As physicists dig deeper into the quantum realm, they are discovering an infinitesimally small world composed of a strange and surprising array of links, knots, and winding. Some quantum Matter exhibit magnetic whirls called skyrmions unique configurations sometimes described as “subatomic hurricanes.” Others host a form of superconductivity that twists into vortices.

Now, in an article published in the journal Nature, a Princeton-led team of scientists has discovered that electrons in quantum matter can link one another in strange new ways. The work brings together ideas in three areas of science – condensed matter physics, topology, and knot theory – in a new way, raising unexpected questions about the quantum properties of electronic systems.Topology is the branch of theoretical mathematics that studies geometric properties that can be deformed but not intrinsically changed. Topological quantum states first came to the public’s attention in 2016 when three scientists, including Duncan Haldane, who is Princeton’s Thomas D. Jones Professor of Mathematical Physics 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 area of research to create a deeper understanding of quantum mechanics, such as in the field of “quantum topology,” which seeks to explain an electron’s state as described by a property called its wave function. This was the catalyst that led to the current research, said M. Zahid Hasan, the Eugene Higgins Professor of Physics at Princeton University and the senior author of the study.

“We’re studying properties related to the shape of the wave functions of electrons,” said Hasan. “And we have now taken the field to a new frontier.”The essential building block of this new frontier is a quantum mechanical structure known as a Weyl loop, which involves the winding of massless electron wave functions in a crystal. In previous groundbreaking work, published in Science in 2019, the massless Weyl loops were discovered in a compound composed of cobalt, manganese, and gallium, with chemical formula Co2MnGa. This research was led by Hasan and included many of the authors of the new study. At that time, they understood that the massless Weyl loops produce exotic behaviors under applied electric and magnetic fields. These behaviors persisted up to room temperature.

By itself, a Weyl loop is an example of the kind of quantum wave function winding that is already well known. “Previous examples of topology in physics often involved the winding of quantum mechanical wave functions,” said Hasan, who led the current research. “These have been the focus of the physics community for at least the past decade.” These ideas are derived from the team’s earlier works on crystals made from rhodium and silicon (RhSi), as well as materials called Chern magnets made from the elements terbium, magnesium, and tin (TbMn6Sn6). Both of those discoveries were led by Professor Hasan’s group and reported in Nature in 2019 and then in Nature in 2020.However, the case of Co2MnGa turned out to be different from wave function winding considered in conventional topological theories. “Here instead we have linked loops our newly discovered knotted topology is of a different nature and gives rise to different mathematical linking numbers,” said Tyler Cochran, a graduate student in Princeton’s Department of Physics and co-author of the new study.

The Co2MnGa materials were grown by Professor Claudia Felser and her team at the Max Planck Institute for Chemical Physics of Solids in Germany.An essential insight came when the Princeton team calculated and understood that certain quantum materials such as Co2MnGa could host multiple Weyl loops at the same time. “When multiple Weyl loops co-exist, it becomes natural to ask whether they can link up and knot in certain ways,” Hasan said.

This realization by Hasan’s team sparked fundamental questions about linked Weyl loops and brought together a team of experts from around the world in photoemission spectroscopy, mathematical topology, quantum material synthesis and first-principles quantum calculations to more deeply understand link topology and knotting in quantum matter.

Source: This news is originally published by scitechdaily

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