# A Topological Phonon Database has been built

The discovery of materials with topologically nontrivial electronic bands has led to high-throughput computational efforts that uncovered such bands in most known inorganic crystalline materials. Thus, in 2017, a team of researchers presented what they called Topological Quantum Chemistry (TQC), a new and complete understanding of the structure of bands in a material that links its topological features to the chemical orbitals at the Fermi level. In other words, a description of the universal global properties of all possible band structures and materials.

TQC allowed for a classification of the non-magnetic, non-trivial (topological) band structures through high-throughput methods that have changed our understanding of the number of topological materials existent in nature. An astonishing 40% (at least) of all non-magnetic materials could be classified as topological, leading to a “periodic table” of topological materials.

Then in 2020, TQC was extended to magnetic materials when the team presented a full theory of magnetic indices, co-representations and compatibility relations, together with code to compute the magnetic co-representations directly from *ab initio* calculations. The researchers performed complete electronic structure calculations, including complete topological phase diagrams, on each of 549 magnetic materials whose magnetic structures had been accurately tabulated. Based on these, the researchers were able to predict several novel magnetic topological phases: 130 enforced semimetals and topological insulators in total.

On the other hand, atoms are bonded to other atoms in the crystal. Rather than being independent of one another, the vibrations of adjacent atoms are coupled by virtue of the atomic bonding. These vibrations are coordinated in such a way that travelling lattice waves are produced. Lattice waves may be thought of as elastic waves or simply sound waves, having short wavelengths and very high frequencies, which propagate through the crystal at the velocity of sound. The vibrational thermal energy for a material consists of a series of these elastic waves, which have a range of distributions and frequencies. A single quantum of this vibrational energy is called a phonon.

Phonons play a crucial role in many properties of solid-state systems. Actually, in addition to electronic structure, phonon band structure can also display nontrivial topology. Now, the same team, on the basis of the existing phonon materials databases, have compiled ^{1} a catalogue of topological phonon bands for more than 10,000 three-dimensional crystalline materials.

Using TQC, they calculated the band representations, compatibility relations, and band topologies of each isolated set of phonon bands for the materials in the phonon databases. Additionally, They calculated the real-space invariants for all the topologically trivial bands and classified them as atomic or obstructed atomic bands.

As a result, the researchers have selected more than 1000 “ideal” nontrivial phonon materials to motivate future experiments and built the Topological Phonon Database.

These results, together with the previous complete analysis of the band topology of the electronic states, will be useful in the analysis of the consequences of electron-phonon coupling on the physical properties of the materials when the topology of both subsystems comes into play.

*Author: César Tomé López is a science writer and the editor of Mapping Ignorance*

*Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.*

## References

- Yuanfeng Xu, M. G. Vergniory, Da-Shuai Ma, Juan L. Mañes, Zhi-Da Song, B. Andrei Bernevig, Nicolas Regnault, and Luis Elcoro (2024) Catalog of topological phonon materials
*Science*doi:10.1126/science.adf8458 ↩