by increasing the magnetic field, a prominent bond-like pattern is observed. This corresponds to the wavefunction of the electrons present in the quantum superposition. This means that the electron occupies two non-equivalent sites at the same time.

In particular, this image corresponded to the bond-like structure that Kekulé first recognized for benzene. It consists of alternating single and double bonds. In a single bond, one electron in each atom bonds with an adjacent electron. In a double bond, two electrons from each atom participate.

People speculate that electrons may form such a Kekulé pattern, “said Yazdani. Unless imaged, this electronic state could not be distinguished in any other way. ”

The researchers then used a microscope to map the uniformity of the Kekulé crystal to the defects in graphene or its properties near the defects. One of the notable discoveries they made was a nearby charge defect that discovered that the Kekulé pattern evolved continuously in the pattern around the defect. Graphene The surface of the water.

In collaboration with Michael Zaletel of the University of California, Berkeley, the team has developed a method for extracting the mathematical properties of electron quantum wavefunctions, the so-called phase angles, from STM data. Quantum superposition.. Analysis revealed a pronounced winding of one of these phase angles around the defect and a correlation change of the other angle.

“When the group applied their technique to measure the phase angle over defects in the substrate, they discovered the” vortex “of the Kekulé pattern. It’s like a hurricane, with a phase angle of 12 hours. [as on a clock]”When making predictions about such quantum, nanoscale, and objects, you would hardly think that you could actually” see “the pictures, but the group was able to do just that. “

The team believes that the technology developed to discover this anomalous electron quantum crystal in a strong magnetic field can be applied elsewhere in the magnetic field. Other 2D materials and their stacks may show similar quantum crystals with new defects. The team aims to apply that methodology to a wider class of such materials.

In addition to Yazdani and Zaletel, contributors to this study included the Joseph Henry Institute at Princeton University and the authors of the Department of Physics, Xiaomeng Liu, Gerareh Farahi, and Cheng-Li Chiu. Zlatko Papic, Faculty of Physics and Astronomy, University of Leeds, UK. Kenji Watanabe and Takashi Taniguchi of the National Institute for Materials Science.

Xiaomeng Liu, Gerareh Farahi, Cheng-Li Chiu, Zlatko Papic, Kenji Watanabe, Takashi Taniguchi, Michael Zaletel, Ali Yazdani’s study “Symmetry breaking and phase defects of quantum Hall ferromagnets” on December 2 Published in. Journal 2021 Chemistry..

Generation of “magic” angular graphene and unexpected topological quantum states

For more information:
Xiaomeng Liu et al, Visualization of symmetry breaking and topological defects in quantum Hall ferromagnets, Chemistry (2022). DOI: 10.1126 / science.abm3770

Quote: Scientists have obtained a quantum superposition on February 23, 2022 from https: // (February 23, 2022). Visualize the electron crystal in (day)

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Scientists Visualize Electron Crystals with Quantum Superposition

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