Two Science papers catalog 8,872 atomically thin layers to guide the search for twisted quantum materials

About 46% of the entries landed in the unusual bucket ^[14]. That figure counts two different kinds of electronic order together. One is topology proper, a pattern that cannot change without a fundamental alteration of the electronic structure. The familiar example is the quantum spin Hall insulator, which is insulating inside and carries current along its edges through protected channels ^[18]. The other is an obstructed atomic limit. In one class of it, symmetry forces the centers of electronic charge to sit away from the atoms, and cutting the crystal along particular boundaries can expose distinctive electronic states ^[6].

The first paper extends topological quantum chemistry, a theory that ties a crystal's chemistry and symmetries to the topology of its electronic states, to two-dimensional layers ^[3]. "The symmetry of a crystal gives us rules for how its electronic states can be arranged. We developed those rules for layers and turned them into tools that researchers can apply to thousands of materials," said Luis Elcoro of the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg, senior author of one of the studies ^[12][17].

The design choice I like best is that the catalog keeps the layers with no topology. It records band structures, the energies available to electrons, for layers with and without topology ^[9]. For twisting, the starting electronic structure is the input that counts. The team's recent Nature study of M-point twisting showed that changing it opens different physics ^[10]. "The first catalog gives us the electronic building blocks. We can then ask which ones to combine and twist," said Urko Petralanda of the University of the Basque Country, a first author of one study ^[13][17].

The second paper is there because the number of combinations grows fast. Two identical layers make a homobilayer, two different layers make a heterobilayer, and the twist angle is one more free choice ^[16]. If every one of the 8,872 entries could pair with every other, there would be about 39.4 million distinct heterobilayers before anyone picks an angle ^[15]. That ceiling ignores whether the layers can be made or stacked at all. The second paper puts a finite list in front of that search: more than 1,600 candidates for twisting, with electronic starting points that the collaboration says could enable new kinds of quantum simulators ^[7].

The thing this doesn't tell you is whether any candidate will produce a new state in a device. In my view the catalog saves theorists the most time now. Its value to experimental groups depends on how many of the candidates can be made and twisted. The platforms that set the current bar got there by measurement: twisted graphene and transition metal dichalcogenides have yielded superconductivity and fractional Chern insulators ^[2].

"Every new family of twisted materials gives us a chance to ask a different question about quantum matter. We want to move beyond the few platforms we know and explore the enormous range of physics that other layers and other twists could make possible," said B. Andrei Bernevig, a Princeton physics professor and co-author of both studies ^[11][17].