Almost everything is topological

Overview

An international research team has discovered that topological electronic states are present in nearly every known material. The team’s discovery of ubiquitous band topology, which has appeared in the journal Science, 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 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.  

Topological phases of matter were first discovered 15 years ago. 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, and 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. 

However, using high-throughput computational modeling, the team discovered that over half of the known 3D materials in nature are topological. 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. The team’s data have been made freely available through the publicly accessible Topological Materials Database (https://www.topologicalquantumchemistry.com).

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.

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. “Our database is such a powerful and convenient tool,” notes 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.”