The field of topological physics may soon usher in its outbreak. In the early morning of February 28, three research groups from the Institute of Physics of the Chinese Academy of Sciences, Nanjing University and Princeton University in the United States respectively published the latest relevant research results in the journal Nature. Their research shows that thousands of known materials may have topological properties, that is, about 24% of materials in nature may have a topological structure.
This number is shocking. Because before this, scientists knew only hundreds of topological materials, of which only a dozen have been studied in detail.
When physics meets topology: open a window
Topology, which describes the property that geometric figures or spaces can remain unchanged after continuously changing shapes. For ordinary people, this may be a scientific term in the fog. But when the mathematical concept of "topology" was introduced into the field of physics, on the one hand, it promoted the development of basic physics research, on the other hand, it also prompted a large number of novel topological materials.
In the early 1980s, physicists for the first time linked the macroscopic observation—Hall conductance with mathematical topological invariants, and gave a topological interpretation of the quantum Hall effect.
According to Wan Xiangang, a professor at the School of Physics of Nanjing University, this opens a brand-new window for physics. The 2016 Nobel Prize in Physics was awarded to three theoretical physicists who have made pioneering contributions in topological physics.
For more than 20 years, scientists have further discovered that under different dimensions and symmetries, there are various macroscopic quantum numbers that describe the structure of electronic wave functions, that is, topological invariants. Materials with non-zero topological invariants are called topological materials.
"Topological materials have novel surface states," said Fang Chen, a researcher at the Institute of Physics of the Chinese Academy of Sciences.
For example, the surface state of a two-dimensional topological insulator is called a spiral surface state. When an electron is in such a state, it will not be scattered by impurities during its progress. Therefore, in principle, this feature can be used to achieve energy-free transmission. This makes topological materials a candidate for ultra-low power electronic components.
Another example is a superconducting material with topological properties (referred to as topological superconductor), the boundary state of such materials is called "Majorana zero mode". They have special properties in quantum statistics and are considered to be the possible physical basis for the realization of quantum computers.
More and more scientists are beginning to realize that topological materials may be more common and novel than expected. They are near, but I didn't think of a good way to find them.
From hundreds to thousands: breakthroughs in algorithms
The core property of topological materials is to have non-zero topological invariants. Fang Chen said that most of the newly discovered topological invariants do not correspond to an observable measurement of quantization. Direct observation is quite difficult, while experimental observations are basically indirect.
Since it is a time-consuming and labor-intensive task to observe the topological properties experimentally, it is generally considered that the more efficient method is to first use the method of computational physics to calculate the topological invariants of materials. When it is found in theory that the invariant is indeed not zero, then grow the material and do the experiment.
Therefore, the first step in discovering the topological material is to confirm the topological invariant of the material in calculation. However, because many expressions of topological invariants are very difficult, such calculations require computational physics experts who specialize in this aspect to take a considerable amount of time to complete.
"We adopted the idea of ​​'curving to save the country', which greatly simplified the calculation of invariants." Fang Chen's research group gave up the original complex expressions of invariants and turned to calculate the symmetry data of the energy band of the material, and then based on "The mapping relationship from symmetry information to topological invariants", deduces the information of topological invariants of materials.
The calculation is done automatically, without any artificially adjusted parameters, with 100% repeatability. In this way, they found more than 8,000 topological materials.
Wan Xiangang et al. Gave up the traditional scheme of calculating topological invariants, and judged the topological properties of materials by analyzing whether the expansion coefficient of the atomic energy base symmetry under the base group of the atomic insulator is an integer. On a laptop computer, an atomic insulator base group of 230 space groups can be constructed in half an hour, which is not only much faster, but also very operable.
"The work was done on the computers of our research group and the laboratory. It does not require a supercomputer. It took more than a month to search the entire material database and found thousands of topological materials." Wan Xiangang said .
This excites experimental physicists, "This provides a lot of clues and opportunities for the following experimental work."
From database to new materials: the generation of cross-studies
Scientists integrated their algorithms into a searchable database. Just enter the name of the component of the material and click once to know whether the material has a topological structure.
The database of Fangchen Research Group (http://materiae.iphy.ac.cn) provides more than 8000 topological materials, including almost all important basic information such as the three-dimensional diagram of the crystal structure of the material and the list of topological invariants. The spin-orbit coupling is negligible / non-negligible.
The database of Wanxiangang Research Group (http://ccmp.nju.edu.cn) is manually selected. Although the number of materials in the catalog is slightly smaller, from some perspectives, such as topological materials The physical properties such as specificity are relatively better.
The advantage of the Princeton database (published in the form of an article) is that it takes into account the difficulty of crystalline material synthesis, excluding some materials that cannot be synthesized in a single crystal experiment, so it is called a "high-quality" topological material library.
However, Wan Xiangang admitted that the current research is still limited. Now he is looking for non-magnetic materials. He wants to further develop the existing methods to find magnetic materials, because these materials may also have topological properties.
Fang Chen also said that from a longer-term perspective, magnetic topological materials should be introduced in a suitable way. This requires theoretically a better understanding of the topological invariants in magnetic materials, and the calculation method to deal with the strong correlation effect of electrons in magnetic materials. "Both things are quite difficult, especially the latter."
"We just made the first step, provided some topological material 'candidates', and it's up to the experimental physicists to explore whether it is good or not." Wan Xiangang said.
What Fang Chen wants to see most is the creation of cross-study. For example, it was originally known that a material is a superconductor, and through their database, it was found to have topological properties. For scientists, this may open up new research perspectives and raise new questions.
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