Electrons are found in a crystal to exhibit complex and correlated quantum fluctuations

تعرض الإلكترونات الموجودة في الكريستال تقلبات كمومية مرتبطة ومعقدة

Schematic diagram of the quantum electronic bond in the momentum (velocity) space observed in a topological Weyl magnet2MnGa, determined from advanced optical emission spectroscopy measurements. Credit: Ilya Bilopolsky and M. Zahid Hassan, Princeton University

As physicists delve into the quantum world, they discover a tiny, tiny world made up of a strange and surprising collection of links, nodes, and coils. Some quantum materials display magnetic vortices called skyrmions, unique formations described as “subatomic cyclones”. Others host a form of superconductivity that turns into vortices.

Now, in an article published in temper nature A team of physicists led by Princeton discovered that electrons in Quantity matter They can relate to each other in strange new ways. The work brings together ideas in three scientific areas – condensed matter physics, topology, and knot theory– In a new way that raises unexpected questions about the quantum properties of electronic systems.

Topology is the branch of theoretical mathematics that studies geometric properties that can deform but do not fundamentally change. Topological quantum states first caught the public’s attention in 2016 when three scientists, including Duncan Haldane, Professor of Mathematical Physics at Princeton University, Thomas D. Jones, and Sherman Fairchild University Professor of Physics, were awarded the Nobel Prize for their theoretical prediction of topology in electronic materials.

Since that time, researchers have sought to expand this field of research to create a deeper understanding of quantum mechanics, such as in the field of “quantum topology,” which seeks to explain the state of the electron as described by a property called the wave function. This was the motivating factor that led to the current research, said Zahid Hassan, a professor of physics at Princeton University and lead author of the study.

“We are studying properties related to the shape of the electrons’ wave functions,” Hassan said. “And we have now taken the field to a new frontier.”

The building block of this new frontier is a quantum mechanical structure known as the Weyl loop, which involves spinning massless electron wave functions into the crystal. In previous pioneering work, published in Science In 2019, massless Weyl rings were discovered in a compound composed of cobalt, manganese and gallium, with the chemical formula Co2MnGa. This research was led by Hassan and included several authors of the new study. At the time, they realized that massless Weyl rings produce strange behaviors under applied electric and magnetic fields. These behaviors persisted up to room temperature.

The Weyl loop itself is an example of the type of quantum wavefunction coil already known. “Previous examples of topology in physics have often involved winding quantum mechanical wave functions,” said Hassan, who led the current research. “This has been the focus of the physics community at least for the past decade.” These ideas derive from the team’s previous work on crystals made of rhodium and silicon (RhSi), as well as materials called Chern magnets made from the elements terbium, magnesium, and tin (TbMn).6Sn6). Both of these discoveries were led by Professor Hassan’s group and were published in temper nature In 2019 and then in temper nature in the year 2020.

However, the case of Co2Turns out MnGa is different from wave function Filtering is considered in traditional topological theories. “Here instead, we’ve linked continuum loops — the newly discovered topologies of the nodes are of a different nature and lead to different mathematical linking numbers,” said Tyler Cochran, a graduate student in Princeton’s Department of Physics and a co-author on the new study.

Share2MnGa materials were developed by Professor Claudia Felser and her team at the Max Planck Institute for the Chemical Physics of Solids in Germany.

تم العثور على الإلكترونات في بلورة لإظهار التقلبات الكمومية المترابطة والمعقدة

Signatures of associated node loops in Co2MnGa. credit: temper nature (2022). DOI: 10.1038 / s41586-022-04512-8

A basic idea emerged when the Princeton team calculated and understood some quantum materials such as Co2MnGa can host multiple Weyl episodes at the same time. “When multiple Weyl rings coexist, it becomes natural to ask if they can bind and contract in certain ways,” Hassan said.

This realization by Hassan’s team raised fundamental questions about correlated Weyl loops and brought together a team of experts from around the world in optical emission spectroscopy, mathematical topology, quantum material synthesis, and elementary quantum computations to more deeply understand the correlation topology and entanglement in quantum matter. .

To observe the link experimentally, the international team collaborated for more than five years to expand on their previous work on topological magnets. The team conducted advanced optical emission spectroscopy experiments at advanced synchrotron radiation facilities in the United States, Switzerland, Japan and Sweden.

The study’s lead author, Ilya Bilopolsky, who was a former graduate student in Hassan’s lab at Princeton University and is now a postdoctoral researcher at the RIKEN Center for Emerging Materials Science near Tokyo, Japan, said. “Unraveling the intricacies of this same sophisticated continuum quantum structure requires more than three years of high-resolution, high-resolution measurements at the world’s leading spectroscopy facilities.”

Analysis of the experimental data revealed an unintuitive object that folded in and twisted across a higher dimensional hoop. “Understanding object structure requires a new bridge between quantum mechanics, mathematical topology and knot theory,” said Guoqing Chang, the study’s author and now an assistant professor of physics at Nanyang Technological University in Singapore. While a former postdoctoral researcher with Hassan at Princeton University, Zhang led one of the early theoretical studies of correlation topology in 2017 in pioneering work in Physical Review Letters.

In fact, the research team found that the current quantum theory of matter was not able to adequately explain the appearance of this structure. But they realized that knot theory might hold some clues.

“We realized that some aspects of knot theory are very powerful in explaining the quantum properties of topological materials that were not previously understood,” Hassan said. “This is the first example we know of where knot theory can be applied to understand the behavior of topological magnets. And that’s very exciting.”

The results continue and extend the decades-long conversation between physics and topology, this time bringing new mathematical ideas to explain experiments with quantum ferromagnets. “Historically, some of the most important scientific discoveries arose when humans noticed new connections between mathematics and natural phenomena,” Hassan said. “It is always exciting to find unexpected examples of exact mathematics in our experiments.” “More than that, it was interesting that the mathematical correlation was in the field of topology, which has continued to appear again and again in various forms in the study of quantum materials. “

The researchers intend to expand their research in multiple directions. Although Hassan and his team focused their efforts on the behavior of topological magnets, they contend that the theory has the potential to help explain other quantum behaviors. “We believe knot theory can also be applied to many topological conductors, superconductors, qubits, and many other things,” he said.

And although the researchers didn’t think of practical applications—”we were involved in the basic research,” Hassan emphasized—their insights may aid the development of quantum computing, particularly the development of new types of topological qubits.

Progress and prospects in magnetic topological materials

more information:
Ilya Bilopolsky et al., Observing a correlated-loop quantum state in a topological magnet, temper nature (2022). DOI: 10.1038 / s41586-022-04512-8

Ilya Belopolski et al, Discovery of Weyl fermion topological lines and drum head surface states in room temperature magnets, Science (2019). DOI: 10.1126 / science.aav2327

Daniel S. Sanchez et al, Chiral topological crystals with helical arc quantum states, temper nature (2019). DOI: 10.1038 / s41586-019-1037-2

Jia Xin Yin et al., Topological magnetism of a quantum boundary Chirn in TbMn6Sn6, temper nature (2020). DOI: 10.1038 / s41586-020-2482-7

Guoqing Chang et al, Hopf and Chain Link semi-metallic states and their application to Co2MnGa, Physical Review Letters (2017). DOI: 10.1103/ PhysRevLett.119.156401

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