Usually, cooking is merely a matter of following a recipe - that is, mix specific quantities of specific ingredients in the right manner way and then one will probably end up with a tasty meal eventually. However, in physics, those same rules don't apply.
In spite of an in-depth understanding of the properties of separate atoms - the "ingredients" that constitute a crystal - researchers discovered that, when these atoms are combined together they usually exhibit new, unexpected characteristics, thereby making efforts to engineer novel materials with unique properties little more than guesswork.
In order to make that procedure more predictable, Tokyo University Professor Haruki Watanabe and Harvard Graduate Student Hoi Chun (Adrian) Po Professor of Physics Ashvin Vishwanath partnered to create a new system to denote band structures - that is, energy bands which are analogous to electron orbital running through solids - to rapidly infer the characteristics of a specified material. The study has been reported in a recently-published paper in Science Advances.
Vishwanath informed that in the past 10 years, many researchers have been searching for the so-called topological insulators. These materials are insulators inside, but metallic on the outside. In recent times, generalizations of topological insulators known as topological semimetals and topological crystalline insulators have also attracted a great deal of attention. The crystals’ symmetries play an important role in realizing these phases.
A lot of the effort in the early days was on being able to predict whether a material would be an insulator or metallic. But about 10 or 20 years ago, people realized we could produce these topological materials, (which was exciting) because they have electronic properties that are very desirable. For example, they could be exploited to use the spin of the electron, rather than its charge to perform computation in a more energy efficient way. They may also help create the hardware for a topological quantum computer, one that performs computing in a radically new way.
Insight into band structures would help us find real materials with these topological properties. Right now the way people do this is really more of a guess...and what we are trying to do is to come up with efficient ways of diagnosing whether the material or materials you're interested in have a good chance of having topological properties.
Ashvin Vishwanath, Professor of Physics
However, predicting which type of material is topological is not easy, Vishwanath said.
"The first problem is the huge number of ways in which atoms can form crystals," he said. "Even if you forget about the chemical complexity, forget about which elements are in there, just in the structure...there are 230 ways in which you can put atoms together into crystals."
However, the complication doesn't end there - Vishwanath, Po, and Watanabe, had a keen interest in magnetism. When magnetism is introduced to the mix, the number of potential structures increases considerably to 1,651.
"So there's a huge complexity there and that's one of the challenges," stated Vishwanath. "If we wanted, we could just come up with a long list of options, but that's a very inelegant solution, and doesn't give you any insight into the problem.
"We took a different approach," he continued. "The key idea was...we found a way to represent certain key attributes of band structures as a vector in some high-dimensional space".
With the help of that tool, the team - Vishwanath, Watanabe, and Po - successfully classified all 1,651 possibilities based on whether they were topological insulators, metallic, or simple insulators.
"While each magnetic space group would previously have taken a graduate student a day to figure out, our new formulation allows for a simple automation of the task which is completed on a laptop for all 1,651 instances in half a day," Po stated.
Armed with that data, scientists can now make more informed choices when developing novel materials. Vishwanath said.
"This is a way to narrow down the options," he said. "There are other ways to do it, but we like to think this approach has some advantages."
As a case in point, Vishwanath pointed to the periodic table, whose arrangement is designed to offer information regarding different elements and also about how those particular elements are linked to one another.
"You could list all the elements alphabetically, which would make them easy to look up and find," said Vishwanath. "But the periodic table gives you more information. Our system is similar - we can group structures together based on how they're related to each other."
In the literature, there already exists a highly mathematical way (the so-called K-theory) of classifying topological insulators. However, this approach hasn't been really used for materials search so far because it requires a high-level of abstract mathematics and is hard to compute. The advantage of our approach is its simplicity - it only involves linear algebra and group theory, both of which are undergraduate math subjects. This means that many researchers in the world can implement the scheme themselves and find candidate magnetic topological materials.
Professor Haruki Watanabe
Vishwanath and coworkers are now working closely with materials scientists to model the predicted properties of novel materials by using the system, and are further continuing to study what data can be extracted from the system.
"In some ways, this mirrors our attempts to understand atoms," he stated. "What atomic physics did for chemistry was organize things. It explained the periodic table. We are trying to get a similar understanding not for single atoms, but for collections of atoms, and we hope this is one of the organizing principles for that."
The National Science Foundation, a Simons Investigator Award, and the Japan Society for the Promotion of Science funded the study.