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Volume 547 Issue 7663, 20 July 2017

The past few decades have revealed the surprising fact that the rules of mathematical topology can determine the properties of materials. But which structures have topological features and which ones don’t? Predicting whether a material might be topologically interesting is a challenging task and physicists have so far found only a few hundred  Eopological� compounds. In this issue, an international collaboration of physicists, mathematicians and chemists offers a potential solution in the form of a new and complete theory for calculating the topological properties of the electronic band structures of materials. They bring together the thus-far disconnected points of view of physicists and chemists by combining the conventional band-structure approach � which considers electron properties in nonlocal, momentum space � with local chemical bonding. As a result, they complete the theory of electronic band structure, which can now classify the band structures for all of the 230 possible crystal symmetry groups that arise from local atomic orbitals situated on lattice sites. Using this they are able to determine which structures are topologically nontrivial, and they apply the theory to discover several new classes of materials. The theory should greatly simplify the search for further materials with exotic properties and also shed light on the underlying physics of existing topological materials. Cover illustration by JVG.

Editorial

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Article

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