Topological electronic states are present in almost every known material, contrary to previous assumptions, if the number of electrons in the material is allowed to vary slightly. This phrase nicely sums up ubiquitous band topology — a concept that is the subject of an article in Science this week written by an international team of researchers. There, the team, which includes members of the MPI CPfS, shows that the results of examining earlier experimental data for overlooked topological features suggest that the century-old field of band theory should be restructured: topology given equal footing with chemistry and geometry.
For a century, students of chemistry, materials science, and physics have been taught to model solid-state materials (i.e., to predict the properties of solids through quantum mechanical calculations) by considering their chemical composition, the number and location of their electrons, and ultimately the role of more complicated interactions. However, an international team of scientists from the Donostia International Physics Center, Princeton University, the University of the Basque Country, the Max Planck Institute for Chemical Physics of Solids, the Ecole Normale Supérieure, the CNRS, and MIT recently found that an additional ingredient is the mathematical notion of electronic band topology, which must be considered as well as materials chemistry, geometry, and interactions.
First codified in the 1980s by Michael Berry, Joshua Zak, and S. Pancharatnam, band topology is a physical property that distinguishes electronic states in materials with the same symmetry. Topological phases of matter in 3D materials were first predicted 15 years ago by researchers that included Andrei Bernevig. A year later, Molenkamp’s team was able to realize the prediction. Topological materials exhibit unusually robust states at their exposed surfaces and edges and have been proposed as a venue for observing and manipulating exotic effects, including the conversion of electric current and electron spin, the simulation of exotic theories from high-energy physics, and even, under the right conditions, the storage and manipulation of quantum information. Although a handful of topological materials have been uncovered through chemical intuition, topological electronic states in solids were generally considered rare and esoteric.
Surprising findings
Using high-throughput computational models, however, the team discovered that more than half of the known 3D materials in nature are topological. As the team writes today in the journal Science, they performed full high-throughput first-principles calculations, looking for topological states in the electronic structures of all 96196 crystals recorded in the Inorganic Crystal Structural Database, an established international repository for recording experimentally studied materials. As Nicolas Regnault of Princeton University and the Ecole Normale Supérieure Paris, CNRS, pointed out, “this was a daunting task, requiring more than 25 million hours of computation.” Through a combined chemical and topological analysis, the team grouped the electronic structures into about 38000 unique materials.
The team’s data were made freely available as part of a major overhaul of the publicly available Topological Materials Database (https://www.topologicalquantumchemistry.com) and represent a culmination of the team’s efforts over the past six years to develop a modern position-space theory of band topology known as “topological quantum chemistry.”
Perhaps most surprising was that only ~10% of the materials contained no topological states (thus exhibiting the phenomena previously considered esoteric), but that the extreme, reverse case was also present. “Looking at our data, surprisingly, we saw materials with topology everywhere,” said Maia Vergniory of the Donostia International Physics Center (DIPC) and the Max Planck Institute for Chemical Physics of Solids. That’s because the team found (in addition) that 2% of known materials are “supertopological,” meaning that every electronic band above the tightly bound core electrons is topological across the entire energy spectrum. Among the materials with overlooked supertopology was bismuth, one of the best-studied solid-state materials historically.
“The evidence has always been there. Now we have a concrete key to deciphering all the surface features in spectroscopic material experiments.”
- Benjamin Wieder
“Our database is such a powerful and practical tool,” adds Claudia Felser of the Max Planck Institute for Chemical Physics of Solids. “When I’m interested in a topological property, the database immediately shows me the best candidates. Then I just have to grow the samples in my lab no more guesswork.”
“Reviewing previous experiments from new points of view is an amazing first step,” says Andrei Bernevig of Princeton University and Ikerbasque Visiting Professor at the Donostia International Physics Center (DIPC). “But we can look to an even more exciting future, where materials with advanced functionality will be developed through a marriage of human intuition and artificial intelligence, built on the foundation of the Topological Materials Database and topological quantum chemistry.”
