An efficient new method to find out whether a material hosts topological states or not could help increase the number of known topological materials from a few hundred to thousands. The technique is very different to conventional target-oriented searches and uses algorithms to sort materials automatically according to their chemical properties and properties related to symmetries in their structure.
Topological materials – exotic materials whose surface properties are very different to those in their bulk – have created a flurry of interest in recent years and are currently revolutionizing modern condensed matter physics thanks to their unique properties that come from their topology. Topological phases of matter are so-called because they are mathematically described by global invariants that are unaffected by imperfections, such as defects or other variations, in a material.
An example of a topological material is a topological insulator (also known as a 2D quantum spin Hall insulator). These are materials that are electrical insulators in the bulk but which can conduct electricity extremely well on their edge via special topologically protected electronic states. Electrons can only travel in one direction along these states and do not backscatter. This means that they can carry electrical current with near-zero dissipation of energy and so could be used to make energy-efficient electronic devices in the future.
Topological insulators were discovered over 10 years ago and we now know of a few hundred materials that belong to this category of material. Only a dozen or so of these appear to be suitable for real-world applications, however.
Symmetry indicators theory
To predict whether a material can host topological states, researchers mainly rely on complex theoretical calculations. Two teams, one at Princeton University in New Jersey and the other at Harvard University in Cambridge, Massachusetts, recently put forward a new approach based on the recently established theory of symmetry indicators, however, to speed up this search process. In these studies, the physicists use algorithms to sort materials automatically according to their chemical properties and properties that come from symmetries in their structure. These symmetries define where electrons move in the crystal lattice and can be used to predict how electrons will behave – and therefore whether a material can host topological states or not.
Researchers at Nanjing University in China led by Xiangang Wan together with the Harvard team, led by Ashvin Vishwanath, have now shown that the computation of symmetry indicators for any crystalline symmetry setting can readily be integrated into standard first-principle calculations. “In stark contrast to conventional target-oriented searches, our technique does not presuppose any specific phase of matter but instead automatically identifies all nontrivial electronic band structures and then classifies them as either topological insulators, topological semi-metals or topological crystalline insulators,” explains Wan.
To show how powerful their algorithm is, the researchers began by analysing crystalline materials in eight different space groups (which represent a description of the symmetryof a crystal) and say they have unearthed hundreds of materials capable of hosting topological phases.
“Two topological crystalline insulators in particular are worth mentioning,” says Wan. “The β-MoTe2 (space group 11) with screw-protected hinge states, and the BiBr (space group 12) with a rotation anomaly. The existence of the novel topological feature in β-MoTe2 was verified in a later study (arXiv:1806.11116).”
In traditional topological-material-discovery algorithms, we have to first pre-assume a specific topological phase and then calculate the corresponding topological invariant(s), a process that is usually very time-consuming,’ says Wan. “Our new technique is very fast and we have used it to comprehensively search for topological materials in 230 space groups in all (arXiv:1807.09744),” he tells Physics World.
3D topological insulators go photonic
The researchers, reporting their work in Nature Physics 10.1038/s41567-019-0418-7, say that many of the topological materials they have discovered using their approach could be promising for making next-generation electronic devices. Indeed, their work has already attracted much attention.
The approach is not just limited to topological materials either and could be extended to other 2D and magnetic materials, says Wan. “Our present work focuses on electronic band topology, but the symmetry indicators of phonons, photons and magnons could also be built and used to search for topologically non-trivial phases in these systems.”