Old treasure maps were drawn from hearsay: someone found gold by a river, someone else in the mountains, and each person dug in their own spot. High-temperature superconductors went the same way: cuprates were found in some compounds, iron pnictides in others, nickelates in yet others, and there was no common map.
In this work, the map was drawn not from hearsay but from data. They took 4253 experimentally confirmed superconductors, described each with 147 numbers: properties of the elements, density, volume per atom, hidden features from neural networks that learned on crystal structures. Then, without any hint about the critical temperature, they looked at how the materials group themselves in this space.
And then something unexpected happened: cuprates, iron pnictides, and nickelates, despite their different chemistries, clustered into one pile. It was as if three expeditions searching for treasure in different parts of the world had independently arrived at the same bay. The remaining question was which two coordinates lead to this bay.
The first coordinate is the spread of electronegativities, that is, how much the atoms in a compound differ in their ability to attract electrons. The second is the average number of valence electrons, the ones that participate in bonds. It turned out that the upper bound of achievable critical temperature grows with the spread of electronegativities, and the optimal number of valence electrons lies in the range from 7 to 8.
With this map, you can search for new treasures. A two-step filter first checks whether a candidate falls into the coveted region, then estimates its critical temperature. Among hundreds of thousands of materials in the database, the filter retrospectively found La4Ni3O10 with a predicted temperature of 6.8 kelvin, and then proposed new compounds, such as Sr2CoO4 and Cs2TaCl6, which no one has synthesized yet.
The map does not explain why these materials superconduct, but now any future theory has a benchmark: the mechanism must explain why a large difference in electronegativities and an intermediate number of valence electrons favor a high temperature. And experimentalists have a compass that points to where to dig next.
Matthias's rules, formulated in the 1950s, stated that good superconductors have on average 5 or 7 valence electrons per atom. The new analysis finds an optimum in the range 7–8, which is surprisingly close to the old empirical rule, but now backed by machine learning on thousands of compounds.
In Arthur C. Clarke's novel 'Childhood's End', room-temperature superconductors transform the energy and transport of an entire civilization. The search for such materials in reality often proceeds blindly; this work offers a compass that could bring science fiction closer to the laboratory bench.