Everything is Topological

May 20, 2022

An international research team has discovered that topological electronic states are present in nearly every known material for every electron in the crystal configuration. Appearing this week in Science, the team’s discovery of ubiquitous band topology has motivated re-examining previous experimental data for overlooked topological features, and suggests that the century-old field of band theory should be restructured, with topology joining chemistry and geometry on equal footing.

For the past century, chemistry, materials science, and physics students have been taught to model solid-state materials by considering their chemical composition, the number and location of their electrons, and lastly, 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, l’Ecole Normale Supérieure, the CNRS, and MIT has recently discovered that an additional ingredient – the mathematical notion of electronic band topology - must also be considered on the same footing as material 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 discovered 15 years ago by researchers including Andrei Bernevig, a member of the research team.  One year later, Molenkamp's team was able to realise the prediction. Topological materials exhibit unusually robust states on their exposed surfaces and edges, and have been proposed as venues for observing and manipulating exotic effects, including the interconversion of electrical current and electron spin, the tabletop simulation of exotic theories from high-energy physics, and even, under the right conditions, the storage and manipulation of quantum information.  Though a handful of topological materials have been uncovered through chemical intuition, topological electronic states in solid-state materials were generally considered to be rare and esoteric. 

Suprising insights

However, using high-throughput computational modeling, the team discovered that over half of the known 3D materials in nature are topological.  Writing today in Science, the team performed complete high-throughput first-principles calculations searching for topological states throughout the electronic structures of all of the 96,196 recorded crystals in the Inorganic Crystal Structural Database, an established international repository for reporting experimentally studied materials. As stressed by Nicolas Regnault, from Princeton University and the Ecole Normale Supérieure Paris, CNRS, “This was a daunting task that took more than 25 million hours of computing time.“  Through a combined chemical and topological analysis, the team grouped the electronic structures into roughly 38,000 unique materials.  The team’s data have been made freely available through a massive overhaul of the publicly accessible Topological Materials Database (https://www.topologicalquantumchemistry.com), representing a culmination of the team’s efforts over the past six years developing the modern position-space theory of band topology known as “Topological Quantum Chemistry.”

The team also surprisingly discovered that almost all materials – nearly 90% – host topological electronic states away from their intrinsic numbers of electrons, known as the Fermi level.  Though these states lie dormant in many experimental probes, they are still straightforwardly accessible through techniques including chemical doping, electrostatic gating, hydrostatic pressure, and photoexcitation spectroscopy. 

Perhaps most surprising was that, if ~10% of materials did not contain any topological states, the extreme opposite case also existed.  “Looking at our data, we amazingly saw materials with topology basically everywhere!” exclaimed Maia Vergniory from the Donostia International Physics Center (DIPC) and the Max Planck Institute for Chemical Physics of Solids.  The team found that 2% of known materials are “supertopological,” in that every electronic band above the tightly-bound core electrons was topological across the entire energy spectrum.  Among the materials with overlooked supertopology was bismuth, one of the most historically well-studied solid-state materials. 

No more guesswork

The ubiquity of topological features observed in numerical simulations lead to a natural question: if the results were to be believed, experimental signatures of topological states should have already been observed in earlier investigations of many materials.  Combing through data from earlier photoemission experiments, the team indeed discovered this to be the case.  For example, in experimental studies of Bi2Mg3 performed four years ago, the authors observed unexplained “surface resonances,” which were recognized in the current study to be overlooked topological surface states away from the Fermi level.  “The evidence had always been there,” noted Benjamin Wieder, a postdoctoral researcher at MIT.  “We now have a concrete key towards decoding all of the surface features in spectroscopic material experiments.”  “Our database is such a powerful and convenient tool,” added Claudia Felser from the Max Planck Institute for Chemical Physics of Solids. “If I am interested in a topological property, the database instantly tells me the best candidates.  Then I just grow the samples in my lab, no more guesswork.” 

“Revisiting previous experiments with new perspective is an amazing first step,” says Andrei Bernevig from Princeton University and an Ikerbasque visiting professor at the Donostia International Physics Center (DIPC).  “But we can look to an even more exciting future, in which materials with advanced functionality are designed through a marriage of human intuition and artificial intelligence, built on the foundation of the Topological Materials Database and Topological Quantum Chemistry.”

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