Magnetic Topological Quantum Chemistry, ab initio calculations included

Photo: Gustavo Candido da Silva / Unsplash

Topological materials have special universal properties, which are protected against perturbations. Such properties are theoretically described by topology, a branch of mathematics concerned with the properties of geometrical objects that are unchanged by continuous deformations. Topological materials behave like an ordinary insulator in the bulk but have conducting states on their boundaries, i.e., edges or surfaces. The conducting surface is not what makes topological materials unique, but the fact that this surface state is particularly robust.

Non-magnetic topological materials have dominated the landscape of topological physics for the past two decades. Research in this field has led to a rapid succession of theoretical and experimental discoveries and, though topological materials were once believed to be rare and esoteric, recent advances in non-magnetic topological materials have found that topological insulators and enforced semimetals are much more prevalent than initially thought.

On this respect, a milestone was reached in 2017, when Topological Quantum Chemistry (TQC) and the equivalent method of symmetry-based indicators provided a description of the universal global properties of all possible atomic limit band structures in all non-magnetic symmetry groups, in real and momentum space. This 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 can be classified as topological, leading to a “periodic table” of topological materials.

What about magnetic materials? One may ask. The short answer being that the breakthroughs in non-magnetic materials have not yet been matched by similar advances in magnetic compounds, due to some big challenges. To start with, there is no theory similar to TQC or equivalent methods. If that was not enough, the ab initio calculation of magnetic compounds is notoriously inaccurate for complicated magnetic structures beyond ferromagnets. Actually, the number of accurately predicted magnetic topological materials has not reached ten.

The above was true till now, when a team of researchers has presented a full theory 1 of magnetic indices, co-representations, compatibility relations, code to compute the magnetic co-representations directly from ab initio calculations.

They have also performed complete electronic structure calculations 2, including complete topological phase diagrams, on each of 549 magnetic materials whose magnetic structures have been accurately tabulated (through the careful analysis of neutron-scattering data). Based on these, the researchers are able to predict several novel magnetic topological phases: 130 enforced semimetals and topological insulators in total.

These results represent the culmination of 4 years of work on the subject, and of over 70 years of research on the group theory, symmetry, and topology of magnetic materials. All of which has been made freely available to the public on World Wide Web repositories.

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

Disclaimer: Parts of this article might have been copied verbatim or almost verbatim from the referenced research paper.


  1. Luis Elcoro, Benjamin J. Wieder, Zhida Song, Yuanfeng Xu, Barry Bradlyn, B. Andrei Bernevig (2020) Magnetic Topological Quantum Chemistry arXiv:2010.00598 [cond-mat.mes-hall]
  2. Yuanfeng Xu, Luis Elcoro, Zhida Song, Benjamin J. Wieder, M. G. Vergniory, Nicolas Regnault, Yulin Chen, Claudia Felser, and B. Andrei Bernevig (2020) High-throughput calculations of magnetic topological materials Nature doi:10.1038/s41586-020-2837-0

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